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NX Nastran Basic Dynamic Analysis User's Guide

1. 7 10 NX Nastran Basic Dynamic Analysis User s Guide Enforced Motion Figure 7 4 Displacements and Accelerations for the Two DOF Model This model was analyzed with several values of large mass Table 7 1 shows the results Note that the model with the 109 mass ratio is the model discussed earlier Peak frequency response results are compared for each model and the natural frequencies are compared to those of the constrained model in Real Eigenvalue Analysis The table shows that a mass ratio of 109 is a good value to use for this model Table 7 1 Models with Different Large Mass Ratios Ratio of Response Peaks m sec Large Mass Frequencies to Structure 02 0552 1 0003 0 9995 0 0 4 7876 02 2830 1 0000 0 9999 0 2909 NX Nastran Basic Dynamic Analysis User s Guide 7 11 Chapter 7 Enforced Motion Table 7 1 Models with Different Large Mass Ratios Ratio of Response Peaks m sec Large Mass Frequencies to Structure X X3 X3 Um es intii i Yn 02 2830 1 0000 1 0000 1Resonant frequencies for the constrained model are 4 7876 and 5 2909 Hz This model can also be changed to apply constant velocity or constant displacement at its base Figure 7 5 is an abridged input file for the model showing the Bulk Data entries required for enforced constant acceleration enforced constant velocity and enforced constant displacement Note that only one of these is usually applied to any model
2. next to it is restartable if the run that created the version did not terminate with UWM 784 For more advanced users this DBDIR FMS statement can also be used to check the database directory for the existence of data blocks e g UG If the job fails very early in the run e g error in the FMS section then a new version may not be created It is always good practice to back up the database on a regular basis If the system aborts the run e g disk space exhausted or time quota exceeded on a system level then there 1s a chance that the database is corrupted and will not allow restarts Another good practice to ensure that only good models are retained in the database is to perform the following e Use RESTART VERSION a KEEP 6 99 where a is a version number e Ifa version contains errors or is no longer of interest then use the FMS statement DBCLEAN to remove obsolete or incorrect versions of the model from the database Removing these versions allows the Executive System to reuse some of this space for new versions 8 6 Examples The examples perform a typical series of runs starting from a normal modes run and restarting into transient and frequency response analyses Table 8 3 summarizes this series of nine runs NX Nastran Basic Dynamic Analysis User s Guide 8 7 Chapter 8 Restarts in Dynamic Analysis along with a brief description Listings of the nine runs are also included Figures 8 2 through 8 10
3. Field Contents TID Table identification number X1 Table parameter Xl yi Tabular values ENDT Ends the table input The TABLED2 entry uses the algorithm yY yy x XI Equation 6 28 The TABLEDS entry has the following format B a Field Contents TID Table identification number X1 X2 Table parameters Xl yl Tabular values ENDT Ends the table input The TABLEDS entry uses the algorithm 6 18 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis mE ST Y YT yo Equation 6 29 The TABLED4 entry has the following format Field Contents TID Table identification number Xi Table parameters X2 0 0 X3 lt X4 Ai Coefficients The TABLED4 entry uses the algorithm i 1 i j N y a t J X2 Q Equation 6 30 N is the degree of the power series When x lt X3 X3 is used for x when x gt X3 X4 is used for x This condition has the effect of placing bounds on the table there 1s no extrapolation outside of the table boundaries ENDT ends the table input DAREA Example Suppose the following command is in the Case Control Section DLOAD 35 in addition to the following entries in the Bulk Data Section cas 3 3 3 3G e L4 L5 I Puoww uo ama pum pm pm O Sid mow js ps m fo i id soma sib pont owewepoux OO O Sid bam s m fifo o sd eom fso fom owes OO L pum n m k bw
4. 0 is replaced by Pot Kl ug B fig Equation 6 12 Regardless of the initial conditions specified the initial acceleration for all points in the structure is assumed to be zero constant initial velocity The format for the TIC entry is Field Contents SID Set ID specified by the IC Case Control command G Grid scalar or extra point C Component number UO Initial displacement VO Initial velocity Initial conditions may be specified only in direct transient response In modal transient response all initial conditions are set to zero Initial conditions may be specified only in the a set see Advanced Dynamic Analysis Capabilities 6 3 Modal Transient Response Analysis Modal transient response is an alternate approach to computing the transient response of a structure This method uses the mode shapes of the structure to reduce the size uncouple the equations of motion when modal or no damping is used and make the numerical integration more efficient Since the mode shapes are typically computed as part of the characterization of the structure modal transient response is a natural extension of a normal modes analysis 6 6 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis As a first step in the formulation transform the variables from physical coordinates uj to modal coordinates bj by QUO 60 1t5C01 Equation 6 13 The mode shapes f are used to transform the pro
5. Howlett James T Applications of NASTRAN to Coupled Structural and Hydrodynamic Responses in Aircraft Hydraulic Systems NASTRAN Users Exper pp 407 420 September 1971 NASA TM X 2378 Huang S L Rubin H Static and Dynamic Analysis F 14A Boron Horizontal Stabilizer NASTRAN Users Exper pp 251 264 September 1971 NASA TM X 2378 Hurwitz Myles M New Large Deflection Analysis for NASTRAN Sixth NASTRAN Users Colloq pp 235 256 October 1977 NASA CP 2018 Hussain M A Pu 8 L Lorensen W E Singular Plastic Element NASTRAN Implementation and Application Sixth NASTRAN Users Colloq pp 257 274 October 1977 NASA CP 2018 Ishikawa Masanori Iwahara Mitsuo Nagamatsu Akio Dynamic Optimization Applied to Engine Structure The MSC 1990 World Users Conf Proc Vol I Paper No 31 March 1990 Iwahara Mitsuo Dynamic Optimization Using Quasi Least Square Method The Fifth MSC NASTRAN User s Conf in Japan October 1987 in Japanese Jakovich John Van Benschoten John SDRC SUPERTAB Interactive Graphics as a Front End to MSC NASTRAN Dynamic Analysis Proc of the MSC NASTRAN Users Conf March 1979 Jones Gary K The Response of Shells to Distributed Random Loads Using NASTRAN NASTRAN Users Exper pp 393 406 September 1971 NASA TM X 2378 Kalinowski Anthony J Steady Solutions to Dynamically Loaded Periodic Structures Eighth NASTRAN Users Colloq pp 131 164 Octob
6. NX Nastran Basic Dynamic Analysis User s Guide 4 3 Chapter 4 Rigid Body Modes Treatment of SUPORT by Eigenvalue Analysis Methods The eigenvalue extraction methods treat the SUPORT entry differently as described below EIGR Methods Each of the eigenvalue extraction methods selected on the EIGR Bulk Data entry AHOU HOU MHOU and SINV treats the SUPORT in the same manner Eigenvalues are first computed using the information on the EIGR Bulk Data entry The frequencies of the first N modes where N is the number of SUPORT DOFs are replaced with a value of 0 0 Hz The first N eigenvectors are replaced by modes that are calculated by moving each SUPORT DOF a unit distance and then mass orthogonalizing them with respect to the other modes The fact that the eigenvectors are calculated via kinematics is the reason that the SUPORT entry produces cleaner rigid body modes as opposed to the rigid body modes computed without the use of the SUPORT entry Note that NX Nastran has no built in checks to warn if any of the N eigenvalues are not rigid body modes This replacement can hide potential modeling problems The results from UIM 30835 should be carefully checked see Examples The strain energy term for each SUPORT DOF should be zero A poor choice of DOFs on the SUPORT entry can adversely affect the computation of the flexible modes for the SINV method Flexible modes computed with the other methods AHOU HOU and MHOU ar
7. 5 503882E 00 5 023013E 00 2 703873E 00 8 3 3 702303E 01 829170E 01 099580E 01 4 915230E 01 3 323378E 02 7 173043E 01 5 821075E 01 4 938418E 01 8 124324E 01 Figure G 2 GPWG Output for the Four Concentrated Mass Model The MO matrix represents the rigid body mass properties of the structure and is generally not needed for model checkout This matrix represents an intermediate step in computing the inertia properties of the structure The S matrix should always be equal to the identity matrix G 2 NX Nastran Basic Dynamic Analysis User s Guide Grid Point Weight Generator when the mass is the same in each coordinate direction which is the typical case If this matrix is not the identity matrix inspect the model for inconsistent masses Following the S matrix are the mass and center of gravity locations These are the most commonly used information of the GPWG output Because the mass may be different in the three translational directions the mass is printed for every coordinate direction For the same reason the center of gravity location is given for each of the three translational masses If the mass is the same in all directions a unique center of gravity exists and is located at the x component of the y or z mass the y component of the x or z mass and the z component of the x or y mass If the mass is not the same in all three directions it is likely due to the CONM1 CMASSi1 or
8. Conf Proc Paper No 27 June 1994 Jiang L Liew K M Lim M K Low S C Vibratory Behaviour of Delaminated Honeycomb Structures a 3 D Finite Element Modeling Computers and Structures v 55 n 5 Jun 3 1995 Ju Yeuan Jyh Ting Tienko Modelling and Analysis of an Accelerometer Using MSC ARIES and MSC NASTRAN MSC 1995 World Users Conf Proc Paper No 22 May 1995 Kabe Alvar M Mode Shape Identification and Orthogonalization AIAA ASME ASCE AHS ASC 29th Structures Structural Dynamics and Materials Conf Paper No 88 2354 1988 Kajiwara Itsuro Nagamatsu Akio Optimum Design of Structure and Control Systems by Modal Analysis 1994 MSC Japan Users Conf Proc Kam T Y Yang C M Wu J H Determination of Natural Frequencies of Laminated Composite Space Structures Via The Experiemental and Finite Element Approaches The Sixth Annual MSC Taiwan Users Conf Proc Paper No 5 November 1994 Kang J M Kim J Y Lee K J Yum D J Seol Y S Rashed S Kawahara A Simulation of 3 D Sloshing and Structural Response in Ship s Tanks Taking Account of Fluid Structure Interaction 1994 MSC Japan Users Conf Proc Paper No 29 December 1994 Kasai Manabu Better Accuracy of Response Derived from Modal Analysis The Second MSC NASTRAN User s Conf in Japan October 1984 in Japanese NX Nastran Basic Dynamic Analysis User s Guide l 23 Appendix References and Bibliography Katnik Richard B Yu
9. Finite Element Input Data Because these effects are difficult to quantify damping values are often computed based on the results of a dynamic test Simple approximations are often justified because the damping values are low Viscous and Structural Damping Two types of damping are generally used for linear elastic materials viscous and structural The viscous damping force is proportional to velocity and the structural damping force is proportional to displacement Which type to use depends on the physics of the energy dissipation mechanism s and is sometimes dictated by regulatory standards The viscous damping force f is proportional to velocity and is given by f bu Equation 2 6 where b viscous damping coefficient H velocity The structural damping force f is proportional to displacement and is given by f i G k u Equation 2 7 where G structural damping coefficient k stiffness u displacement i 4 1 phase change of 90 degrees For a sinusoidal displacement response of constant amplitude the structural damping force 1s constant and the viscous damping force is proportional to the forcing frequency Figure 2 2 depicts this and also shows that for constant amplitude sinusoidal motion the two damping forces are equal at a single frequency At this frequency Gk a Gk bw or b Equation 2 8 where w is the frequency at which the structural and viscous damping forces are
10. Primary Structure Grid Point 2 Figure 5 8 Two DOF Model FILE bd05two dat TWO DOF SYSTEM S CHAPTER 5 FREQUENCY RESPONSE TIME 5 SOL 111 S MODAL FREQUENCY RESPONSE CEND TITLE TWO DOF SYSTEM SUBTITLE MODAL FREQUENCY RESPONSE LABEL 20 N FORCE APPLIED TO PRIMARY MASS S SPECIFY SPC SPC 996 S SPECIFY MODAL EXTRACTION METHOD 10 S SPECIFY DYNAMIC INPUT DLOAD 999 FREQ 888 SDAMPING 777 S S SELECT OUTPUT SET 11 1 2 DISPLACEMENT PHASE PLOT 11 S S XYPLOTS X Y plot commands 2 BEGIN BULK PEE o Sande on ie Hace s VPE Galea sce p PPP Dass ao ars e Lu i rua S ENTRIES FOR FREQUENCY RESPONSE LOAD DEFINITION SRLOAD1 SID DAREA TC NX Nastran Basic Dynamic Analysis User s Guide 5 27 Chapter 5 Frequency Response Analysis RLOAD1 999 997 901 SDAREA SID EX C1 Al DAREA 997 2 2 20 0 TABLED1 TID TABL1 S TABL1 X1 Y1 X2 Y3 ETC TABLED1 901 TAB901 TAB901 0 0 1 0 10 0 1 0 ENDT S ALTERNATE LOAD DEFINITION USING DLOAD SDLOAD SID 5 S1 RLOAD1 SDLOAD 999 1 0 1 0 998 SRLOAD1 SID DAREA TC RLOAD1 998 997 901 S FREQUENCY RANGE 2 10 HZ SFREQ1 SID F1 DEF NDF a 888 2 0 05 160 S MODAL DAMPING OF 5 CRITICAL STABDMP1 TID TYPE TABD1 S TABD1 F1 G1 F2 G2 ETC TABDMP1 777 CRIT TABD7 TABD7 0 0 05 100 0 05 ENDT MODAL EXTRACTION SEIGRL SID V1 V2 ND MSGLVL EIGRL 10 0 1 20 0 S basic model ENDDATA
11. R3 R3 R3 R3 Frequency Response Analysis 0 12 E z z n ar 0 014 e E z a m AL E 2 Frequency Hz 10 Figure 5 13 Displacement Response Magnitudes With the Auxiliary Structure 0 02 m placem ent 2 Dis 2 Frequency Hz 10 Figure 5 14 Displacement Response Magnitude Without the Auxiliary Structure Cantilever Beam Model Consider the cantilever beam shown in Figure 5 15 This model is a planar model of the cantilever beam introduced in Real Eigenvalue Analysis with unrestrained DOFs in the T2 and R3 directions Two loads are applied one at grid point 6 and the other at grid point 11 The loads have the frequency variation shown in Figure 5 16 The loads in the figure are indicated with a heavy line in order to emphasize their values The load at grid point 6 has a 45 degree phase lead and the load at grid point 11 is scaled to be twice that of the load at grid point 6 Modal frequency response is run across a frequency range of 0 to 20 Hz Modal damping is used with 2 critical damping between 0 and 10 Hz and 5 critical damping above 10 Hz Modes to 500 Hz are computed using the Lanczos method NX Nastran Basic Dynamic Analysis User s Guide 5 31 Chapter 5 Frequency Response Analysis pf 2 pf Figure 5 15 Cantilever Beam Model with Applied Loads rd 4 0 Qi 3 0 r B E BD a 0 OC 5b a f T T T 1 di e
12. Sabahi Dara Rose Ted Special Applications of Global Local Analysis The MSC 1990 World Users Conf Proc Vol II Paper No 49 March 1990 Sabahi Dara Rose Ted MSC NASTRAN Superelement Analysis of the NASA AMES Pressurized Wind Tunnel The MSC 1990 World Users Conf Proc Vol II Paper No 50 March 1990 Shein Shya Ling Marquette Brian Rose Ted Superelement Technology Application and Development in Dynamic Analysis of Large Space Structures The MSC 1991 World Users Conf Proc Vol I Paper No 26 March 1991 Suzukiri Yoshihiro Component Mode Synthesis Application of MSC NASTRAN V66 The 2nd Annual MSC Taiwan Users Conf Paper No 10 October 1990 Suzukiri Yoshihiro Component Mode Synthesis Application of MSC NASTRAN V66 Proc of the First MSC NASTRAN Users Conf in Korea Paper No 17 October 1990 Tong Edward T Chang Craig C J An Efficient Procedure for Data Recovery of a Craig Bampton Component MSC 1994 World Users Conf Proc Paper No 26 June 1994 Wamsler M Komzsik L Rose T Combination of Quasi Static and Dynamic System Mode Shapes Proc of the 19th MSC European Users Conf Paper No 13 September 1992 Wang Bo Ping Synthesis of Structures with Multiple Frequency Constraints AIAA ASME ASCE AHS 27th Structures Structural Dynamics and Materials Conf Part 1 pp 394 397 May 1986 DYNAMICS DAMPING El Maddah M Imbert J F A Comparison of Damping Syn
13. Table 8 3 Typical Series of Restart Runs Run Sequence Name of Input File Number bdO8barl dat bdO8bar2 dat bdO8bar3 dat bdO8bar4 dat 8 8 NX Nastran Basic Dynamic Analysis User s Guide Solution Sequence Description of Number lunc Version Created Version Deleted Perform a normal modes cold start analysis and save the database Restart from run number 1 and request eigenvector output The first two modes of the structure are very close to one of the forcing frequencies The structure is modified in order to stay away from resonance This run 103 restarts from run number 2 to delete the old PBAR entry and replace it with the modified PBAR entry The modes are recalculated and the eigenvector output is requested in this run This run deletes the data blocks in the database previously occupied by Version 1 This space can then be reused by future restarts Note that the statement DBCLEAN does not reduce the database size It merely removes some of its contents so that this space can be reused A new version is not created as a result of this run This is an optional run especially if disk space is of no concern to you Restarts in Dynamic Analysis Table 8 3 Typical Series of Restart Runs Bun Solution Sequence Description of Sequence Name of Input File d P Version Created Version Deleted Number Number Runs using the solution from run number 5 The purpose of this run is to req
14. e Examples NX Nastran Basic Dynamic Analysis User s Guide 6 1 Chapter 6 Transient Response Analysis 6 1 Overview Transient response analysis is the most general method for computing forced dynamic response The purpose of a transient response analysis is to compute the behavior of a structure subjected to time varying excitation The transient excitation is explicitly defined in the time domain All of the forces applied to the structure are known at each instant in time Forces can be in the form of applied forces and or enforced motions see Enforced Motion The important results obtained from a transient analysis are typically displacements velocities and accelerations of grid points and forces and stresses in elements Depending upon the structure and the nature of the loading two different numerical methods can be used for a transient response analysis direct and modal The direct method performs a numerical integration on the complete coupled equations of motion The modal method utilizes the mode shapes of the structure to reduce and uncouple the equations of motion when modal or no damping is used the solution is then obtained through the summation of the individual modal responses The choice of the approach is problem dependent The two methods are described in Direct Transient Response Analysis and Modal Transient Response Analysis 6 2 Direct Transient Response Analysis In direct transient respo
15. DELAY 262 6 2 0 1 S basic model 2 ENDDATA Figure 6 11 Input File Abridged for the Beam Example Table 6 9 shows the relationship between the Case Control commands and the Bulk Data entries The DLOAD Bulk Data entry references two TLOAD2 entries each of which references separate DAREA entries A TLOAD2 entry also references a DELAY entry to apply the time delay to the load at grid point 6 Table 6 9 Relationship Between Case Control Commands and Bulk Data Entries for the Bar Model Case Control Bulk Data METHOD EIGRL TSTEP TSTEP SDAMPING TABDMP1 NX Nastran Basic Dynamic Analysis User s Guide 6 31 Chapter 6 Transient Response Analysis Table 6 9 Relationship Between Case Control Commands and Bulk Data Entries for the Bar Model Case Control Bulk Data DLOAD TLOAD 2 231 R DAREA DLOAD TLOAD2 232 DAREA DELAY Plotted output is shown in the following figures Figure 6 12 shows the applied loads at grid points 6 and 11 Figure 6 13 shows the plots of the displacements for grid points 6 and 11 Figure 6 14 shows the accelerations for grid points 6 and 11 Figure 6 15 shows the bending moment at end A in plane 1 for element 6 Figure 6 16 shows the modal displacements for modes 1 and 2 6 32 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis Force 11 N Time sec Figure 6 12 Applied Loads at Grid Points 6 and 11 NX Nastran Basic Dynamic Analysis User s Guide 6
16. Lembregts PhD E Furini PhD F Storrer O Modal Test on the Pininfarina Concept Car Body ETHOS 1 Actes de la 2 me Conf rence Francaise Utilisateurs des Logiciels MSC Toulouse France September 1995 Brughmans M Lembregts F Ph D Furini F Ph D Modal Test on the Pininfarina Concept Car Body ETHOS 1 MSC 1995 World Users Conf Proc Paper No 5 May 1995 Buchanan Guy Superelement Data Recovery via the Modal Acceleration Method The MSC 1988 World Users Conf Proc Vol I Paper No 40 March 1988 Budynas R Kolhatkar S Modal Analysis of a Robot Arm Using Finite Element Analysis and Modal Testing Proc of the 8th Int Modal Analysis Conf Vol I pp 67 70 January 1990 Budynas R G Krebs D Modal Correlation of Test and Finite Element Results Using Cross Orthogonality with a Reduced Mass Matrix Obtained by Modal Reduction and NASTRAN s Generalized Dynamic Reduction Solution Proc of the 9th Int Modal Analysis Conf Vol I pp 549 554 April 1991 I 20 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Butler Thomas G Muskivitch John C Application of Flanigan s Mode Acceleration in MSC NASTRAN Version 66 The 1989 MSC World Users Conf Proc Vol I Paper No 25 March 1989 Caldwell Steve Wang B P Application of Approximate Techniques in the Estimation of Eigenvalue Quality The MSC 1993 World Users Conf Proc Paper No 11 May 1993 C
17. NASA TM X 3278 Chang H T Cao Tim Hua Tuyen SSF Flexible Multi Body Control Structure Interaction Simulation The MSC 1993 World Users Conf Proc Paper No 15 May 1993 Chang W M Lai J S Chyuan S W Application of the MSC NASTRAN Design Optimization Capability to Identify Joint Dynamic Properties of Structure The Sixth Annual MSC Taiwan Users Conf Proc Paper No 1 November 1994 Chargin M Miura H Clifford Gregory A Dynamic Response Optimization Using MSC NASTRAN The MSC 1987 World Users Conf Proc Vol I Paper No 14 March 1987 l 2 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Chen J T Chyuan S W You D W Wong H T A New Method for Determining the Modal Participation Factor in Support Motion Problems Using MSC NASTRAN The Seventh Annual MSC NASTRAN Users Conf Proc Taiwan 1995 Chen J T Wong H T Applications of Modal Reaction Method in Support Motion Problems Techniques in Civil Engineering Vol 4 pp 17 30 March 1996 in Chinese Chen J T Hong H K Chyuan S W Yeh C S A Note on the Application of Large Mass and Large Stiffness Techniques for Multi Support Motion The Fifth Annual MSC Taiwan Users Conf Proc November 1993 Chen Yohchia Improved Free Field Analysis for Dynamic Medium Structure Interaction Problems The MSC 1992 World Users Conf Proc Vol I Paper No 18 May 1992 Chen Yohchia
18. S MLS M SI M S M S M S Equation G 16 The 5 matrix for the example is given by 432 902 5 902 432 0 0 0 1 Equation G 17 The S matrix is printed after the MO matrix as shown in Figure G 2 This represents the transformation relating the basic coordinate system to the principal mass axes Again if there is no coupling between the translational mass component which is the case for most problems the eigensolution is not required and the S matrix is set equal to the identity matrix This example was selected to demonstrate all of the features of the GPWG module but it is not a typical problem 4 The next step is to determine the principal masses and the center of gravity location in the principal mass axes system as shown in Equations G 18 G 12 NX Nastran Basic Dynamic Analysis User s Guide Grid Point Weight Generator M My M M y 2 f M M33 The centers of gravity are EF T rr M M M X Y E E X M A M A M rr rr rr y M53 y M 7 Mz M 9 M a rr EF Ir X M37 y M3 7 M33 M 3 M z Equation G 18 As can be seen the center of gravity location is not a unique location The center of gravity location is computed separately for the for x y and z directions relative to the principal mass axes Only if the mass is the same in each direction which is typical is there a unique center of
19. SDAMPING 25 S METHOD 10 PHYSICAL OUTPUT REQUEST SET 11 1 11 DISPLACEMENT PLOT 11 ACCELERATION PLOT 11 XYPLOTS S X Y plot commands 2 BEGIN BULK LARGE MASS OF 1 0E9 SCONM2 EID G CID M CONMZ 15 1 1 0E9 CONSTRAIN MASS IN 1 6 DIRECTIONS SPC 21 1 16 DYNAMIC LOADING SDLOAD SID S S1 L1 DLOAD 22 1 0E9 0 102 23 STLOAD1 SID DAREA DELAY TYPE TID TLOAD1 23 24 0 25 NX Nastran Basic Dynamic Analysis User s Guide 7 15 Chapter 7 Enforced Motion SDAREA SID Pl Cl Al DAREA 24 1 2 0 15 STABLED1 TID TABL1 StTABLI X1 Y1 X2 Y2 ETC TABLED1 25 TABLI1 TTABLI 0 0 0 0 0 05 1 0 0 052 0 0 0 1 0 0 TABL2 TABL2 ENDT S S CONVERT WEIGHT TO MASS MASS S G 9 81 m sec 2 WTMASS PARAM WTMASS 0 102 S 1 G FWEIGHT 1 G 0 102 SEIGRL SID V1 V2 MSGLVL BlGRL 10 1 3000 0 STSTEP SID NI DT1 NO1 TSTEP 27 1000 0 001 1 MODAL DAMPING OF 5 IN ALL MODES STABDMP1 TID TYPE TABD S TABD F1 Gl F2 G2 ETC TABDMP1 25 CRIT TABD TLABD 0 0 05 1000 0 05 ENDT S basic model ENDDATA Figure 7 8 Abridged Input File for Enforced Acceleration A large mass of 1 0E9 kg is placed at grid point 1 This grid point 1s constrained in the T1 and R3 directions but is free in the T2 direction The load is scaled to give a peak input acceleration of 0 15m sec This scaling is performed by applying a scale factor of 1 0E9 in the S field field 3 of the DLOAD entry a s
20. T T Co mumumu o sm m kb h k k mazo pe E unear 0 1 po po pao po e wr 1 NX Nastran Basic Dynamic Analysis User s Guide 6 19 Chapter 6 Transient Response Analysis The DLOAD Set ID 35 in the Case Control selects the TLOAD1 entry in the Bulk Data having a Set ID 35 On the TLOAD1 entry is a reference to DAREA Set ID 29 DELAY Set ID 31 and TABLED1 Set ID 40 The DAREA entry with Set ID 29 positions the loading on grid point 30 in the 1 direction with a scale factor of 4 0 applied to the load The DELAY entry with Set ID 31 delays the loading on grid point 30 in the 1 direction by 0 2 units of time The TABLED1 entry with Set ID 40 defines the load time history in tabular form The result of these entries 1s a dynamic load applied to grid point 30 component T1 scaled by 4 0 and delayed by 0 2 units of time Figure 6 4 shows the TABLED1 time history and the applied load scaled by the DAREA entry and time shifted by the DELAY entry 1 0 Amplitude on TABLED Pi 0 5 1 5 2 25 Time sec 40 Ld Force j Amplitude D ri 0 5 1 0 1 5 2 2 5 Time sec Figure 6 4 Time History from the TABLED1 Entry Top and Applied Load Bottom Static Load Sets LSEQ Entry NX Nastran does not have specific data entries for many types of dynamic loads Only concentrated forces and moments can be specified directly using D
21. i zx T Ll m B Qi 6 0 Lr LI La i r m a 100 n di J di Cs m a 0 Frequency Hz 20 Figure 5 16 Applied Loads The abridged input file is shown below The output quantities as defined in the Case Control Section are the applied loads OLOAD for grid points 6 and 11 physical displacements DISPLACEMENT for grid points 6 and 11 solution set displacements SDISPLACEMENT for modes 1 and 2 and element forces ELFORCE for element 6 These output quantities are plotted rather than printed FILE bd05bar dat S CANTILEVER BEAM MODEL S CHAPTER 5 FREQUENCY RESPONSE S 5 32 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis SOL 111 MODAL FREQUENCY RESPONSE TIME 10 CEND TITLE CANTILEVER BEAM SUBTITLE MODAL FREQUENCY RESPONSE SPC 21 2 DLOAD 22 FREQ 27 SDAMPING 20 2 METHOD 10 SET 15 6 11 OLOAD PHASE PLOT 15 PHYSICAL OUTPUT REQUEST SEI 11 6 11 DISPLACEMENT PHASE PLOT 11 S MODAL SOLUTION SET OUTPUT SET 12 1 2 SDISP PHASE PLOT 12 S ELEMENT FORCE OUTPUT SET 13 6 ELFORCE PHASE PLOT 13 XYPLOTS X Y plot commands BEGIN BULK S S p Qiu dcs eee s me Oe dak wow x Cacia Eusko reese B tae we d P cara teak TU a sh S EIGRL 10 zu 500 O TN 27 0 0 0 05 400 abouti 20 CRIT TABD1 TABD1 0 0 0 02 10 0 0 02 10 01 0 05 25 0 0 05 TABD2 TABD2 ENDT
22. o2 4 J 8 e 7 8 J 9 0 The LSEQ Bulk Data entry contains a reference to a DAREA Set ID and a static Load Set ID The static loads are combined with any DAREA entries in the referenced set The DAREA Set ID does not need to be defined with a DAREA Bulk Data entry The DAREA Set ID is referenced by an RLOADi entry This reference defines the temporal distribution of the dynamic loading The Load Set ID may refer to one or more static load entries FORCE PLOADi GRAV etc All static loads with the Set ID referenced on the LSEQ entry define the spatial distribution of the dynamic loading NX Nastran converts this information to equivalent dynamic loading Figure 5 6 demonstrates the relationships of these entries To activate a load set defined 1n this manner the DLOAD Case Control command refers to the Set ID of the selected DLOAD or RLOADi entry and the LOADSET Case Control command refers to the Set ID of the selected LSEQ entries The LSEQ entries point to the static loading entries that are used to define dynamic loadings with DAREA Set ID references Together this relationship defines a complete dynamic loading To apply dynamic loadings in this manner the DLOAD and LOADSET Case Control commands and the RLOADi and LSEQ Bulk Data entries must be defined A DAREA Bulk Data entry does not need to be defined since the RLOADi and LSEQ entries reference a common DAREA ID The LSEQ entry can also be interpreted as an internal DAREA entr
23. un t y ut t 4 o 4 H Basic Model 4 47 c d s p t pt Iwo Large Masses at Each End pit One Large Mass and One RBE2 Element Figure 7 1 Clamped Clamped Bar Undergoing Enforced Acceleration 7T 4 User Interface for the Large Mass Method There 1s no special user interface for the large mass method other than to specify a large mass at excitation DOFs and to specify the large force For transient response the type of enforced motion displacement velocity or acceleration must be specified on the TLOADi entries The remainder of the input is identical to that of frequency response Frequency Response Analysis or transient response Transient Response Analysis analysis NX Nastran Basic Dynamic Analysis User s Guide 7 5 Chapter 7 Enforced Motion The force applied at a point is the product of terms from the DLOAD DAREA and TABLEDi entries The scaling of the large force is arbitrary it can be on any one or more of these entries These entries follow DLOAD Format DAREA Format TABLED1 Format rasteDi mT TABLED2 Format mmu fm aE pq j m jq e pe Be Be pee 5 TABLED3 Format mapLeps mD ee es pe Jj TABLED4 Format COC e e hs I l The TABLED4 entry defines a power series and is convenient in frequency response for enforced constant velocity or displacement Frequency Response If a DLOAD entry is used
24. 1986 NX Nastran Basic Dynamic Analysis User s Guide 1 11 Appendix References and Bibliography Cronkhite J D Development Documentation and Correlation of a NASTRAN Vibration Model of the AH 1G Helicopter Airframe NASTRAN Users Exper pp 273 294 October 1976 NASA TM X 3428 Dascotte E Von Estorff O Wandinger J Validation and Updating of MSC NASTRAN Finite Element Models Using Experimental Modal Data Proc of the 20th MSC European Users Conf Paper No 10 September 1993 de Boer A Kooi B W A DMAP for Updating Dynamic Mathematical Models with Respect to Measured Data Proc of the MSC NASTRAN Eur Users Conf May 1986 Deger Yasar Modal Analysis of a Concrete Gravity Dam Linking FE Analysis and Test Results Proc of the 20th MSC European Users Conf September 1993 Deutschel Brian W Katnik Richard B Bijlani Mohan Cherukuri Ravi Improving Vehicle Response to Engine and Road Excitation Using Interactive Graphics and Modal Reanalysis Methods SAE Trans Paper No 900817 September 1991 Dirschmid W Nolte F Dunne L W Mathematical Model Updating Using Experimentally Determined Real Eigenvectors Proc of the 17th MSC Eur Users Conf Paper No 4 September 1990 Drago Raymond J Margasahayam Ravi Stress Analysis of Planet Gears with Integral Bearings 3 D Finite Element Model Development and Test Validation The MSC 1987 World Users Conf Proc Vol I Paper No
25. 3 419880E 01 3 431904E 00 Masa Ax cS for the Center of Gravity 463246E 00 Principal 075616E 00 x 893001E 00 Moments of Inertia Transformatian from the Principal Q 201511E 01 4 586845E 01 5 205678E 01 Direction 717336E 01 8 885992E 01 2 687111E 01 of the 858298E 01 0 000000E 00 8 104341E 01 Momental Ellipsoid to the Principal Mass Axes Before showing how each of the matrices are computed a few items should be noted for this model NX Nastran Basic Dynamic Analysis User s Guide G 5 Appendix G Grid Point Weight Generator User Warning Message 3042 is printed to inform you that inconsistent scalar masses were used This message occurs because there are different scalar masses in the three components In general if you are using structural mass and or CONM2s you should not get this message The rigid body mass matrix MO is computed with respect to the reference grid point1 in the basic coordinate system Grid point 1 is used for this example because PARAM GNDPNT 1 is entered in the Bulk Data Section The mass and center of gravity location shown are not in the basic coordinate system for this example The mass and center of gravity are computed and printed in the principal mass coordinate system This principal mass coordinate system should not be confused with the principal axes discussed in most text books The principal mass axes in NX Nastran are the axes that have no coupling terms between the tran
26. 4 March 1987 Ferg D Foote L Korkosz G Straub F Toossi M Weisenburger R Plan Execute and Discuss Vibration Measurements and Correlations to Evaluate a NASTRAN Finite Element Model of the AH 64 Helicopter Airframe National Aeronautics and Space Administration January 1990 NASA CR 181973 Graves Roger W Interfacing MSC NASTRAN with SDRC IDEAS to Perform Component Mode Synthesis Combining Test Analytical and F E Data The MSC 1988 World Users Conf Proc Vol II Paper No 58 March 1988 Hehta Pravin K Correlation of a NASTRAN Analysis with Test Measurements for HEAO 2 Optics MSC NASTRAN Users Conf Proc Paper No 17 March 1984 Herbert Andrew A Currie A O Wilson W Analysis of Automotive Axle Carrier Assembly and Comparison with Test Data The MSC 1987 World Users Conf Proc Vol I Paper No 6 March 1987 Herting D N Parameter Estimation Using Frequency Response Tests MSC 1994 World Users Conf Proc Paper No 18 June 1994 Jiang K C Finite Element Model Updates Using Modal Test Data The 1989 MSC World Users Conf Proc Vol II Paper No 48 March 1989 Kabe Alvar M Mode Shape Identification and Orthogonalization AIAA ASME ASCE AHS ASC 29th Structures Structural Dynamics and Materials Conf Paper No 88 2354 1988 Kammer Daniel C Jensen Brent M Mason Donald R Test Analysis Correlation of the Space Shuttle Solid Rocket Motor Center Segment J of Space
27. COMPLEX Dis MAGNITUDE PHASE T2 2 377640E 03 357 2761 2 400612E 03 357 1805 2 424619E 03 357 0823 2 449710E 03 356 9813 2 475939E 03 356 8773 TYPE T1 T3 Q Q a a c c j co C CC CO0 C505 C50 cC5C j Cc co j co j C C C CO CC C C5CoCcoCco CCo c co c C2 c C CO CC CCo Coco 0C cC 2 000000E 00 COMPLEX REAL IMAGINARY TYPE T1 T2 T3 G 0 0 2 813051E 03 0 0 0 0 0 0 2 107985E 04 0 0 0 0 G 0 0 2 374954E 03 0 0 0 0 0 0 1 129933E 04 0 0 0 0 2 050000E 00 NX Nastran Basic Dynamic Analysis User s Guide O O O O C O O O O O PLACEMENT R1 DISPLACEMENT R1 V VECTOR C Cc j CODD CoCcoCco0c Cc C C C By d E O a R C c c CO CC C0 C5CoCco CCCo c gt C Magnitude Phase Output in SORT2 Format VECTOR C O0 Oc CO Oc R2 2 R2 2 R2 5 29 oOoOo0oo0o0o0oo0oo0oo0oo0O oOo0oo0o0o0oo0oo0oo0o0oO C Cc c C ODODDVOCCOO00 co c j c C CCCo Coco Cocco OOO R3 CO OC O0cCc5o0c00ccC0 R3 CO CC Coco CoCcoCoOCoco R3 O O O O O R3 O O O O C R3 CC OO Chapter 5 Frequency Response Analysis COMPLEX DISPLACEMENT VECTOR REAL IMAGINARY POINT ID TYPE T1 T2 T3 R1 R2 1 G 0 0 2 866640E 03 0 0 0 0 0 0 0 0 0 0 2 2291 63E 04 0 0 0 0 0 0 0 0 2 G 0 0 2 397706E 03 0 0 0 0 0 0 0 0 0 0 1 180853E 04 0 0 0 0 0 0 0 00 FREQUENCY 2 100000E 00 COMPLEX DISPLACEMENT VECTOR REAL IMAGINARY
28. DYNAMIC LOADING SDLOAD SID S S1 L1 S2 L2 DLOAD 22 1 0 1 0 231 1 0 232 RLOAD2 SID DAREA DELAY DPHASE TB TP RLOAD2 231 241 261 25 RLOAD2 232 242 25 SDAREA SID P1 L1 Al DAREA 241 6 2 1 0 DAREA 242 11 2 2 0 SDPHASE SID P1 Cd THAT DPHASE 261 6 2 45 STABLED1 TID TABLI S TABL1 X1 Y1 X2 X2 ETC TABLED1 25 TABL1 TABLI 0 l 5 0 Ju 15 0 3 0 20 0 l TABL2 TABL2 25 0 1 ENDT S basic model ENDDATA Figure 5 17 Input File Abridged for the Beam Example Table 5 9 shows the relationship between the Case Control commands and the Bulk Data entries Note that the DLOAD Bulk Data entry references two RLOAD2 entries each of which references a separate DAREA entry and a common TABLED1 entry The RLOAD2 entry for grid point 6 also references a DPHASE entry that defines the 45 degree phase lead Table 5 9 Relationship Between Case Control Commands and Bulk Data Entries for the Beam Model Bulk Data EIGRL FREQ1 TABDMP1 NX Nastran Basic Dynamic Analysis User s Guide 5 33 Chapter 5 Frequency Response Analysis Table 5 9 Relationship Between Case Control Commands and Bulk Data Entries for the Beam Model Case Control Bulk Data RLOAD 231 DAREA DLOAD DPHASE wmm Lo ona The RLOAD2 entry describes a sinusoidal load in the form P taBgne t Pon Equation 5 29 f where A 1 0 for grid point 6 and 2 0 for grid point 11 entered on the DAREA entry B function defined on the TABLED1 entry f
29. Figure 5 9 Input File Abridged for the Two DOF Example Table 5 8 shows the relationship between the Case Control commands and the Bulk Data entries Note that the RLOAD1 entry references the DAREA and TABLED1 entries The input file also shows an alternate way to specify the dynamic load by using a DLOAD Bulk Data entry Because there is only a single RLOAD1 entry the DLOAD Bulk Data entry is not required Table 5 8 Relationship Between the Case Control Commands and Bulk Data Entries for the Two DOF Model Bulk Data EIGRL FREQ1 TABDMP1 RLOAD1 Bars 3 ABLED iTO 2nft The RLOAD1 entry describes a sinusoidal load in the form VU ALC DGO e Equation 5 28 H where A 20 0 entered on the DAREA entry C 1 0for all frequencies entered on the TABLED1 entry D 0 0 field 7 of the RLOAD1 entry is blank q 0 0 field 5 of the RLOAD1 entry is blank t 0 0 field 4 of the RLOADI entry is blank 5 28 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis Output can be printed in either real imaginary or magnitude phase format and in either SORTI or SORT2 format These formats are illustrated in Figure 5 10 Figure 5 11 and Figure 5 12 showing a portion of their printed output NM N N N N NM N N N FP NM N N N N N N N N FP POINT ID FREQUENCY 000000E 00 050000E 00 100000E 00 150000E 00 200000E 00 POINT ID FREQUENCY 000000E 00 05
30. H e Oe e e e e Oo MWNOFPRFPRPODOO HmnpmpB bmpbmpbmpbmpmnprmb eH 4S I0 0I ND OON COO 000 2O0Y Ot iS CO IND ES ODIO OO O OO DOO P190 90 014 C9 f I2 IPS IPS OO 00 1 OY O1 4S CO hO IPS I5 XO OO 10 O1 4S CO PO ES OvOde e OO ENDDATA Figure 3 9 Input File for the First Beam Model The first two resulting y direction modes are illustrated in Figure 3 10 Displacements in the y direction displacements are controlled by the I1 term Because the structure is also free to displace in the z direction similar modes occur in that direction and are controlled by the I2 term NX Nastran Basic Dynamic Analysis User s Guide 3 23 Chapter 3 Real Eigenvalue Analysis Figure 3 10 First Two Mode Shapes in the Y Direction Printed output is shown in Figure 3 11 Note that modes 1 and 8 are y direction T2 modes and modes 2 and 4 are z direction T3 modes REAL EIGENVALUES MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALI ZE NO ORDER MASS STIFFNESS i 1 1 629657E 02 1 276580E 01 2 031740E 00 1 000000E 00 1 629657E4 2 2 1 742047E 02 1 319866E 01 2 100632E 00 1 000000E 00 1 74204 7E4 3 3 6 258656E 03 7 911166E 01 1 259101E 01 1 000000E 00 6 258656E 4 4 4 6 690287E 03 8 179417E 01 1 301795E 01 1 000000E 00 6 69028 7E4 5 6 4 809111E 04 2 192968E 02 3 490218E 01 1 000000E 00 4 809111E 4 6 5 5 140773E 04 2 267327E 02 3 608563E 01 1 000000E 00 5 140773E4 EIGENVALUE 1
31. POINT ID TYPE T1 T2 T3 R1 R2 1 G 0 0 2 923141E 03 0 0 0 0 0 0 0 0 0 0 2 358381E 04 0 0 0 0 0 0 0 0 2 G 0 0 2 421475E 03 0 0 0 0 Da 0 0 0 0 1 234173E 04 0 0 0 0 0 0 0 00 FREQUENCY 2 150000E 00 COMPLEX De i PLACEMENT VECTOR REAL IMAGINARY POINT ID TYPE T1 T2 T3 R1 R2 1 G 0 0 2 982731E 03 0 0 0 0 0 0 0 0 0 0 2 496362E 04 0 0 0 0 0 0 0 0 2 G 0 0 2 446311E 03 0 0 0 0 0 0 0 0 0 0 1 290072E 04 0 0 0 0 Du 0 00 FREQUENCY 2 200000E 00 COMPLEX DISPLACEMENT VECTOR REAL IMAGINARY POINT ID TYPE T1 T2 T3 R1 R2 l G 0 0 3 045608E 03 0 0 0 0 0 0 0 0 0 0 2 643907E 04 0 0 0 0 0 0 0 0 2 G 0 0 2 472263E 03 0 0 0 0 0 0 0 0 0 0 1 348744E 04 0 0 0 0 DO 0 0 Figure 5 12 Real Imaginary Output in SORT1 Format Figure 5 13 shows the plots of the resulting displacement magnitudes for grid points 1 and 2 Note that the response for grid point 1 1s nearly an order of magnitude larger than that of grid point 2 This large difference in response magnitudes is characteristic of dynamic absorbers also called tuned mass dampers in which an auxiliary structure i e the small mass and stiffness is attached to the primary structure in order to decrease the dynamic response of the primary structure If this same model 1s rerun without the auxiliary structure the response of the primary structure grid point 2 at 5 03 Hz is twice what it was with the auxiliary structure attached as shown 1n Figure 5 14 5 30 NX Nastran Basic Dynamic Analysis User s Guide
32. Paper No 14 May 1993 Tonin Renzo Vibration Isolation of Impacts in High Rise Structures The Second Australasian MSC Users Conf Paper No 11 November 1988 DYNAMICS FREQUENCY RESPONSE Balasubramanian B Wamsler M Identification of Contributing Modes in MSC NASTRAN Modal Frequency Response Analyses Proc of the MSC NASTRAN Eur Users Conf May 1987 Barnett Alan R Widrick Timothy W Ludwiczak Damian R Combining Acceleration and Displacement Dependent Modal Frequency Responses Using An MSC NASTRAN DMAP Alter MSC 1996 World Users Conf Proc Vol II Paper No 17 June 1996 Bellinger Dean Dynamic Analysis by the Fourier Transform Method with MSC NASTRAN MSC 1995 World Users Conf Proc Paper No 10 May 1995 Bianchini Emanuele Marulo Francesco Sorrentino Assunta MSC NASTRAN Solution of Structural Dynamic Problems Using Anelastic Displacement Fields Proceedings of the 36th AIAA ASME ASCE AHS ASC Structures Structural Dynamics and Materials Conference and AIAA ASME Adpative Structures Forum Part 5 of 5 New Orleans 1995 Blakely Ken Matching Frequency Response Test Data with MSC NASTRAN MSC 1994 World Users Conf Proc Paper No 17 June 1994 Carlson David L Shipley S A Yantis T F Procedure for FRF Model Tuning in MSC NASTRAN The MSC 1993 World Users Conf Proc Paper No 71 May 1993 I 18 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliogra
33. Proc of the Conf on Finite Element Methods and Technology Paper No 12 March 1981 Mastrorocco David T Predicting Dynamic Environments for Space Structure Appendages The MSC 1992 World Users Conf Proc Vol II Paper No 56 May 1992 Mayer Lee S Zeischka Johann Scherens Marc Maessen Frank Analysis of Flexible Rotating Crankshaft with Flexible Engine Block Using MSC NASTRAN and DADS MSC 1995 World Users Conf Proc Paper No 35 May 1995 McLaughlin A Finite Element Dynamic Analysis of Production Aircraft 4th Eur Rotorcraft and Powered Lift Aircraft Forum Assoc Ital di Aeronaut ed Astronaut pp 20 1 20 7 September 1978 Melli R Rispoli F Sciubba E Tavani F Structural and Thermal Analysis of Avionic Instruments for an Advanced Concept Helicopter Proc of the 15th MSC NASTRAN Eur Users Conf October 1988 l 6 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Mikami Kouichi Dynamic Stress Analysis System for Ship s Hull Structure Under Wave Loads The Second MSC NASTRAN User s Conf in Japan October 1984 in Japanese Moharir M M NASTRAN Nonlinear Capabilities in Dynamic Solutions MSC NASTRAN Users Conf Proc Paper No 9 March 1985 Moore Gregory J Nagendra Gopal K Dynamic Response Sensitivities in MSC NASTRAN The MSC 1991 World Users Conf Proc Vol I Paper No 4 March 1991 Mulcahy T M Turula P Chung H Jendrzejez
34. TABDMPI Modal damping table INot required for initial conditions The DAREA ID is required the DAREA Bulk Data entry is not required if an LSEQ entry is used 6 9 Examples This section provides several examples showing the input and output These examples are Transient Response Bulk Output Data Entries E bd06two TSTEP TIC X Y plots EIGRL TSTEP TABDMP1 DLOAD bd06bar TLOAD2 DAREA DELAY X Y plots EIGRL TSTEP TABDMPI bdO6bkt TLOAD1 LSEQ TABLEDI X Y plot PLOADA These examples are described in the sections that follow Two DOF Model Consider the two DOF system shown in Figure 6 6 Direct transient response SOL 109 is run with an initial displacement of 0 1 meter at grid point 2 The analysis is run for a duration of 10 seconds with a At of 0 01 second Damping is neglected in the analysis Part of the input file is shown below 6 26 NX Nastran Basic Dynamic Analysis User s Guide Grid Point 1 Grid Point 2 en PP PPP PI P maat ataata ata anan atat an a at a a a a a aa gian uut ataata aat ana ataa aat aaa Figure 6 6 Two DOF Model FILE bd06two dat IWO DOF SYSTEM S CHAPTER 6 TRANSIENT RESPONSE SOL 109 DIRECT TRANSIENT RESPONSE CEND TITLE TWO DOR SYSTEM SUBTITLE DIRECT FREQUENCY RESPONSE LABEL INITIAL DISPL AT GRID 2 S SPECIFY SPC SPC 996 S S SPECIFY DYNAMIC INPUT TSTEP 888 do 777 S S SELECT OUTPUT SET 11 1 2 DISPLACEMENT PLOT 11 S S XYPL
35. bdO3carb dat Rest of Bulk Data Figure 3 21 Basic Input File for the Car Model S FILE bd 3cars dat S SPRINGS CONNECTED TO GROUND GRIDS 1059 1562 1428 1895 HAVE THE SAME COORDS AS 59 562 428 895 S GRID L059 192 012 232 7904 2 9000D 123456 GRID 1502 152 012 324 964 67 100D 123456 GRID 1428 35 6119 30 9257 0 666067 123456 GRID 1995 2520119 30 9257 093333 123456 S CELASZ I001 1000 59 1 1059 1 CELAS2 1002 500 59 2 1059 2 CELAS2 1003 1000 59 3 1059 3 CELAS2 1011 1000 562 1 1562 1 CELAS2 l012 500 562 2 1502 2 CELAS2 1013 1000 562 3 1562 3 CELAS2 1021 1000 428 1 1428 1 CELAS2 1022 500 428 2 1428 Z2 CELAS2 1023 1000 428 3 1428 3 CELAS 031 1000 9095 1 1995 1 CELAS2 1032 500 995 2 19895 2 CELASA2 1035 1000 695 3 1695 3 Figure 3 22 Input File for the Springs indicates that the translational mass is 0 8027 lb sec2 in This type of information is useful in verifying your model Figure 3 24 shows some of the rest of the output The eigenvalue analysis summary indicates that there are 12 modes below 50 Hz The large element strain energies in the first six modes indicate that these are primarily suspension modes comprised of the car frame acting as a rigid body supported by the flexible springs Approximately 95 of the total strain energy is represented by spring deformation as opposed to frame deformation Modes 7 and above show insignificant spring strain energy indicating that these are primarily fr
36. default is YES the printout of singularities 1s suppressed except when singularities are not going to be removed If PARAM SPCGEN is set to 1 default 0 the automatically generated SPCs are placed in SPCi Bulk Data entry format on the PUNCH file AUTOSPC provides the correct action for superelements in all contexts It does not provide the correct action for the residual structure in SOL 129 PARAM AUTOSPCR not AUTOSPC is used for the o set omitted set in the residual structure in SOL 106 D 4 NX Nastran Basic Dynamic Analysis User s Guide BAILOUT CB1 CB2 CK1 CK2 CK41 CK42 CM1 CM2 COUPMASS Common Commands for Dynamic Analysis 0 for superelement sequences for non superelement sequences Default 2 See MAXRATIO Default 1 0 CB1 and CB2 specify factors for the total damping matrix The total damping matrix is B CB1 Bi CB2 B A where B ij is selected via the Case Control command E and Bx comes from CDAMPi or CVISC element Bulk Data entries These parameters are effective only if B2GG is selected in the Case Control Section Default 1 0 CK1 and CK2 specify factors for the total stiffness matrix The total stiffness matrix exclusive of GENEL entries is K CK1 K CK2 K7 where K2 j is selected via the Case Control command K2GG and K is LA from structural element e g CBAR entries in the Bulk Data These are effective only if K2GG is select
37. mode The printed ESE ota 27492 The eigenvectors are printed for each mode the element corner stresses are printed for the first and second modes and the element strain energies are printed for the third mode Only the headers are shown in the figure in order to save space EIGENVALUE ANALYSIS BLOCK SIZE USED NUMBER OF DECOMPOSITIONS NUMBER OF ROOTS FOUND NUMBER OF SOLVES REQUIRED TERMINATION MESSAGE REQUIRED NUMBER OF EIGENVALUES FOUND SUMMARY LANCZOS ITERATION Co CO h2 OY REAL EIGENVALUES MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIz NO ORDER MASS STIPE NES 1 i 3 930304E 03 6 269214E 01 9 977763E 00 1 000000E 00 349303045 2 2 2 878402E 04 1 696586E 02 2 700200E 01 1 000000E 00 2 8784025 9 9 5 498442E 04 2 344876E4 02 3 731985E 01 1 000000E 00 5 4984425 EIGENVALUE 3 930304E 03 CYCLES 9 977763E 00 REAL EIGENVECTOR NO 1 EIGENVALUE 2 878402E 04 CYCLES 2 700200E 01 REAL EIGENVECTOR NO 2 EIGENVALUE 5 498442E 04 CYCLES 3 731985E 01 REAL EIGENVECTOR NO 3 EIGENVALUE 3 930304E 03 STRESSES I N QUADRILATERAL ELEMENTS QUAD 4 OPTIC EIGENVALUE 2 878402E 04 SP PRESSES I N QUADRILATERAL ELEMENTS QUAD 4 OPTIC ELEMENT STRAIN ENERGIES ELEMENT TYPE QUAD4 TOTAL ENERGY OF ALL ELEMENTS IN PROBLEM MODE Figure 3 16 Abridged Output from the Bracket Model TYPE QUAD4 SUBTOTAL TOTAL ENERGY OF ALL ELEMENTS IN SET e 2 49221E 04 100 0000 2 749221E 04 2 14
38. pp 363 392 September 1971 NASA TM X 2378 Schweiger W de Bruyne F Dirschmid W Fluid Structure Interaction of Car Fuel Tanks Proc of the MSC NASTRAN Eur Users Conf May 1984 l 8 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Shein Shya Ling Generation of the Space Station Freedom On Orbit Dynamic Loads Analysis Model Using MSC NASTRAN V66A Superelements The 2nd Annual MSC Taiwan Users Conf Paper No 7 October 1990 Shiraki K Hashimoto H Sato N Nasu S Kinno M Japanese Experiment Module JEM On Orbit Structural Dynamic Analysis 1993 MSC Japan s 11th User s Conf Proc Paper No 10 Shivaji M Raju V S N Dynamic Analysis of R C C Chimneys MSC 1995 World Users Conf Proc Paper No 34 May 1995 Singh Ashok K Nichols Christian W Derivation of an Equivalent Beam Model From a Structural Finite Element Model The MSC 1988 World Users Conf Proc Vol I Paper No 14 March 1988 Singh Sudeep K Engelhardt Charlie Dynamic Analysis of a Large Space Structure Using External and Internal Superelements The MSC 1991 World Users Conf Proc Vol I Paper No 27 March 1991 Skattum Knut S Modeling Techniques of Thin Walled Beams with Open Cross Sections NASTRAN Users Exper pp 179 196 September 1972 NASA TM X 2637 Smith Michael R Rangacharyulu M Wang Bo P Chang Y K Application of Optimization Techniques to He
39. 0 cosw t w H H Equation 1 9 Equation 1 9 is the solution for the free vibration of an undamped SDOF system as a function of its initial displacement and velocity Graphically the response of an undamped SDOF system is a sinusoidal wave whose position in time 1s determined by its initial displacement and velocity as shown in Figure 1 2 Amplitude utt Time 1 Figure 1 2 SDOF System Undamped Free Vibrations If damping is included the damped free vibration problem is solved If viscous damping is assumed the equation of motion becomes 1 6 NX Nastran Basic Dynamic Analysis User s Guide Fundamentals of Dynamic Analysis mii t bu t ku t O Equation 1 10 Damping Types The solution form in this case is more involved because the amount of damping determines the form of the solution The three possible cases for positive values of b are e Critically damped e Overdamped e Underdamped Critical damping occurs when the value of damping is equal to a term called critical damping 6 The critical damping is defined as b 2Jkm 2m r Equation 1 11 For the critically damped case the solution becomes iti 16 430 Equation 1 12 Under this condition the system returns to rest following an exponential decay curve with no oscillation A system is overdamped when 6 gt 6 and no oscillatory motion occurs as the structure returns to its undisplaced position Underdamped System The most co
40. 005 second This efficiency reduces the amount of output Damping in Direct Transient Response The damping matrix B is used to represent the energy dissipation characteristics of a structure In the general case the damping matrix is comprised of several matrices xxi 2 G 1 b B 5 i a t Wy Cele Equation 6 5 where Bl damping elements CVISC CDAMPi B2GG B2 B2PP direct input matrix transfer functions G overall structural damping coefficient PARAM G W _ frequency of interest in radians per unit time PARAM W3 for the conversion of 3 overall structural damping into equivalent viscous damping K global stiffness matrix Gp element structural damping coefficient GE on the MAT entry W frequency of interest in radians per unit time PARAM W4 for conversion of element structural damping into equivalent viscous damping Kg element stiffness matrix Transient response analysis does not permit the use of complex coefficients Therefore structural damping 1s included by means of equivalent viscous damping To appreciate the impact of this on the solution a relation between structural damping and equivalent viscous damping must be defined The viscous damping force 1s a damping force that is a function of a damping coefficient b and the velocity It is an induced force that is represented in the equation of motion using the B matrix and velocity vector M lt 5 ii r y c I amp iu tt iP t
41. 01 291809E 01 409399E 01 474014E 01 200278E U1 zn 505838E 01 3 R2 0 886937E 01 624463E 01 316833E 01 183568 E 01 5932863E 02 lt 219953E 01 764997E 01 839685E 01 368715E 01 500190E 01 4 R2 0 163791E 01 791260E 01 112445E 01 611744E 01 000213E 01 898637E 01 308033E 01 067952E 00 184692E 00 213704E 00 No No NNN hO This second model was rerun changing the mass from lumped the default to coupled by adding PARAM COUPMASS 1 to the Bulk Data The resulting frequencies are shown below and are compared to those of the lumped mass model and the theoretical results Note that the frequency difference 1s greater at higher frequencies For most production type models 1 e complex three dimensional structures this difference 1s negligible Frequencies Hz Lumped Mass Model 2 076 2 066 13 010 1 36 428 Coupled Mass Model 71 384 Bracket Model This example 1s a steel bracket as shown in Figure 3 13 3 26 NX Nastran Basic Dynamic Analysis User s Guide 1095635 01 291808E 01 4209396E 01 ATAUIDE QI 500274E 01 505833E 01 R3 0 ms xm l cua s ca pm x TU Ls 847615E 02 2608970E 01 79536595B 01 141396E 01 436876E 01 647399E 01 783234E 01 857874E 01 888214E 01 894636E 01 R3 0 163812E 01 791277E 01 112443E 01 611722E 01 000244E 01 898660E 01 308035E 01 067950E 00 184688E 00 213700E 00 R3 0 886905E
42. 2 6 Normal to Plane 3 Figure 4 2 Statically Determinate r set There are special cases where a model need not have six rigid body modes A planar model has only three rigid body modes while an airplane with a free rudder has seven for example If you use the SUPORT it is your responsibility to determine all the modes of rigid body motion then provide r set DOFs that define these rigid body modes Another special case is the application of enforced motion by the large mass technique see Enforced Motion If the input points describe redundant load paths diagnostics are produced that indicate overconstraint For this case these diagnostics may be safely ignored Poorly constrained rigid body modes result from either constraining DOFs with relatively little stiffness or from constraining a set of DOFs that are almost linearly dependent on one another An example of the former is a model of a very thin cylindrical shell The degrees of freedom normal to the shell and their associated bending degrees of freedom may all be too soft to avoid numerical conditioning problems A modeling cure for this condition is to connect many grid 4 8 NX Nastran Basic Dynamic Analysis User s Guide Rigid Body Modes points to a new reference grid point with an RBE3 element and then to place the reference grid point in the r set The RBE3 element does not affect the flexible modes when applied in this manner An example of a structure whose r set shows poo
43. 5401 SYSTEM FATAL MESSAGE 5401 REIGL LANCZOS METHOD IS UNABLE TO FIND ALL EIGENVALUES IN RANGE ACCEPTED EIGENVALUES AND ADDITIONAL ERROR MESSAGES MAY BE LISTED ABOVE USER ACTION RERUN WITH ANOTHER METHOD OR ANOTHER SETTING ON EIGRL ENTRY This message can be issued if insufficient memory is available for Lanczos with sparse decomposition It can also be issued if UFM 5299 occurs See the NX Nastran Numerical Methods User s Guide This condition can be related to the occurrence of UWM 5411 UWM 5402 USER WARNING MESSAGE 5402 THE PROBLEM HAS NO STIFFNESS MATRIX The problem requires a stiffness matrix Verify that property entries are specified correctly UIM 5403 USER INFORMATION MESSAGE 5408 CPU TIME AT START OF LANCZOS ITERATION Since several Lanczos iterations may be executed during one application of the Lanczos method each shift is followed by at least one iteration this information is given to measure the time required for the individual iterations UWM 5404 USER WARNING MESSAGE 5404 NEGATIVE MODAL MASS TERM IS ENCOUNTERED DURING INVERSE ITERATION PROCESS ABORTED The modal mass matrix should have unit diagonal terms for mass normalization Negative terms may indicate negative eigenvalues If these negative terms are computational zeroes rigid body modes for example then the negative terms are acceptable If the negative terms are finite values there may be a modeling problem UW
44. Analysis User s Guide 8 1 Chapter 8 Restarts in Dynamic Analysis 8 1 Overview A restart is a logical way of continuing from a previous run without having to start from the beginning The savings can be in terms of both time and money Some forms of restarts are used practically every day perhaps without you realizing it An example of a restart can be as simple as reading a book Normally you probably do not finish reading a book in one continuous stretch You may read a hundred pages today and another fifty pages tomorrow and so on Each time that you continue from where you left off previously is a restart It is much more time consuming and impractical to start from page one every time that you pick up the book This analogy can be applied to NX Nastran In the case of a static analysis the most expensive and time consuming part of the run is the decomposition of the stiffness matrix This fact is especially true for large models Now suppose after completing the original run you want to obtain additional output e g stresses displacements etc or add more load cases You can always start from the beginning and redo the whole problem or you can perform a restart at a fraction of the time and cost In the case of additional output requests and additional load conditions the decomposition of the stiffness matrix which was performed in the previous run is not redone if restart is used In dynamic analysis the calculation of norm
45. BRACKET MODEL S CHAPTER 3 NORMAL MODES TIME 10 SOL 103 NORMAL MODES ANALYSIS CEND S TITLE BRACKET MODEL SUBTITLE NORMAL MODES ANALYSIS SPC 1 5 S SELECT EIGRL METHOD 777 OUTPUT REQUESTS DISPLACEMENT ALL SUBCASE 1 MODES 2 S USE FOR FIRST TWO MODES STRESS CORNER ALL SUBCASE 3 bob ALL S BEGIN BULK Dude P E D ipu qua vx DO Dive dc x xd Cu whe as dks eee D eec T ses ach S SEIGRL SID V1 V2 ND MSGLVL MAXSET SHFSCL NORM EIGRL qud 100 S CONCENTRATED MASS SUPPORTED WITH AN RBE2 ELEMENT GRID 999 3 0 3 0 3 8 SCONM2 EID G CID M x1 X2 X3 CON1 STCON1 I11 I21 I22 I31 I32 L33 CONM2 999 999 0 0906 CM1 CM1 0 35 D Sb 0 07 S RBE2 999 999 123456 126 127 91 81 80 RB1 3 28 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis RB1 90 95 129 128 96 86 85 228 RB2 RB2 229 199 189 190 200 195 227 226 RB3 RB3 194 184 185 STEEL M AS S DENSITY FOR RHO MATI 1 3 7 1 153 7 7 16 4 S basic model ENDDATA Figure 3 15 Abridged Input File for the Bracket Model Figure 3 16 shows an abridged version of the resulting NX Nastran output The circular total element strain energy ESE for each mode of the entire model is ESE w2 2for the i th mode when f Mf 1 The frequency of the third mode is 234 49 radians per second squared therefore the total strain energy of the model is ESE 4 4 234 49 2 2 27493 for the third
46. Basic Dynamic Analysis User s Guide Grid Point Weight Generator Table G 2 Output from the Grid Point Weight Generator USER WARNING MESSAGE 3042 MODULE GPWG INCONSISTENT SCALAR MASSES HAVE BEEN USED EPSILON DELTA 3 8054429E 02 Rigid Body REFERENCE POINT MO Mass 250000E 00 9 330128E 01 1 075000E 01 0 000000E 00 3 000000E 00 0 000000E 00 6 058013E 00 000000E 00 0 000000F 00 2 000000E 01 5 000000E 00 1 000000E 01 0 000000E 00 Matrix OOO000E 00 3 000000F 00 5 000000E 00 8 000000E 00 2 500000E400 1 500000E 00 0 6 390 1298 01 000000E 00 Q 000000E 00 000000E 00 4 966506ET00 Properties 000000E 00 000000E 00 000000E 01 2 500000E 00 S00000E 00 000000E 00 for the 966506E 00 058013E 00 000000E 00 1 500000E 00 000000E 00 495513E 00 Reference Point Transformation from the 4 321332E 01 9 018098E 01 0 000000F 00 Gao 9 018098E 01 4 321332E 01 0 000000EF 00 Principal x 0 000000E 00 0 000000E 00 1 000000E 00 Mass to the Basic Direction Center of Gravity Relative DIRECTION MASS AXIS SYSTEM S MASS X C G NC eG Z C G to the X 1 119709E 01 3 480388F 02 6 023980F 01 2 512494E 01 8 802916E 00 6 515555E 03 4 426965E 02 2 484108E 01 Reference 2 000000E 01 90 385824E 03 5 589382F 01 0 000000E 00 Point in the Principal Mass Axes System Moments of Inertia with Respect to 376953E 00 8 768300E 01 624477E 01 768300E 01 5 623007E 00 3 419880E 01 Principal 624477E 01
47. CO O O ene P23 Sy 3s 024 24 P Roe R3 0 499062E 20 1 252464E 19 N NKNPPpPd 845365E 18 9022025E 189 338691E 18 631772E 18 240218E 18 749993E 18 4S 1655582 8 L53 elie te Deals aoe YMAX FRAME ALL DATA 328 L79E 03 328179E 0 3 R3 3 208819E 19 0 3 549737E 19 359 2066 8 302084E 17 170 2924 7 877973E 17 146 6783 7 006467E 17 122 9200 8 308275E 18 33 8900 2 421647E 18 20 3631 1 024487E 21 180 7005 1 0123495E 21 180 6966 YMAX FRAME ALL DATA 936970E 03 936970E 03 594344E 02 594344E 02 20 25 59 28 s57 26 7171846E 18 mH O1 O01 N NO Do L3 LA Restarts in Dynamic Analysis Figure 8 14 Partial Output from a Database Directory Run NX Nastran Basic Dynamic Analysis User s Guide 8 17 Chapter 9 Plotted Output e Overview e Structure Plotting e X Y Plotting NX Nastran Basic Dynamic Analysis User s Guide 9 1 Chapter 9 Plotted Output 9 1 Overview Plotted output is important in verifying your model and understanding its results Plots show information in a format that is much easier to interpret than printed output Plots are especially important for dynamic analysis because the analysis can produce voluminous output For example consider a transient response analysis for which there are 1000 output time steps 100 grid points of interest and 10 elements of interest Printed output is too large to interpret efficiently and eff
48. Che Hsi Wolf Walt Interactive Modal Animation and Structural Modification Proc of the 6th Int Modal Analysis Conf Vol I pp 947 952 February 1988 Kelley William R Isley L D Using MSC NASTRAN for the Correlation of Experimental Modal Models for Automotive Powertrain Structures The MSC 1993 World Users Conf Proc Paper No 8 May 1993 Kientzy Donald Richardson Mark Blakely Ken Using Finite Element Data to Set Up Modal Tests Sound and Vibration June 1989 Knott George Ishin Young Chargin M A Modal Analysis of the Violin The MSC 1988 World Users Conf Proc Vol II Paper No 42 March 1988 Kodiyalam Srinivas Graichen Catherine M Connell Isobel J Finnigan Peter M Design Optimization of Satellite Structures for Frequency Strength and Buckling Requirements Aerospace Sciences Meeting and Exhibit AIAA January 1993 Krishnamurthy Ravi S Stress and Vibration Analysis of Radial Gas Turbine Components Sixteenth NASTRAN Users Colloq pp 128 137 April 1988 NASA CP 2505 Lapi M Grangier H Modal Effective Parameters an Application to Shipboard Support Structures to Reduce Vibrations Transmission Proc of the 17th MSC Eur Users Conf Paper No 5 September 1990 Larkin Paul A Miller Michael W MSC NASTRAN Superelement Analysis MSC NASTRAN Users Conf Proc Paper No 10 March 1982 Lawrie Geoff The Determination of the Normal Modes of a Gliding Vehicle The S
49. Conf Proc Vol V Paper No 47 June 1996 Chen J T Chyuan S W You D W Wong H T A New Method for Determining the Modal Participation Factor in Support Motion Problems Using MSC NASTRAN The Seventh Annual MSC NASTRAN Users Conf Proc Taiwan 1995 Clary Robert R Practical Analysis of Plate Vibrations Using NASTRAN NASTRAN Users Exper pp 325 342 September 1971 NASA TM X 2378 Cohen Allan R Laurenson Robert M Application of a Substructure Technique for STS Payload Coupled Modal Analysis Proc of the MSC NASTRAN Users Conf March 1979 Concilio A Del Gatto S Lecce L Miccoli G Simple and Cheap Noise and Vibration Active Control System Using Collocated Piezoelectric Devices on a Panel Proceedings of the 11th International Modal Analysis Conference Florida 1993 Courtney Roy Leon NASTRAN Modeling Studies in the Normal Mode Method and Normal Mode Synthesis NASTRAN Users Exper pp 181 200 September 1971 NASA TM X 2378 Cronkhite James D Smith Michael R Experiences in NASTRAN Airframe Vibration Prediction at Bell Helicopter Textron American Helicopter Soc Dynamics Specialists Mtg Section 6 Vibrations Session I Paper No 1 November 1989 Cross C Rao A Comparison of Modal Performance of Alternate Compressor Bracket Design seventh Australasian Users Conf Proc Sydney October 1993 Deger Yasar Modal Analysis of a Concrete Gravity Dam Linking FE Analysi
50. DMIG input If the reference point is specified with PARAM GRDPNT 0 and S is the identity matrix then the center of gravity location is given in the basic coordinate system For the example the mass of the structure is 13 0 and the center of gravity location is 0 5384 0 2307 0 3846 in the basic coordinate system If a grid point ID is used for the reference point and S is an identity matrix then the center of gravity location is in a coordinate system parallel to the basic coordinate system with an origin located at the grid point If the S matrix is equal to the identity matrix then the S matrix represents the inertia matrix of structure for the center of gravity with respect to the basic coordinate system the Q matrix is the corresponding principal moments of inertia matrix and Q represents the transformation from the principal directions to the basic coordinate system The following additional comments on the GPWG should be noted e The scale factor entered with parameter WTMASS is applied to the assembled element mass before the GPWG The GPWG module however converts mass back to the original input units that existed prior to the scaling effect of the parameter WTMASS Note that the parameter WTMASS is not applied to M2GG or M2PP input but the M2GG mass is assembled into the mass matrix prior to GPWG Therefore for GPWG output only the M2GG mass is scaled by the same parameter as the element mass M2GG input may
51. Data Entries Required Section ENDDATA Required Delimiter This order must be followed as shown for all NX Nastran input files For details regarding the statements commands and entries see the NX Nastran Quick Reference Guide 8 4 User Interface There are two types of runs cold start and restart runs which are described below Cold Start Run The first run which is called the cold start run is identical to what you usually do for submitting an NX Nastran job with the exception that the database must be saved In addition to your normal output files e g F06 file four database files are created as a result of this run assuming that the default database initialization values are used The convention for the filenames is machine dependent therefore you should refer to the machine dependent documentation for your specific computer for the exact syntax For a typical UNIX machine with an NX Nastran input file called runl dat the following sample submittal command can be used nastran runt where nastran is the name of the shell script for executing NX Nastran Note that the above submittal command assumes that you have not modified the scr no option as your default nastran submittal option The scr no option saves the database at the end of the run which is required if you intend to perform restarts The following four database files are created as a result of the above command runl DBALL runl MASTER r
52. Dynamic Model with Test Data Using Linwood Tenth NASTRAN Users Colloq pp 74 86 May 1982 NASA CP 2249 Zeischka H LMS Link Correlating and Validating F E A for Dynamic Structure Behaviour with Experimental Modal Analysis Proc of the MSC NASTRAN Eur Users Conf May 1987 DYNAMICS COMPONENT MODE SYNTHESIS Barnett Alan R Ibrahim Omar M Sullivan Timothy L Goodnight Thomas W Transient Analysis Mode Participation for Modal Survey Target Mode Selection Using MSC NASTRAN DMAP MSC 1994 World Users Conf Proc Paper No 8 June 1994 Bedrossian Herand Rose Ted DMAP Alters for Nonlinear Craig Bampton Component Modal Synthesis The MSC 1993 World Users Conf Proc Paper No 25 May 1993 Brillhart Ralph Hunt David L Kammer Daniel C Jensen Brent M Mason Donald R Modal Survey and Test Analysis Correlation of the Space Shuttle SRM Proc of the 6th Int Modal Analysis Conf pp 863 870 February 1988 Brown J J Lee J M Parker G R Zuhuruddin K Procedure for Processing and Displaying Entire Physical Modes Based on Results Generated Through Component Mode Synthesis The MSC 1988 World Users Conf Proc Vol I Paper No 15 March 1988 Call V Mason D Space Shuttle Redesigned Solid Rocket Booster Structural Dynamic Predictions and Correlations of Liftoff AIAA SAE ASME ASEE 26th Joint Propulsion Conf Paper No AIAA 90 2081 July 1990 l 14 NX Nastran Basic Dynamic Analys
53. Dynamic Response of Reinforced Concrete Box Type Structures The MSC 1992 World Users Conf Proc Vol I Paper No 24 May 1992 Chiu Chi Wai Spacecraft Dynamics During Solar Array Panel Deployment Motion The Fifth Annual MSC Taiwan Users Conf Proc November 1993 Chung Y T Kahre L L A General Procedure for Finite Element Model Check and Model Identification MSC 1995 World Users Conf Proc Paper No 38 May 1995 Cicia C Static Thermal and Dynamic Analysis of the Liquid Argon Cryostat for the ICARUS Experiment Proc of the 15th MSC NASTRAN Eur Users Conf October 1988 Cifuentes Arturo O Dynamic Analysis of Railway Bridges Using MSC NASTRAN The MSC 1988 World Users Conf Proc Vol II Paper No 44 March 1988 Cifuentes A O Dynamic Response of a Beam Excited by a Moving Mass Finite Elements in Analysis and Design Vol 5 pp 237 246 1989 Citerley R L Woytowitz P J Ritz Procedure for COSMIC NASTRAN Thirteenth NASTRAN Users Colloq pp 225 233 May 1985 NASA CP 2373 Ciuti Gianluca Avionic Equipment Dynamic Analysis MSC 1995 European Users Conf Proc Italian Session September 1995 Coates Dr Tim Matthews Peter Transient Response in Dynamic and Thermal Behaviour The Second Australasian MSC Users Conf Proc Paper No 4 November 1988 Coppolino Robert N Bella David F Employment of MSC STI VAMP for Dynamic Response Post Processing The MSC 1987 World Us
54. EEE EE E E 7 2 The Large Mass Method in Direct Transient and Direct Frequency Response 1 2 The Large Mass Method in Modal Transient and Modal Frequency Response 1 4 User Interface for the Large Mass Method 0 0 0 0 2c cee ee ee ee ee 7 5 is i Ls 4 2 234 20800 5 29 98 00 35 3 48 29089 209 9 49 3 2293 879 19 59 99 OEE Ee Oe ee eG eee 8 1 8 Restarts in Dynamic AnalysiS 4d dc 6046664 OR Ro CROCO ERROR CR ORTU 8 1 diri a ee ee ee re ee 8 2 PEC RUIT ausos ROS E E RX Eee E oes eee Fk tee hes RAE ESS 8 2 Structure of the Input File 0 0 0 0 00 cens 8 3 Ree A l e PENAT ee ee SEES BEE AE REEE ETER EERTE GORE RES EA 8 3 Determining the Version fora Restart 2 0 0 eel 8 7 Le oe a ee oe ee ee Lee eee rer ee eee ore a ne eek eer E eer ae 8 7 btn CHER ee ee NEPEAN 9 1 b ee 244 444 439 ee a re ee ee EA 9 2 PPPOE FOLIE 4 x ETTET2TTcc It T t ETERS EDAD E EAE GALE RR AAA EDK 9 2 DE Pe ok aS EE EEE TEASEE 293 Au AA RUE AE eR RE UE EESS EXEE SR 9 7 Guidelines for Effective Dynamic Analysis cce enn n 10 1 Bo 2o Aen 10 2 Overall Analysis Strategy lt 6 44444444 RHA EDA HAR OEM RC3COE GXOCE A X COR RO HORE GE n 10 2 EHE Lua 422229 19244299252 X95 2252 5 eh oe ees 10 5 BINE 212129 9 97 9 94494349349 ee OOS ORS ORE ESE 9 294 04 29 4 5 5 10 5 LOU 43d 4 99 4 d 4 3 T UP Und 3 3 Xd xor acd 3 4 3o ROCA 4 Roi E oig P d 3 9 9E OE 3 10 5 Boundary Conditions 44 oco Ee EEK EEE COCOA eO
55. Example Sol 101 time 10 cend include subl dat begin bulk S include bulkil dat include bulk2 dat S rest of bulk data file enddata This run reads a file called sub1 dat with all the Case Control commands contained in it It also reads two additional files bulk1 dat and bulk2 dat in the Bulk Data Section You may for example want to include all your grid Bulk Data entries in the file bulk1 dat and all your element connectivities in bulk2 dat As you can see the include statement can be a handy tool For parametric studies you can potentially save a tremendous amount of disk space by using the include statement instead of having multiple files with duplicate input data Summary Due to the default values very little knowledge of the NX Nastran FMS statements and database structure is required for small to medium size problems For large problems however some knowledge of the FMS statements and database structure can help you to optimize your computer resources NX Nastran Basic Dynamic Analysis User s Guide E 7 Appendix F Numerical Accuracy Considerations F 1 Overview NX Nastran is an advanced finite element analysis program Because speed and accuracy are essential NX Nastran s numerical analysis capabilities are continually enhanced to provide the highest level of each This appendix provides a brief overview for detecting and avoiding numerical ill conditioning problems
56. IGE rower NX Nastran Basic Dynamic Analysis User s Guide 2 2 1 1 Ja 3 6 6 T N V EX T3 o 052335E 02 008020E 02 966642E 02 443303E 01 SUMMARY EIGENVALUES CYCLES 066473E 00 066473E 00 280626E 01 280626E 01 549883E 01 5049883E 01 883875E 01 883875E 01 O R N O R1 C CO OC cC C O0 O0 cC5 cC5 ALL EIGENVALUES FOUND IN RANGE 6 202180E 09 3 820101E 01 6 215970E 09 3 828595E 01 2 R2 R3 0 0 0 0 9 057010E 02 1 464532E 09 1 678406E 01 2 716750E 09 2 319480E 01 3 758543E 09 2 832321E 01 4 594735E 09 224631305901 5 234397E 09 3 501587E 01 5 692031E 09 3 681249E 01 5 988579E 09 3 779972E 01 6 152242E 09 3 820101E 01 6 219055E 09 3 828595E 01 6 233260E 09 3 R2 R3 0 0 0 0 5 937006E 07 4 571418E 01 Sie Doon 6 358200E 01 1 289605E 07 5 612913E 01 Sv 1239L8E 07 2 867391E 01 1 426249E 07 1 098159E 01 6 984853E 07 5 378201E 01 1 184615E 06 9 121327E 01 1 522753E 06 1 172494E 00 1 689206E 06 1 300660E 00 1 730573E 06 1 332512E 00 4 R2 R3 0 0 0 0 4 571424E 01 1 427123E 08 6 355204E 01 3 100643E 07 5 6012913E 01 7 615052E 07 2 867385E 01 1 006117E 06 1 098168E 01 7 569575E 07 5 378208E 01 4 733732E 08 9 121327E 01 1 181005E 06 1 172493E 00 2 239405E 06 1 300659E 00 2 875692E 06 1 332511E 00 3 057266E 06 STURM INVERSE POWER 8 6 68 GENERALIZED GENERALIZ MASS STIFFENE 1 000000E 00 1 685851 F 1 000000E 00 1 685851 F 1 000000E 00
57. M or B exists The transient solution is obtained by decomposing A4 and applying it to the right hand side of the above equation In this form the solution behaves like a succession of static solutions with each time step performing a forward backward substitution FBS on a new load vector Note that the transient nature of the solution is carried through by modifying the applied force matrix Ay with the A5 and A4 terms In its simplest form the M B and K matrices are assumed to be constant throughout the analysis and do not change with time Special solution methods are available in NX Nastran for variations in these matrices see the NX Nastran Advanced Dynamic Analysis User s Guide A significant benefit presents itself if At remains constant during the analysis With a constant At the A41 matrix needs to be decomposed only once Each progressive step in the analysis is only an FBS of a new load vector If At is changed A41 must be redecomposed which can be a costly operation in large problems Another efficiency in the direct transient solution 1s that the output time interval may be greater than the solution time interval In many cases it 1s not necessary to sample output response at NX Nastran Basic Dynamic Analysis User s Guide 6 3 Chapter 6 Transient Response Analysis each solution time For example if the solution is performed every 0 001 second the results can be output every fifth time step or every 0
58. NX Nastran Basic Dynamic Analysis User s Guide Appendix C The Set Notation System Used in Dynamic Analysis The set notation system used for dynamic analysis in NX Nastran continues and expands the set notation system for static analysis Because of the great variety of physical quantities and displacement sets used in dynamic analysis you should understand the set notation system in NX Nastran C 1 Displacement Vector Sets When you create a model in NX Nastran equations are allocated for the purpose of assembling the necessary structural equations These equations are rows and columns in the matrix equations that describe the structural behavior Six equations are created per grid point one equation is created per SPOINT or EPOINT The model details elements properties loads etc are used to create the appropriate row and column entries in the matrices e g stiffness coefficients Certain data entries 1 e SPCs MPCs ASETs etc cause matrix operations to be performed in the various stages of the solution process To organize the matrix operations NX Nastran assigns each DOF to displacement sets Most matrix operations used in a structural analysis involve partitioning merging and or transforming matrix arrays from one subset to another All components of motion of a given type form a vector set which is distinguished from other vector sets A given component of motion can belong to many sets In NX Nastran there are tw
59. NX Nastran Basic Dynamic Analysis User s Guide 5 3 Chapter 5 Frequency Response Analysis iat ixy 1u ye Equation 5 2 where u W is a complex displacement vector Taking the first and second derivatives of Equation 5 2 the following is obtained Iib ietu m 1e 9 fet iuis Equation 5 3 When the above expressions are substituted into Equation 5 1 the following is obtained e MV u o e 9 im B u w ter K fu w te Plow 1e Equation 5 4 which after dividing by e simplifies to oM iwB K u w 1P a 1 Equation 5 5 The equation of motion is solved by inserting the forcing frequency w into the equation of motion This expression represents a system of equations with complex coefficients if damping is included or the applied loads have phase angles The equations of motion at each input frequency are then solved in a manner similar to a statics problem using complex arithmetic Damping in Direct Frequency Response Damping simulates the energy dissipation characteristics of a structure Damping in direct frequency response is represented by the damping matrix B and additions to the stiffness matrix K The damping matrix is comprised of several matrices B B B7 Equation 5 6 where B1 damping elements CVISC CDAMPi and B2GG B2 B2PP direct input matrix and transfer functions In frequency response PARAM G and GE on the MAT entry do not form a damping matrix Inste
60. NX Nastran effectively The default maximum size for MASTER is 5000 blocks DBALL This 1s the DBset where the permanent data blocks are stored by default The default maximum size 1s 25000 blocks This DBset stores the source file for user created DMAP The default maximum USRSOU o size 1s 5000 blocks USROBJ This DBset stores the object file for user created DMAP The default maximum size is 5000 blocks This DBset is used as the temporary workspace for NX Nastran In general SCRATCH this DBset 1s deleted at the end of the run The default maximum size is 350100 blocks For most solutions USRSOU and USROBJ are not needed and may be deleted or assigned as temporary for the duration of the run see ASSIGN For a typical UNIX based workstation with an NX Nastran input file called dyn1 dat the following sample submittal command can be used nastran dynl scr no where nastran 1s the name of shell script for executing NX Nastran The following four physical database files are created as a result of the above command dynl MASTER dynl DBALL dynl USROBJ dvnl USRBSQU Unless otherwise stated the input filename is assumed to be dyn1 dat in this appendix E 4 File Management Commands The File Management Section 1s intended primarily for the attachment and initialization of NX Nastran database sets DBsets and FORTRAN files For many problems due to the default values the use of the FMS is either transparent or not r
61. Nam Nonlinear Perturbation Methods in Dynamic Redesign MSC NASTRAN Users Conf Proc Paper No 16 March 1983 Barber Pam Arden Kevin Dynamic Design Analysis Method DDAM Using MSC NASTRAN MSC 1994 World Users Conf Proc Paper No 31 June 1994 NX Nastran Basic Dynamic Analysis User s Guide l 1 Appendix References and Bibliography Bedrossian Herand Veikos Nicholas Rotor Disk System Gyroscopic Effect in MSC NASTRAN Dynamic Solutions MSC NASTRAN Users Conf Proc Paper No 12 March 1982 Bernstein Murray Mason Philip W Zalesak Joseph Gregory David J Levy Alvin NASTRAN Analysis of the 1 8 Scale Space Shuttle Dynamic Model NASTRAN Users Exper pp 169 242 September 1973 NASA TM X 2893 Berthelon T Capitaine A Improvements for Interpretation of Structural Dynamics Calculation Using Effective Parameters for Substructures Proc of the 18th MSC Eur Users Conf Paper No 9 June 1991 Birkholz E Dynamic Investigation of Automobile Body Parts Proc of the 15th MSC NASTRAN Eur Users Conf October 1988 Bishop N W M Lack L W Li T Kerr S C Analytical Fatigue Life Assessment of Vibration Induced Fatigue Damage MSC 1995 World Users Conf Proc Paper No 18 May 1995 Blakely Ken Howard G E Walton W B Johnson B A Chitty D E Pipe Damping Studies and Nonlinear Pipe Benchmarks from Snapback Tests at the Heissdampfreaktor NUREG CR 3180 March 1
62. Power Bandwidth Excitation Frequency Figure 5 7 Half Power Bandwidth For maximum efficiency an uneven frequency step size should be used Smaller frequency spacing should be used in regions near resonant frequencies and larger frequency step sizes should be used in regions away from resonant frequencies 5 8 Solution Control for Frequency Response Analysis The following tables summarize the data entries that can be used to control a frequency response analysis Certain data entries are required some data entries are optional and others are user selectable In the Executive Control Section of the NX Nastran input file a solution must be selected using the SOL 1 statement where 1 is an integer value chosen from Table 5 3 Table 5 3 Frequency Response Solutions in NX Nastran i Rigid Formats Structured Solution Sequences Be 8 X Solutions 108 and 111 are the preferred SOLs these are the ones used in the examples that follow In the Case Control Section of the NX Nastran input file you must select the solution parameters associated with the current analysis 1 e frequencies loads and boundary conditions and also the output quantities required from the analysis The Case Control commands directly related to frequency response analysis are listed in Table 5 4 They can be combined in the standard fashion with the more generic entries such as SPC MPC etc Table 5 4 Case Control Commands for Frequency Respo
63. Real Figure 5 2 Complex Plane where 2 2 u HU us magnitude q phase angle tan u u U real component u cos q Ui imaginary component usin q Two different numerical methods can be used in frequency response analysis The direct method solves the coupled equations of motion in terms of forcing frequency The modal method utilizes the mode shapes of the structure to reduce and uncouple the equations of motion when modal or no damping is used the solution for a particular forcing frequency is obtained through the summation of the individual modal responses The choice of the method depends on the problem The two methods are described in Direct Frequency Response Analysis and Modal Frequency Response Analysis 5 2 Direct Frequency Response Analysis In direct frequency response analysis structural response is computed at discrete excitation frequencies by solving a set of coupled matrix equations using complex algebra Begin with the damped forced vibration equation of motion with harmonic excitation IMMO BIG K x P m 1e 9 Equation 5 1 The load in Equation 5 1 is introduced as a complex vector which is convenient for the mathematical solution of the problem From a physical point of view the load can be real or imaginary or both The same interpretation 1s used for response quantities For harmonic motion which is the basis of a frequency response analysis assume a harmonic solution of the form
64. Repeater Output Frequency Set Applied Load Output Request Output Time Set Solution Set Acceleration Output Request Solution Set Displacement Output Request Solution Set Eigenvector Output Request Solution Set Velocity Output Request Velocity Output Request D 3 Bulk Data Entries for Dynamic Analysis This appendix lists the Bulk Data entries that are often used for dynamic analysis Entries that apply to generic modeling or statics such as GRID or FORCE are not listed Bulk Data entries are listed alphabetically The description of each entry is similar to that found in the NX Nastran Quick Reference Guide The descriptions in this guide have been edited to apply specifically to the dynamic analysis capabilities described herein The NX NASTRAN Quick Reference Guide describes all of the Bulk Data entries The Bulk Data entries described in this appendix are summarized as follows Mass Properties CMASS1 Scalar Mass Connection CMASS2 Scalar Mass Property and Connection CMASS3 Scalar Mass Connection to Scalar Points Only CMASS4 Scalar Mass Property and Connection to Scalar Points Only CONMI1 Concentrated Mass Element Connection General Form CONM2 Concentrated Mass Element Connection Rigid Body Form D 2 NX Nastran Basic Dynamic Analysis User s Guide Common Commands for Dynamic Analysis PMASS Scalar Mass Property Damping Properties CDAMP1 Scalar Damper Connection CDAMP2 Scalar Damper Property and Connection CDAMP3 s
65. Response Analysis Overview of Transient Response analysis Transient response analysis is the most general method of computing the response to time varying loads The loading in a transient analysis can be of an arbitrary nature but is explicitly defined 1 e known at every point in time The time varying transient loading can also include nonlinear effects that are a function of displacement or velocity Transient response analysis is most commonly applied to structures with linear elastic behavior Transient response analysis is described in Transient Response Analysis Additional types of dynamic analysis are available with NX Nastran These types are described briefly in Advanced Dynamic Analysis Capabilities and will be described fully in the NX Nastran Advanced Dynamic Analysis User s Guide 1 14 NX Nastran Basic Dynamic Analysis User s Guide Chapter 2 Finite Element Input Data e Overview e Mass Input e Damping Input e Units in Dynamic Analysis e Direct Matrix Input NX Nastran Basic Dynamic Analysis User s Guide 2 1 Chapter 2 Finite Element Input Data 2 1 Overview When you use NX Nastran to perform a dynamic analysis how you construct the model depends upon the desired results and the type of dynamic loading For example you need to obtain stress data you would only need to define a finer finite element mesh if you needed to obtain system level displacement patterns Many of the modeling cons
66. User s Guide Lanczos Method The Lanczos method overcomes the limitations and combines the best features of the other methods It requires that the mass matrix be positive semidefinite and the stiffness be symmetric Like the transformation methods it does not miss roots but has the efficiency of the tracking methods because it only makes the calculations necessary to find the roots requested by the user This method computes accurate eigenvalues and eigenvectors Unlike the other methods its performance has been continually enhanced since its introduction giving it an advantage The Lanczos method is the preferred method for most medium to large sized problems since it has a performance advantage over other methods Householder Methods The Householder modal extraction method require a positive definite mass matrix all degrees of freedom must have mass There is no restriction on the stiffness matrix except that it must be symmetric These matrices always result in real positive eigenvalues The Householder method is the most efficient method for small problems and problems with dense matrices when a large portion of the eigenvectors are needed This method finds all of the eigenvalues and as many eigenvectors as requested While this method do not take advantage of sparse matrices they are efficient with the dense matrices sometimes created using dynamic reduction see Advanced Dynamic Analysis Capabilities The Householde
67. VALID FOR RESTART PURPOSES USER ACTION SUBSEQUENT RESTARTS SHOULD REFERENCE VERSION xxx OR A PRIOR VALID VERSION If the version is not restartable you must restart from a previous valid version The xxx and yyy above denote version numbers The zzz denotes a project description provided by you This project description is alphanumeric and can contain up to 40 characters the default is blank The project description 1s often not used and is an optional statement If for some reason the records for the old runs are no longer available then the DBDIR FMS statement can be used to query the database contents to find out which versions are being stored in the database The following simple setup 1s all that is required for this purpose ASSIGN MASTER ddddd MASTER DBDIR VERSION PROJECT ENDJOB where ddddd MASTER 1s the name of the database being used The Executive Control Case Control or Bulk Data Section is not required in this case Furthermore a new version is not created in this case Near the top of the F06 output a PROJECT VERSION DIRECTORY TABLE 1s printed listing all the versions in the database A next to a version number indicates that this particular version was deleted from the database This deletion may be due to the NOKEEP option or the use of the DBCLEAN command when performing a restart run A version number with a next to it is not restartable A version number without a
68. a set of grid points VELOCITY Grid point velocity results for a set of grid points Frequency response output is in realimaginary format the default or magnitude phase format the phase angle is in degrees Frequency response output is also in SORT1 or SORT2 format In SORT1 format the results are listed by frequency in SORT2 format the results are listed by grid point or element number SORT 1 is the default for direct frequency response analysis SOL 108 and SORT2 is the default for modal frequency response analysis SOL 111 PARAM CURVPLOT 1 and PARAM DDRMM 1 are necessary to obtain SORT1 output in SOL 111 These output formats are specified with the Case Control commands The command DISPLACEMENT PHASE SORT2 ALL NX Nastran Basic Dynamic Analysis User s Guide 5 25 Chapter 5 Frequency Response Analysis prints displacements in magnitude phase and SORT2 formats The output formats are illustrated in the first example in Examples Table 5 6 Element Output from a Frequency Response Analysis Case Control Command ELSTRESS or STRESS Element stress results for a set of elements ELFORCE or FORCE Element force results for a set of elements TRAIN Element strain results for a set of elements A number of Bulk Data entries are unique to frequency response analysis These entries can be combined with other generic entries in the Bulk Data Bulk Data entries directly related to frequency response analysis are su
69. accuracy since detailed local stresses and forces are subject to mode truncation and may not be as accurate as the results computed with the direct method 6 4 Modal Versus Direct Transient Response Some general guidelines can be used in selecting modal transient response analysis versus direct transient response analysis These guidelines are summarized in 6 2 In general larger models may be solved more efficiently in modal transient response because the numerical solution is a solution of a smaller system of uncoupled equations This result is certainly true if the natural frequencies and mode shape were computed during a previous stage of the analysis Using Duhamel s integral to solve the uncoupled equations is very efficient even for very long duration transients On the other hand the major portion of the effort in a modal transient response analysis is the calculation of the modes For large systems with a large number of modes this operation can be as costly as direct integration This is especially true for high frequency excitation To capture high frequency response in a modal solution less accurate high frequency modes must be computed For small models with a few time steps the direct method may be the most efficient because it solves the equations without first computing the modes The direct method is more accurate than the modal method because the direct method NX Nastran Basic Dynamic Analysis User s Guide 6 13 Chapte
70. accurately describe the spatial and temporal distribution of the dynamic load Simplifying assumptions must not change the character of the load in magnitude location or frequency content 6 8 Solution Control for Transient Response Analysis The following tables summarize the data entries that can be used to control a transient response analysis Certain data entries are required some data entries are optional while others are user selectable In the Executive Control Section of the NX Nastran input file you must select a solution using the SOL 1 statement where i is an integer value chosen from 6 3 Table 6 3 Transient Response Solutions in NX Nastran SS Rigid Formats Structured Solution Sequences Direct 09 We have applied these solutions in the examples that follow In the Case Control Section of the NX Nastran input file you must select the solution parameters associated with the current analysis 1 e time steps loads and boundary conditions and also the output quantities required from the analysis The Case Control commands directly related to transient response analysis are listed in Table 6 4 They can be combined in the standard fashion with the more generic commands such as SPC MPC etc Table 6 4 Transient Response Case Control Commands Commands Modal ha ae Select the dynamic load T Select the TSTEP entry Select the eigenvalue METHOD Modal Required extraction parameters Select the LSEQ set fro
71. applied forces are known at each forcing frequency Forces can be in the form of applied forces and or enforced motions displacements velocities or accelerations Phase Shift Oscillatory loading is sinusoidal in nature In its simplest case this loading is defined as having an amplitude at a specific frequency The steady state oscillatory response occurs at the same frequency as the loading The response may be shifted in time due to damping in the system The shift in response is called a phase shift because the peak loading and peak response no longer occur at the same time An example of phase shift is shown in Figure 5 1 Phase Shift Loading Response e PEE i N Pe f E F A uA n i yf RR pog S j Y Fi i Jj 7 7 A i vo I Time Q4 Jj NE w i i w i l M i i i wo 4 wo 47 Figure 5 1 Phase Shift Complex Numbers The important results obtained from a frequency response analysis usually include the displacements velocities and accelerations of grid points as well as the forces and stresses of elements The computed responses are complex numbers defined as magnitude and phase with respect to the applied force or as real and imaginary components which are vector components of the response in the real imaginary plane These quantities are graphically presented in Figure 5 2 5 2 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis i Imaginary r
72. are the sorted Bulk Data sequence number of the first and last entries in the sequence to be removed respectively In the event that K2 K the following two entries are identical Rig a Tyt The values of K1 and K2 can be obtained in the F06 file of your cold start run as long as the Bulk Data is echoed with the ECHO SORT Case Control command which is the default option From Figure 8 1 the sorted Bulk Data count for PARAM GRDPNT 0 is 7 therefore the delete entry in this case can be either 7 7 or 7 No additional Bulk Data entry is required for this restart run since there are no other changes involved for this model Note that the same SPC and METHOD commands are used in both the cold start and restart runs since neither the actual boundary condition nor the desired eigenvalue calculation has changed SORTED BULK DATA E C HO 7 du 23456 2 123456 1 TOTAL COUNT Figure 8 1 Echo of the Sorted Bulk Data Input for the Cold Start Run You can include as many of these delete entries as necessary However if the case requires many changes it is probably more convenient to delete the entire old Bulk Data Section from the database and replace it with the fully revised Bulk Data Section including the new and modified entries This operation can be accomplished by including the full new Bulk Data plus the following entry in the Bulk Data Section of the restart run l4 where 1 1s any positive inte
73. at the end of the current run proj ID NOKEEP If this option 1s used then the version that you are restarting from is deleted at the end of the current run This is the default Example RESTART The current run uses the last version in the database for restart At the end of the run this last version 1s deleted from the database This statement 1s probably the most commonly used format for RESTART RESTART VERSION 5 KEEP The current run version 6 or higher uses version 5 in the database for restart At the end of the run version 5 is also retained in the database This format is used most often when you want to ensure that a specific version is saved in the database i e a large normal modes run RESTART PROJ xyz VERSION 3 The current run uses version 3 with a proj ID of xyz in the database for restart At the end of the run version 3 with a proj ID of xyz is deleted from the database E 6 NX Nastran Basic Dynamic Analysis User s Guide File Management Section INCLUDE Purpose Inserts an external file at the location where this include statement is used This is nota pure FMS statement because it can be used anywhere in the input file not just in the FMS Section The include statement must not be nested in other words you cannot attach a file that contains an include statement Format Include filename filename Physical filename of the external file to be inserted at this location
74. automatically differentiates a specified velocity once or a specified displacement twice to obtain an acceleration The remaining required user actions are the same as for enforced acceleration In summary the user actions for direct frequency and direct transient response are e Remove any constraints from the enforced degrees of freedom e Apply large masses m with CMASSi or CONMi Bulk Data entries to the DOFs where the motion is enforced The magnitude of m should be approximately 106 times the entire mass of the structure or approximately 109 times the entire mass moment of inertia of the structure if the component of enforced motion is a rotation e In the case of direct frequency response apply a dynamic load computed according to Equation 7 4 to each enforced degree of freedom e In the case of direct transient response Indicate in field 5 of the TLOAD1 and TLOAD2 entries whether the enforced motion is a displacement velocity or acceleration m Apply a dynamic load to each enforced degree of freedom equal to m u ormQj depending on whether the enforced motion 1s a displacement velocity or acceleration Be careful when using PARAM WTMASS The WTMASS parameter multiplies the large mass value which changes the effective enforced acceleration to i LE O O O m WIMASS Equation 7 5 Enforced velocity and enforced displacement are changed likewise You may well ask whether a stiff spring may be used ins
75. be scaled independently using the CM2 parameter e The GPWG is performed on the g size mass matrix which is the mass matrix prior to the processing of the rigid elements MPCs and SPCs e The mass at scalar points and fluid related masses are not included in the GPWG calculation e The GPWG for a superelement does not include the mass from upstream superelements Therefore the GPWG for the residual structure includes only the mass on the residual points The center of gravity location is also based on the mass of the current superelement only e Ifa large mass is used for enforced motion the large mass dominates the structural mass For model checkout 1t is recommended to remove the large mass and constrain the driving point A static analysis is a convenient way to generate a mass matrix and obtain output from the GPWG e The output from the GPWG is for information purposes only and is not used in the analysis G 3 Example with Direction Dependent Masses In the previous section the mass was the same in each of the three coordinate directions thereby producing a unique center of gravity location However if scalar masses are used the total mass may have different properties in each direction and the center of gravity may not be a unique NX Nastran Basic Dynamic Analysis User s Guide G 3 Appendix G Grid Point Weight Generator location This effect is shown in the output by providing the direction and center of gravity for each
76. but all three are shown here for comparison purposes ENTRIES FOR ENFORCED MOTION Ur LARGE MASS AT BASE GRID POINT CONMZ 999 3 1 087 LOAD DEFINITION SDLOAD SID S S1 RLOAD1 DLOAD 999 1 0E7 1 0 998 SDAREA SID P1 Cl Al DAREA 997 3 2 1 0 UNIQUE ENTRIES FOR ENFORCED CONSTANT ACCELERATION MAGNITUDE SRLOAD1 SID DAREA TC RLOAD1 998 997 901 STABLED4 TID X1 X2 X3 X4 TAB4 TABLEDA 901 0 1 0 100 TAB901 S TAB4 AO Al A2 A3 A4 A5 TAB901 1 0 ENDT UNIQUE ENTRIES FOR ENFORCED CONSTANT VELOCITY MAGNITUDE SRLOAD1 SID DAREA TD RLOADI 998 997 902 STABLED4 TID X1 X2 X3 X4 TAB4 TABLED4 902 0 1 0 100 TAB902 S TAB4 AO Al A2 A3 A4 A5 TAB902 0 0 6 283185 ENDT UNIQUE ENTRIES FOR ENFORCED CONSTANT DISPLACEMENT MAGNITUDE SRLOAD1 SID DAREA TC RLOAD1 998 997 903 STABLEDA TID X1 X2 X3 X4 TAB4 TABLED4 903 0 1 0 100 TAB903 S TAB4 AO Al A2 A3 A4 A5 TAB903 0 0 0 0 39 4784 ENDT Figure 7 5 Bulk Data Entries for Enforced Constant Motion Each input utilizes the TABLED4 entry The TABLED4 entry uses the algorithm 7 12 NX Nastran Basic Dynamic Analysis User s Guide Enforced Motion oe Gay r yale Equation 7 12 where x is input to the table Y is returned and N is the degree of the power series When x lt X3 X83 is used for x when x gt X4 X4 is used for x This condition has the effect of placing bounds on the TABLED4 entry note that there is no extrapolation
77. especially as they relate to dynamic analysis For more information regarding NX Nastran s numerical analysis algorithms see the NX Nastran Numerical Methods User s Guide F 2 Linear Equation Solution The basic statement of the linear equation solution is A ixt ibi Equation F 1 where A is a square matrix of known coefficients and usually symmetric for structural models b is a known vector and x is the unknown vector to be determined The methods used for solution in NX Nastran are based on a decomposition of A to triangular matrices and are followed by forward backward substitution to get x The equations for this solution technique are A LLC Equation F 2 where L is a lower triangular matrix and U an upper triangular matrix and Llivt ib Equation F 3 where y 1s an intermediate vector Equation F 3 is called the forward pass because the solution starts with the first row where there 1s only one unknown due to the triangular form of L The backward pass starts with the last row and provides the solution NX Nastran Basic Dynamic Analysis User s Guide F 1 Appendix F Numerical Accuracy Considerations Ulixe aye Equation F 4 F3 Eigenvalue Analysis The general eigensolution equation is K pB p MMut 0 Equation F 5 where pis the complex eigenvalue This equation can always be transformed to a special eigenvalue problem for a matrix A A A I t 0 Equatio
78. figure shows classical rigid body modes whereby one mode is purely x translation another is purely y translation and another is purely z rotation about the center of the beam Because rigid body modes are a special case of 4 2 NX Nastran Basic Dynamic Analysis User s Guide Rigid Body Modes repeated roots any linear combination of these displacement shapes also comprises a valid set of rigid body modes Figure 4 1 Rigid Body Modes of a 2 D Beam 4 2 SUPORT Entry Rigid body modes are computed in NX Nastran without requiring special user intervention although the use of a SUPORT Bulk Data entry makes the mode shapes look cleaner The SUPORT entry also makes the rigid body mode shapes repeatable when the mass or stiffness of the model changes and the model is reanalyzed The SUPORT note spelling entry does not constrain the model it simply provides a frame of reference for the rigid body shape calculations by defining the r set components of motion The SUPORT entry is not required for any of the dynamic analysis methods except for response spectrum analysis see Advanced Dynamic Analysis Capabilities If the SUPORT is used one DOF should be specified for each rigid body mode or mechanism The form of the SUPORT entry is shown below Field Contents IDi Grid or scalar point identification number Ci Component numbers 0 or blank for scalar points and any unique combination of the integers 1 through 6 for grid points
79. in order to see the variation in response versus frequency Deformed structure plots at a frequency near a resonant frequency can also help to interpret the results If structure plots are made look at the imaginary component because the single degree of freedom SDOF displacement response at resonance is purely imaginary when damping is present this response does not occur in practice because the response is usually due to several modes If you have time dependent loads perform transient response SOL 109 or SOL 112 analysis If your structure 1s constrained apply the load very quickly over one or two time NX Nastran Basic Dynamic Analysis User s Guide 10 3 Chapter 10 Guidelines for Effective Dynamic Analysis steps as a step function and look at the displacement results The duration of the analysis needs to be as long as the period of the lowest frequency mode For an SDOF system a quickly applied load results in a peak displacement response that is twice the response resulting from the same load applied statically This peak response does not occur in your actual model because of multiple modes and damping but the results should be close If your structure is unconstrained the displacements will grow with time unless the rigid body modes are excluded in a modal transient response analysis However the stresses should be roughly twice those from the static analysis In any event examine the results via X Y plots to ensure reasonab
80. is an approximate method response spectrum analysis is often used as a design tool Response spectrum analysis is also called shock spectrum analysis There are two parts to response spectrum analysis 1 generation of the spectrum and 2 use of the spectrum for dynamic response such as stress analysis Both are available in NX Nastran Figure 11 1 depicts the generation of a response spectrum d E f e c f gt 3 max Peak b We 2 oz R i ee Ah l esponse l i _ Japi L b f f a Transient SETIER of I 23 Wb Response Oscillators Resonant Frequency Base Transient Structure Excitation Transient excitation a is applied to a base structure b from which transient response c is computed for each floor his response is applied to a series of oscillators d for which the peak response is plotted e Steps d and e are repeated for different damping values to form response spectra as shown below 5 critical damping 2 critical damping 0 critical damping Peak amping Response Resonant Frequency f Figure 11 1 Response Spectrum Generation Note that the peak response for one oscillator does not necessarily occur at the same time as the peak response for another oscillator Also note that there is no phase information since only the magnitude of peak response is computed It is assumed in this process that each oscillator mass is very small relative to the base struc
81. is proportional to the amount of coupling between that degree of freedom and the degree of freedom with a higher value of k If the terms of the k th row and above are not connected to the remaining rows the k th term of NX Nastran Basic Dynamic Analysis User s Guide F 5 Appendix F Numerical Accuracy Considerations D goes to zero Because of numerical truncation the term may be a small positive or negative number instead If a term of D is calculated to be identically zero it is reset to a small number because of the indeterminacy of its calculation The existence of such a small term defines a mechanism in static analysis in NX Nastran A mechanism is a group of degrees of freedom that may move independently from the rest of the structure as a rigid body without causing internal loads in the structure A hinged door for example is a mechanism with one rigid body freedom If the hinges are disconnected the door mechanism has six rigid body freedoms Mechanisms are characterized by nondimensional numbers derived by dividing the terms of D into the corresponding diagonal term of A If these matrix diagonal to factor diagonal ratios are large numbers various warning and fatal messages are produced depending on the context F 8 Sources of Nonpositive Definite Matrices A negative semidefinite element stiffness matrix which is defined as one whose eigenvalues are all negative or zero implies that the element has an energy sourc
82. linear independence Default 1 MODACC 0 selects the mode acceleration method for data recovery in dynamic analysis PARAM DDRMM 1 must also be specified Default 1 NONCUP selects either a coupled or noncoupled solution algorithm in modal transient response analysis By default the noncoupled solution algorithm is selected unless the dynamic matrices KHH MHH or BHH have off diagonal terms NONCUP 1 requests the coupled algorithm and 2 the uncoupled algorithm regardless of the existence of off diagonal terms in the dynamic matrices User Information Message 5222 indicates which algorithm is used in the analysis NX Nastran Basic Dynamic Analysis User s Guide D 7 Appendix D Common Commands for Dynamic Analysis 1 SOL 30 NOSORTI 1 SOL 31 Default NOSORT1 controls the execution of the SDR3 module which changes SORT1 modal solutions to SORT2 In SOL 30 where SORT1 output is the default option NOSORT1 is set to branch over this operation In SOL 31 where SORT2 output is usually desired PARAM NOSORT1 1 may be used when only SORT1 output is desired WTMASS Default 1 0 The terms of the structural mass matrix are multiplied by the value of this parameter when they are generated This parameter is not recommended for use in hydroelastic problems W3 W4 Default 0 0 The damping matrix for transient analysis is assembled from the equation Baal Ung Bag grs Uu yz Ua The default value
83. mass matrices can be compared using the CROD element Assume the following properties ee Torsion s Torsion Length L Translation 3 Translation Area A lorsional Constant Young s Modulus E L Shear Modulus C Mass Density p Polar Moment of Inertia p l 4 are D egrees of Freedom CROD Element Stiffness Matrix The CROD element s stiffness matrix K is given by NX Nastran Basic Dynamic Analysis User s Guide 2 3 Chapter 2 Finite Element Input Data AE _AE o ofi 0 0 2 A AE y AE ola L L GJ GJ c c Tn Equation 2 1 The zero entries in the matrix create independent uncoupled translational and rotational behavior for the CROD element although for most other elements these degrees of freedom are coupled CROD Lumped Mass Matrix The CROD element classical lumped mass matrix is the same as the NX Nastran lumped mass matrix This lumped mass matrix is M pAL O O oS Mie gt o Ni c 0 Equation 2 2 The lumped mass matrix is formed by distributing one half of the total rod mass to each of the translational degrees of freedom These degrees of freedom are uncoupled and there are no torsional mass terms calculated The CROD element classical consistent mass matrix is 2 4 NX Nastran Basic Dynamic Analysis User s Guide Finite Element Input Data 3 T lc 1 1 gt i 6 3 o e pg LP 6A 3A Equation 2 3 This classical mass m
84. max sizei l the i th file Example INIT DBALL LOGICAL DBALL 50000 This statement creates the DBALL DBset with a logical name of DBALL and the maximum size of 50000 NX Nastran blocks instead of 25000 blocks which is the default value for DBALL Unless an ASSIGN statement is also used the physical file is given the name dyn1 DBALL assuming that your input file is called dyn1 dat INIT DBALL LOGICAL DB1 35000 DBTWO 60000 This statement creates the DBALL DBset with logical names of DB1 and DBTWO Two physical files dyn1 DB1 and dyn1 DBTWO are created with a maximum size of 35000 and 60000 NX Nastran blocks respectively Format Simplified for the SCRATCH DBset INIT SCRATCH LOGICAL log namel max sizel log name2 max size2 log namei max sizei j SCR300 log nameitl max sizeit l log namen max sizen Log namel through log namei are allocated for regular scratch files as temporary workspace This temporary workspace is not released until the end of the job SCR300 is a special keyword which indicates that the log names are members reserved for DMAP module internal scratch files The space occupied by these SCR300 files is for the duration of the execution of the module This SCR300 space is released at the end of the module execution You can have up to a combined total of 10 logical names for the SCRATCH DBset 1 xi lt 10 Example INIT SCRATCH LOGICAL SCR1 150000 SCR2 100000 SCR300 SC
85. more outside the range F1 and F2 before stopping the search 3 16 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis The SINV method is particularly efficient when only a small number of eigenvalues and eigenvectors are to be computed Often only the lowest mode is of interest The following example illustrates an EIGR entry which extracts only the lowest nonzero eigenvalue 1 2 3 4 5j 6e 7 8 9 10 EIGR i3 SINV joo po B j j It is assumed in the example above that the frequency of the lowest mode is greater than 0 01 cycles per unit time NX Nastran finds one eigenvalue outside the range F1 F2 and then stops the search The eigenvalue found 1s the lowest nonzero eigenvalue or a member of the lowest closely spaced cluster of eigenvalues in cases with close roots provided that there are no negative eigenvalues and that the SUPORT entry has been used to specify the correct number of zero eigenvalues see Rigid body Modes The following examples demonstrate the use of the EIGR data entry In this example the automatic Householder method 1s selected and the lowest 10 modes are requested Since the default MASS eigenvector normalization is requested no continuation entry is needed In this example the same method 1s requested but all the modes below 100 cycles per unit time are requested with MAX vector normalization In this example the Sturm modified inverse
86. not have the off diagonal terms that couple the equations of motion Therefore in this form the modal equations of motion are uncoupled In this uncoupled form the equations of motion are written as a set of uncoupled single degree of freedom systems as 2 o mj5 e e pj Equation 5 12 where m i th modal mass k i th modal stiffness Pi i th modal force The modal form of the frequency response equation of motion is much faster to solve than the direct method because it is a series of uncoupled single degree of freedom systems Once the individual modal responses x W are computed physical responses are recovered as the summation of the modal responses using fx O E w pe Equation 5 13 5 6 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis These responses are in complex form magnitude phase or real imaginary and are used to recover additional output quantities requested in the Case Control Section Damping in Modal Frequency Response If a damping matrix B exists the orthogonality property see Overview of Normal Modes Analysis of the modes does not in general diagonalize the generalized damping matrix 0 B b diagonal Equation 5 14 If structural damping is used the orthogonality property does not in general diagonalize the generalized stiffness matrix 6 K 0 z diagonal Equation 5 15 where K 1 iG K i Ge Kgr In the
87. of DMAP by Generalized CMS in System Identification The Fourth MSC NASTRAN User s Conf in Japan October 1986 in Japanese Kasai Manabu Approach to CMS Subjected to the Boundary Constrained at Single Point The Sixth MSC NASTRAN User s Conf in Japan October 1988 in Japanese Kim Hyoung M Bartkowicz Theodoore J Van Horn David A Data Recovery and Model Reduction Methods for Large Structures The MSC 1993 World Users Conf Proc Paper No 23 May 1993 Kubota Minoru Efficient Use of Component Mode Sysnthesis Using Image Superelements Applied to Dynamic Analysis of Crankshaft MSC NASTRAN Users Conf Proc Paper No 22 March 1986 Lee W M Substructure Mode Synthesis with External Superelement The 2nd Annual MSC Taiwan User s Conf Paper No 16 October 1990 in Chinese MacNeal R H A Hybrid Method of Component Mode Synthesis Computers and Structures Vol 1 No 4 pp 581 601 1971 Martinez D R Gregory D L A Comparison of Free Component Mode Synthesis Techniques Using MSC NASTRAN MSC NASTRAN Users Conf Proc Paper No 18 March 1983 Martinez David R Gregory Danny L A Comparison of Free Component Mode Synthesis Techniques Using MSC NASTRAN Sandia National Laboratories June 1984 SAND83 0025 Murakawa Osamu Hull Vibration Analysis by Modal Synthesis Method The First MSC NASTRAN User s Conf in Japan October 1983 in Japanese Murakawa Osamu Iwahashi Yoshio Sakato Ts
88. of response A sufficient number of modes must be retained to cover the time and spatial distribution of loading For example if the applied transient load has a spatial distribution resembling the fifth mode shape then that mode should be included in the transient response Size of the Integration Time Step The value of the integration time step At denoted by DT on the TSTEP Bulk Data entry is important for the accurate integration of the equations of motion Rough guidelines for the selection of At are as follows e At must be small enough to accurately capture the magnitude of the peak response which means that at least ten time steps per cycle of the highest mode be used For example if the highest frequency of interest 1s 100 Hz then A should be 0 001 second or smaller e At must be small enough to accurately represent the frequency content of the applied loading If the applied loading has a frequency content of 1000 Hz then At must be 0 001 NX Nastran Basic Dynamic Analysis User s Guide 10 11 Chapter 10 Guidelines for Effective Dynamic Analysis second or less preferably much less in order to represent the applied loading with more than one point per cycle The integration time step can be changed in a transient response analysis but it is not recommended Much of the cost of direct transient response occurs with the decomposition of the dynamic matrix which occurs only once if there is a constant At A new decomposit
89. of the three mass principal components When using directional mass the axes about which the inertia matrix i S is calculated are referred to as the principal mass axes The principal mass axes may not necessarily intersect However these axes provide uncoupled rotation and translation mass properties If the structural model is constructed using only real masses the three principal mass values printed out are equal the center of gravity is unique and the principal mass axes intersect at the center of gravity To demonstrate all of the features of the GPWG module the four mass sample problem discussed in the previous section is modified so that the mass is not equal in each of the three translational directions see Figure G 3 Furthermore different displacement coordinate systems are used for the grid points The displacement coordinate system for grid point 1 is the local rectangular system 1 which is oriented at an angle of 45 degrees about the zp axis The displacement coordinate system for grid point 3 1s the local rectangular system 3 which 1s oriented at an angle of 60 degrees about the zj axis The grid point locations and masses are summarized in Table G 1 Figure G 3 Four Concentrated Mass Model Table G 1 Location and Size of Masses Grid ID Location Basic System CP Fields Mass Global System CD Fields gt a w Xe a The GPWG output for the four mass model is shown in G 2 G 4 NX Nastran
90. of units you must ensure that the units in your NX Nastran model are consistent Because there is more input in dynamic analysis than in static analysis it is easier to make a mistake in units when performing a dynamic analysis The most frequent source of error in dynamic analysis is incorrect specification of the units especially for mass and damping Table 2 2 shows typical dynamic analysis variables fundamental and derived units and common English and metric units Note that for English units all lb designations are lbf The use of lb for mass 1 e lb is avoided Table 2 2 Engineering Units for Common Variables Common English Common Metric 1 Variable Dimensions Units L um ts Length fi Ma 18 essi ju Rotation ad rad PhseAnie ae Me o 2 12 NX Nastran Basic Dynamic Analysis User s Guide Finite Element Input Data Table 2 2 Engineering Units for Common Variables Moment Mass Density Young s Modulus Poisson s Ratio rs eee Shear Modulus Pa Torsional Constant m 4 nertia Stiffness Mem Stress Strain ee ee eee Area Moment of L in4 m4 Inertia 2 5 Direct Matrix Input The finite element approach simulates the structural properties with mathematical equations written in matrix format The structural behavior 1s then obtained by solving these equations Usually all of the structural
91. one for each of the following sets of boundary conditions for the quarter model e Symmetric antisymmetric e Antisymmetric symmetric e Symmetric symmetric e Antisymmetric antisymmetric The BC Case Control command identifies multiple boundary conditions The SPCADD Bulk Data entry defines a union of SPC sets 5 FILE bdO3pltl dat S QUARTER PLATE MODEL S CHAPTER 3 NORMAL MODES SOL 103 NORMAL MODES ANALYSIS TIME 10 CEND TITLE SIMPLY SUPPORTED PLATE USING SYMMETRY SUBTITLE NORMAL MODES CASE CONTROL LABEL QUARTER PLATE MODEL S DISPLACEMENT ALL S SUBCASE 1 LABEL SYM ASYM BC 1 METHOD 1 SPC 101 SUBCASE 2 LABEL ASYM s YM BC 2 SPO 102 METHOD 1 SUBCASE 3 LABEL SYM SYM BC 3 SPC 103 METHOD 1 NX Nastran Basic Dynamic Analysis User s Guide 3 37 Chapter 3 Real Eigenvalue Analysis SUBCASE 4 LABEL ASYM ASYM BC 4 SPC 104 METHOD 1 BEGIN BULK S Bw d E uus Dau dg E uu dca s D qr ad EPIS IPIE Oe aot aene 9 uus eho d o p 9 SYM ASYM SPCADD 101 11 1 4 5 ASYM SYM SPCADD 102 ILL 2 3 e SYM SYIM SPCADD 103 11 1 3 5 ASYM ASYM SPCADD 104 11 2 4 SEIGRL SID V1 V2 EIGRL 1 0 1 100 S SPC 1 1 246 0 00 SPC 1 2 246 0 00 etc SPC 11 80 12356 0 00 SPC 11 81 123456 0 00 5 basic model 5 ENDDATA Figure 3 30 Input File Abridged for the Quarter Plate Model Figure 3 31 shows the quarter plate mode shapes and the correspo
92. presence of a B matrix or a complex stiffness matrix the modal frequency approach solves the coupled problem in terms of modal coordinates using the direct frequency approach described in Direct Frequency Response Analysis i o 6 EM IO io 6 BILO 6 KIo Eco 0 P 0 Equation 5 16 Equation 5 16 1s similar to Equation 5 5 for the direct frequency response analysis method except that Equation 5 16 is expressed in terms of modal coordinates X Since the number of modes used in a solution is typically much less than the number of physical variables using the coupled solution of the modal equations 1s less costly than using physical variables If damping is applied to each mode separately the uncoupled equations of motion can be maintained When modal damping is used each mode has damping b where b 2m Wz The equations of motion remain uncoupled and have the form 2 w mS w iwb Zw k50 p w Equation 5 17 for each mode Each of the modal responses is computed using NX Nastran Basic Dynamic Analysis User s Guide 5 7 Chapter 5 Frequency Response Analysis p w ad I m ib k Equation 5 18 The TABDMP1 Bulk Data entry defines the modal damping ratios A table is created by the frequency damping pairs specified on the TABDMP1 entry The solution refers to this table for the damping value to be applied at a particular frequency The TABDMP1 Bulk Data entry has a Table ID A particular TABD
93. reduce the weight com Figure 11 6 Cantilever I Beam Example The optimizer in NX Nastran uses sensitivity analysis The sensitivity matrix S defines the change in response for a perturbation in design variable A term in S is given by OR O l s LI i OX Equation 11 4 NX Nastran Basic Dynamic Analysis User s Guide 11 11 Chapter 11 Advanced Dynamic Analysis Capabilities where Sij 1 J term in LS d partial derivative Ri i th response X j th design variable The sensitivity is depicted in Figure 11 7 in which the sensitivity is the slope of the curve of response versus the design variable value Design optimization and design sensitivity are described in greater depth in the NX Nastran Design Sensitivity and Optimization User s Guide Response R Design Variable X Figure 11 7 Response Sensitivity 11 11 Control System Analysis A control system provides feedback output to an input In aircraft sample control systems are flap settings and actuator positions A control system involves a general input output relationship called a transfer function Transfer functions are represented in NX Nastran by the TF Bulk Data entry Transfer functions can utilize grid points extra points EPOINT and scalar points SPOINT Nonlinearities can be simulated via the NOLINi entries with which nonlinear transient loads are expressed as functions of displacements or velocities Complex eigenvalue analy
94. response analysis this plot can be generated by using a displacement initial condition in modal transient response analysis it can be generated by applying an impulsive force that ramps up and down quickly with respect to the dominant period of response The logarithmic decrement A is the natural log of the amplitude ratio of two successive cycles of free vibration response given by X A In Ai Equation 10 2 The logarithmic decrement provides an approximate damping relationship for lightly damped structures as given by A gt 2T Equation 10 3 In transient response analysis remember to use PARAM W3 or PARAM W4 to include structural damping if GE or PARAM G is used Displacement Time Figure 10 3 Damped Free Vibration Response Both the half power bandwidth method and the logarithmic decrement method assume an SDOF response These approximations are less accurate when there are multiple modes of response however they are useful for verifying that the damping input is within a factor of two or three of the desired damping NX Nastran Basic Dynamic Analysis User s Guide 10 7 Chapter 10 Guidelines for Effective Dynamic Analysis 10 6 Boundary Conditions The proper specification of boundary conditions is just as important for dynamic analysis as it is for static analysis The improper specification of the boundary conditions leads to inc
95. response requires the use of complex force and stress components Once a good set of X Y plot commands is established it is wise to use this set repeatedly The examples that follow provide a good starting point Figure 9 9 shows X Y plot commands for a modal frequency response analysis of the cantilever beam model Plots are made in pairs in magnitude phase format The t as the second letter in XTGRID YTGRID YTLOG and YTTITLE corresponds to the top plot of each pair the letter b corresponds to the bottom plot XBGRID YBGRID etc Plots are made for the applied loads OLOAD at grid points 6 and 11 displacements DISP of grid points 6 and 11 bending moment ELFORCE at end A in plane 1 for element 6 and modal displacements SDISP for modes 1 and 2 For CBAR elements force component 2 is the bending moment component at end A in plane 1 NX Nastran Basic Dynamic Analysis User s Guide 9 7 Chapter 9 Plotted Output for real or magnitude output and force component 10 is the similar component for imaginary or phase output Figure 9 10 shows the resulting plots The plots in this chapter were converted to PostScript format for printing on a PostScript compatible printer The X Y plotter makes reasonable choices of upper and lower bounds for the axes for both the x and y axes on most plots If it does not the bounds can be fixed with the XMIN XMAX YMIN YMAX and their variations for half frame curves Instances where setting
96. second model the cross section is perfectly round making I1 and 12 identical Consider the first model Due to the manufacturing tolerances I1 2 9E 8m4 and I2 3 1E 8m4 The input file is shown in Figure 3 9 FILE bd03barl dat S CANTILEVER BEAM MODEL CHAPTER 3 NORMAL MODES 2 SOL 103 NORMAL MODES ANALYSIS TIME 10 CEND z TITLE CANTILEVER BEAM SUBTITLE NORMAL MODES LABEL MODEL 1 I1 NE I2 SPC e 1 OUTPUT REQUEST DISPLACEMENT ALL SELECT EIGR ENTRY METHOD 10 S BEGIN BULK Vase eee 3 Bu aa Bie disces acsi Raise ad PI Ds eed JG ewean D aae es Desens Ei ere S 3 22 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis SEIGR SID METHOD Fl F2 NE ND EIG S tEIG NORM G C EIGR 10 SINV 0 50 ALUMINUM PROPERTIES E 7 1E10 N m 2 NU 0 33 RHO 2 6554 N m 5 WE I G H T DENSITY SMAT1 MID E G NU RHO MATL 1 7 1 10 0 33 2 65 4 S CONVERT WEIGHT TO MASS MASS S G 9 81 m sec 2 gt WTMASS PARAM WTMASS 0 102 S 1 G FWEIGHT 1 G 0 102 Il AND I2 SLIGHTLY DIFFERENT DUE TO MANUFACTURING TOLERANCE ADD NONSTRUCTURAL WEIGHT OF 2 414 N M PBAR 1 1 6 158 4 2 9 8 3 1 8 6 8 2 414 CBAR CBAR CBAR CBAR CBAR CBAR CBAR CBAR CBAR CBAR GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID SPC1 j KA C OCC cC5cC50 C ODODDDVDVOCCCrKrF Or e n rp C OC Cc 00 cC O ppmpmopmpmmprmn
97. set constraints the f set remains The f set 1s the free DOF of the structure At this stage of the solution the f set is comprised of the remaining equations that represent a constrained structure If the applied constraints are applied properly the f set equations represent a statically stable solution If static condensation is to be performed the f set is partitioned into the o set and the a set The o set degrees of freedom are those that are to be eliminated from the active solution through a static condensation The remaining DOFs reside in the a set The a set 1s termed the analysis set The a set is often the partition at which the solution is performed If the SUPORT entry is used the degrees of freedom defined on the SUPORT entry are placed in the r set When the r set is partitioned from the t set the l set remains This final set 1s termed the leftover set and is the lowest level of partitioning performed in NX Nastran static analysis The set partition is the matrix on which the final solution is performed Under special circumstances the set is divided into two types of DOFs The DOFs that are held fixed in component mode synthesis CMS are called b set points and those DOFs that are free to move in CMS are called c set points C 1 demonstrates the basic partitioning operations When a particular set above has no DOFs associated with it it is a null set Its partition is then applied and the DOFs are moved to the sub
98. specifies 14 frequencies between 2 9 Hz and 9 4 Hz in increments of 0 5 Hz Field Contents SID Set ID specified by a FREQUENCY Case Control command Ios Starting frequency in set cycles per unit time Af Frequency increment cycles per unit time NDF Number of frequency increments NX Nastran Basic Dynamic Analysis User s Guide 5 21 Chapter 5 Frequency Response Analysis FREQ2 The FREQ2 example specifies six logarithmic frequency intervals between 1 0 and 8 0 Hz resulting in frequencies at 1 0 1 4142 2 0 2 8284 4 0 5 6569 and 8 0 Hz being used for the analysis o3 2 83a 4 55 ee s w sPREQ SD Fun Fea e FEQ po go 9 qo o jo ooo Field Contents SID Set ID specified by a FREQUENCY Case Control command Esos Starting frequency cycles per unit time Fend Ending frequency cycles per unit time NF Number of logarithmic intervals FREQ3 The FREQ3 example requests 10 frequencies between each set of modes within the range 20 and 2000 plus ten frequencies between 20 and the lowest mode in the range plus 10 frequencies between the highest mode in the range and 2000 Field Contents SID Set ID specified by a FREQUENCY Case Control command F1 Lower bound of modal frequency range in cycles per unit time Real gt 0 0 F2 Upper bound of modal frequency range in cycles per unit time Real gt 0 0 F2 gt F1 Default F1 LINEAR or LOG Specifies linear or logarithmic interpolation betwee
99. structure For inflatable rotating or tension structures the stiffness and therefore the modes depends upon the applied load and deformation A nonlinear analysis can be restarted into SOL 103 to compute the normal modes of the deformed structure 11 9 Superelement Analysis Superelement analysis is a form of substructuring wherein a model is divided into pieces with each piece represented by a reduced stiffness mass and damping matrix Each superelement is processed individually and the solutions are then combined to solve the entire model The final analysis 1n which all of the individual superelement solutions are combined involves much smaller matrices than would be required if the entire model were solved in a one step process An example of a superelement model 1s shown in Figure 11 5 NX Nastran Basic Dynamic Analysis User s Guide 11 9 Chapter 11 Advanced Dynamic Analysis Capabilities Superelement analysis has the advantage of reducing computer resource requirements especially if changes are made to only one portion superelement of the model in this case only the affected superelement needs to be reanalyzed and the final analysis repeated Superelement analysis presents procedural advantages as well particularly when multiple engineering contractors are involved in an analysis Imagine a model of a rocket and payload one contractor models the booster another contractor models the engines and another contractor model
100. te at watatatat at atat tuat utut wat tuat utut DEEP statatat atat a a a a atat tut utut gar utut ut ee Figure 10 5 Cantilever Beam Model with Static Loads A static analysis SOL 101 is run first Then modal frequency response SOL 111 is run from 0 0 to 20 0 Hz with a damping ratio of 2 critical damping used for all modes Modes are computed up to 500 Hz using the Lanczos method Finally modal transient response SOL112 is run with the time variation shown in Figure 10 6 Modes are computed up to 3000Hz using the Lanczos method and a damping ratio of 2 critical damping is used for all modes 1 0 1 Load Factor 0 003 0 006 Time sec Figure 10 6 Time Variation of Transient Loads Figure 10 2 shows the y displacements for grid points 6 and 11 As expected the frequency response results at 0 0 Hz are the same as the static analysis results see Figure 10 The frequency response results at 2 05 Hz very near the first natural frequency are approximately 25 times the static analysis results The factor of 25 is the dynamic amplification factor at resonance for a damping ratio of 2 critical damping Amplification Factor at Resonance M xam 25 The transient response results are approximately twice the static analysis results The factor of two is the amplification of response for a transient load applied suddenly see Transient Response Analysis Table 10 2 Comparison of Results for the Cantilever B
101. the input file Modal displacements are written to the plot file and are not printed The rigid body mass matrix is computed via the PARAM GRDPNT 0 entry Include files are used to partition the input file into several smaller files The INCLUDE statement inserts an external file into the input file The basic file is bdO3car dat The springs are contained in file bdO3cars dat Figure 3 22 and the rest of the input file is contained in file bdO3carb dat not shown Figure 3 20 Car Frame Model S FILE bdO3car dat S CAR FRAME MODEL 5 CHAPTER 3 NORMAL MODES 9 S MODEL COURTESY LAPCAD ENGINEERING 5 CHULA VISTA CALIFORNIA SOL 103 NORMAL MODES ANALYSIS TIME 30 CEND TITLE CAR MODEL WITH SUSPENSION SPRINGS SUBTITLE MODAL ANALYSIS CASE CONTROL ECHO UNSORT METHOD 1 DISPLACEMENT PLOT ALL SET 99 I001 1002 1003 10115 1012 101 3 1021 10227 10235 1031 10352 1033 ESE 99 BEGIN BULK S NX Nastran Basic Dynamic Analysis User s Guide 3 31 Chapter 3 Real Eigenvalue Analysis TESTTE Cee wees aria ee d ud ud sud Sechs do Rs Onna du Tere apeg EEEE Os brats M INCLUDE bdO03cars dat Car springs SEIGRL SID V1 V2 ND MSGLVL MAXSET SHFSCL NORM EIGRL 1 1 504 Figure 3 23 shows the grid point weight generator output The grid point weight generator SMAT1 MID E G NU RHO MATL L 10E 0 55 2 059E 4 S PRINT RIGID BODY MASS PARAM GRDPNT 0 S ECHOOPRE INCLUDE ENDDATA
102. time spent in the major operations of the real eigensolution module are output Note that the number of eigenvectors requested has a large effect on solution cost USER FATAL MESSAGE 5288 NO ROOT EXISTS ABOVE FMIN This message occurs when the eigenproblem of finding any number of roots above FMIN is expected but the Sturm number indicates that there 1s no root above FMIN Reduce FMIN in order to attempt to find a root SYSTEM FATAL MESSAGE 5299 This text varies depending on the reason for termination see the description given below 1 Insufficient storage for the Lanczos method 2 Factorization error on three consecutive shifts 9 Stack overflow in the Lanczos method 4 Unrecoverable termination from the Lanczos method 5 Insufficient working storage 6 Finite interval analysis error see UIM 6361 This message can also occur for models with two or more widely separated groups of repeated roots An avoidance is to search each group separately This error may also be caused by a massless mechanism which can be confirmed by performing a static analysis See the NX Nastran Numerical Methods User s Guide for more information USER FATAL MESSAGE 5400 INCORRECT RELATIONSHIP BETWEEN FREQUENCY LIMITS You have incorrectly specified V1 gt V2 Check V1 V2 specified on the EIGRL Bulk Data entry NX Nastran Basic Dynamic Analysis User s Guide H 11 Appendix H Diagnostic Messages for Dynamic Analysis SFM
103. to scale RLOAD1 input the applied force magnitude in terms of NX Nastran input is PU soc 5 ALGO DDD Equation 7 7 7 6 NX Nastran Basic Dynamic Analysis User s Guide Enforced Motion where S and S are input on the DLOAD Bulk Data entry A is input on the DAREA entry and C f and D f are input on the TABLEDi entries Note that the i non subscript term in the i If a DLOAD entry is used to scale RLOAD2 input the applied force magnitude in terms of NX Nastran input is expression i D f is Pf S 9 S Aj Bi I Equation 7 8 where S and S are input on the DLOAD Bulk Data entry A is input on the DAREA entry and B f is input on the TABLEDi entry Specification of the large force value depends upon whether acceleration velocity or displacement is enforced Enforced Acceleration Enforced acceleration is the easiest to apply since the required force is directly proportional to the desired acceleration times the large mass p w m ti a Equation 7 9 Enforced Velocity Enforced velocity requires a conversion factor p w iwm i 2nf m u Equation 7 10 For constant velocity if it may be easiest to use the RLOAD1 and TABLED4 entries because the imaginary term i D f of Equation 7 7 and the frequency dependent term 2nf can be specified directly Enforced Displacement Enforced displacement also requires a conversion factor 2 ae p w w m u 2mf m u w Equa
104. where the dynamic load is to be applied and the scale factor to be applied to the loading The DAREA entry provides the basic spatial distribution of the dynamic loading Field Contents SID Set ID specified by RLOADi entries Pi Grid extra or scalar point ID Ci Component number Ai Scale factor A DAREA entry is selected by RLOAD1 or RLOAD2 entries Any number of DAREA entries may be used all those with the same SID are combined NX Nastran Basic Dynamic Analysis User s Guide 5 13 Chapter 5 Frequency Response Analysis Time Delay DELAY Entry The DELAY entry defines the time delay tin an applied load Field Contents SID Set ID specified by an RLOADoi entry Pi Grid extra or scalar point ID Ci Component number t Time delay for Pi Ci Default 0 0 A DAREA entry must be defined for the same point and component Any number of DELAY entries may be used all those with the same SID are combined Phase Lead DPHASE Entry The DPHASE entry defines the phase lead q Field Contents SID Set ID specified by an RLOAD entry Pi Grid extra or scalar point ID Ci Component number q Phase lead in degrees for Pi Ci Default 0 0 A DAREA entry must be defined for the same point and component Any number of DPHASE entries may be used all those with the same SID are combined Dynamic Load Tabular Function TABLEDi Entries The TABLED entries i 1 through 4 each define a tabular function for u
105. 0 Marlow Jill M Lindell Michael C NASSTAR An Instructional Link Between MSC NASTRAN and STAR Proceedings of the 11th International Modal Analysis Conference Florida 1993 Masse Barnard Pastorel Henri Stress Calculation for the Sandia 34 Meter Wind Turbine Using the Local Circulation Method and Turbulent Wind The MSC 1991 World Users Conf Proc Vol II Paper No 53 March 1991 Mindle Wayne L Torvik Peter J A Comparison of NASTRAN COSMIC and Experimental Results for the Vibration of Thick Open Cylindrical Cantilevered Shells Fourteenth NASTRAN Users Colloq pp 187 204 May 1986 NASA CP 2419 Morton Mark H Application of MSC NASTRAN for Assurance of Flight Safety and Mission Effectiveness with Regard to Vibration upon Installation of the Stinger Missile on the AH 64A The MSC 1991 World Users Conf Proc Vol II Paper No 52 March 1991 Neads M A Eustace K I The Solution of Complex Structural Systems by NASTRAN within the Building Block Approach NASTRAN User s Conf May 1979 Nowak William Electro Mechanical Response Simulation of Electrostatic Voltmeters Using MSC NASTRAN The MSC 1993 World Users Conf Proc Paper No 65 May 1993 O Callahan Dr John Avitabile Peter Reimer Robert An Application of New Techniques for Integrating Analytical and Experimental Structural Dynamic Models The 1989 MSC World Users Conf Proc Vol II Paper No 47 March 1989 Ott Walter Kai
106. 0 9139 32 959 EPREOY L000 7 Soe L397 DOs 990999590129 092949 EREO 000 41 1897 4 6 2927 01 3957 002 4 99 7 61 602 S PREC 10007 DE Oy 200 S DAMPING S LDABSDMPIUIQUDOVCEII Ry eee Dale TDAME Oi 7 025 200 ng O02 ENDT 5 ENDDATA Figure 8 9 Input File for Frequency Response Analysis S FILE bd08bar9 dat 5 assign master bd08barl MASTER dbdir endjob Figure 8 10 Input File to Print the Database Dictionary BRAK PARTIAL OUTPUT FROM bd08bar5 f06 Re UE POINT ID 11 D I S PLACEMENT VECTOR TIME TYPE T1 T2 Ao R1 R2 R3 0 0 0 0 0 0 0 5 000000E 03 G 9 024590E 22 1 614475E 21 1 923969E 05 0 3 001072E 05 3 518218E 20 1 000000E 02 G 3 367912E 21 8 536304F 21 7 739825E 05 0 1 118816E 04 1 271978E 19 2 300003E 01 G 3 941339E 19 8 273585E 18 7 832402E 03 0 3 655237E 03 5 515358E 18 2 350003E 01 G 3 956722E 19 8 583470E 18 7 862186E 03 0 3 686721E 03 5 464303E 18 2 400003E 01 G 3 957035E 19 9 029934F 18 7 880123E 03 0 3 709195E 03 5 756178E 18 2 450003E 01 G 3 944803E 19 9 498899E 18 7 886210E 03 50 3 726098E 03 6 049827E 18 2 500003E 01 G 3 927639E 19 9 878397E 18 7 884440E 03 0 3 754001E 03 6 040225E 18 2 550003E 01 G 3 909298E 19 1 020556E 17 7 873885E 03 0 3 796297E 03 5 837433E 18 2 600002E 01 G 3 885339E 19 1 063947E 17 7 844862E 03 0 3 831216E 03 5 8710138 18 2 650001E 01 G 3 848278E 19 1 128651E 17 7 785291E 03 0 3 828911E 03 6 419444E 18 2 700001E 01 G 3 796167E 19 1 207232E 17 7 690622E 03 0 3 77887
107. 0 RAINT R2 R3 0 0 0 0 CELASJA FORCE ELEMENT ID CELAS 2 FORCE ELEMENT ID This example is a fixed free aluminum cantilever beam with properties as shown in Figure3 8 NX Nastran Basic Dynamic Analysis User s Guide 3 21 Chapter 3 Real Eigenvalue Analysis ant at Co a ett aw at at tat wat at tat ee at PPP watt uat utut gatur ut stat atat utat gatur utut ut ee at PPP ett aw at at te Figure 3 8 Cantilever Beam Model L 3 0m r 0 014m J 6 0E 8m4 A 6 158E 4m2 I1 I2 3 0E 8m l p 2 65E4N m E 7 1E10N m2 U 0 33 Nonstructural Weight 2 414N m The r term is the weight density and must be converted to mass density r for consistency of units PARAM WTMASS is used to convert this weight density to mass density 2 WIMASS 1 1 9 81 0 102 sec m l where g 1s the acceleration of gravity in 3 Du Pa WIMASS 2 65b4 0 102 2703 kg m m sec Therefore The nonstructural weight of 2 414 N m 1s added to the beam This nonstructural weight per length 1s also scaled by PARAM WTMASS The example illustrates normal modes analysis SOL 103 using the Sturm modified inverse power method METHOD SINV on the EIGR entry Mass normalization the default 1s chosen for the eigenvectors All frequencies between 0 and 50 Hz are requested Two models are run In the first model manufacturing tolerances make the cross section slightly out of round making I1 and 12 slightly different In the
108. 0 0 1 067134E 01 11 G 4 273806E 34 5 671835E 01 0 0 0 0 0 0 1 067134E 01 EIGENVALUE 1 819082E 09 CYCLES 6 788069E 06 REAL EIGENVECTOR NO 2 POINT ID TYPE T1 T2 T3 R1 R2 R3 1 G 2 993214E701 5 99753608 01 0 0 0 0 0 0 3 291537E 01 2 G 2 953214E 01 4 609875E 01 Du 0 0 0 0 3 291537E 01 3 G 2 953214E 01 3 622414E 01 0 0 0 0 0 0 3 291537E 01 4 G 2 953214E 01 2 634953E 01 0 0 0 0 0 0 3 291537E 01 5 G 2 953214E 01 1 647492E 01 0 0 0 0 0 0 3 291537E 01 6 G 2 953214E 01 6 600305E 02 0 0 0 0 0 0 3 291537E 01 7 G 2 953214E 01 3 274305E 02 0 0 0 0 0 0 3 291537E 01 8 G 2 9932 14E 01 1 314892E 01 0 0 0 0 0 0 3 291538E 01 9 G 2 953214E 01 2 302354E 01 0 0 0 0 0 0 3 291538E 01 10 G 2 953214E 01 3 289815E 01 0 0 0 0 0 0 3 291538E 01 11 G 2 953214E 01 4 277276E O1 0 0 0 0 0 0 3 291538E 01 EIGENVALUE 2 000299E 09 CYCLES 7 118156E 06 REAL EIGENVECTOR NO 3 POINT ID TYPE T1 T2 T3 R1 R2 R3 1 G 2s 993611E 01 5 596586E 01 0 0 0 0 0 0 3 291096E 01 NX Nastran Basic Dynamic Analysis User s Guide 4 11 Chapter 4 Figure 4 6 Unconstrained Beam Modes With Statically Determinate SUPORT SINV Rigid Body Modes 2 G 2 953611E 01 4 609257E 01 0 3 G 2 953611E 01 3 621928E 01 0 4 G 2 953611E 01 2 634599E 01 0 5 G 2 953611E 01 1 647270E 01 0 6 G 2 953611E 01 6 599414E 02 0 7 G 2 953611E 01 3 273870E 02 0 8 G 2 953611E 01 1 314715E 01 0 9 G 2 953611E 01 2 302044E 01 0 10 G 2 953611E 01 3 289373E 01 0 11 G 2 9536
109. 0000E 00 100000E 00 150000E 00 200000E 00 POINT ID MPLEX REAL IMAGINARY T2 2 813052E 03 2 107985E 04 2 866642E 03 2 229164E 04 2 923141E 03 2 398382E 04 2 982732E 03 2 496362E 04 3 045609E 03 2 0643905E 04 IYPE G T1 T3 Q Q QQ oOo0o0o0o0oo0o0o0o0oO0O OoOo0o0o0o0o0o0o0o0O0O OO OOO OOO Oca CODD OCOCO00 CODD OCCO00 CODD Coco C0 cCc COMPLEX D T2 2 374954E 03 129933E 04 2 397706E 03 1 180853E 04 2 421475E 03 1 234173E 04 2 446311E 03 1 290072E 04 2 472262E 03 1 348744E 04 TYPE G T1 G G G G CQ CC Coco CoCcoCoOCocCo C C C5 Coco CoCoCoOC co COCOCOCOCOCO C cCO9 C9 C9 C OC CO0cC5cCc5o 000 cC C OCC C5CoCco CCCo C OC CO0cC5Cc5oCc5 0 CC DISPLACEMENT RI H FU 4 D Q FI e Er Z VECTOR OoO0o0o0o0o0o00o00O oOoOo0oo0o0o0oo0o0oo0oo0O lt Eu Q O ye R C CCCo Coco Cocco OOO OO OOOO Figure 5 10 Real Imaginary Output in SORT2 Format FREQUENCY 000000E 00 050000E 00 100000E 00 150000E 00 200000E 00 POINT ID FREQUENCY 000000E 00 050000E 00 100000E 00 150000E 00 200000E 00 FREQUENCY POINT ID 1 2 FREQUENCY Figure 5 11 COMPLEX T2 2 820939E 03 355 7145 2 875296E 03 3555535 2 932640E 03 20943974 2 993161E 03 3355 2159 3 057064E 03 355 0386 TYPE T1 Q Q a a C j c Cc j ODODDVOCCOO00 j c c c Cc S O O O oOoOo0oo0o0o0oo0oo0oo0o0O c c C c c C OCC C50 000 cC
110. 002588 converts the weight density to mass density for the acceleration NX Nastran Basic Dynamic Analysis User s Guide 2 7 Chapter 2 Finite Element Input Data of gravity g 386 4 in sec The mass density therefore becomes 7 76E 4 lbesec in4 If the weight density of steel is entered as RHO 80000 N m when using metric units then using PARAM WTMASS 0 102 converts the weight density to mass density for the acceleration of gravity g 9 8 m sec The mass density therefore becomes 8160 kg m PARAM WTMASS is used once per run and it multiplies all weight mass input including CMASSi CONMi and nonstructural mass input Therefore do not mix input type use all mass and mass density input or all weight or weight density input PARAM WTMASS does not affect direct input matrices M2GG or M2PP see Direct Matrix Input PARAM CM2 can be used to scale M2GG there is no parameter scaling for M2PP PARAM CM1 is similar to PARAM WTMASS since CM1 scales all weight mass input except for M2GG and M2PP but it is active only when M2GG is also used In other words PARAM CM 1 is used in addition to PARAM WTMASS 1f M2GG is used NX Nastran Mass Input Mass is input to NX Nastran via a number of different entries The most common method to enter mass is using the RHO field on the MAT entry This field is assumed to be defined in terms of mass density mass unit volume To determine the total mass of the element the mass density is m
111. 01 624437E 01 316835E 01 183602E 01 wo os 219917E 01 764996E 01 839722E 01 368777E 01 500259 E 01 Real Eigenvalue Analysis Figure 3 13 Bracket Model A concentrated mass is suspended from the center of the hole in bracket This mass has the following properties m 0 0906 Ib sec in H1 035 in Ib sec 122 0 56 in Ib sec 13 0 07 in Ib sec The concentrated mass grid point 999 is connected to the bracket by an RBE2 element connecting 24 grid points as shown in Figure 3 14 NX Nastran Basic Dynamic Analysis User s Guide 3 27 Chapter 3 Real Eigenvalue Analysis i LT is ye 9 Y Figure 3 14 Bracket Model Showing RBE2 Element Dashed Lines The bracket 1s clamped by constraining six degrees of freedom for each of 12 grid points near the base This example illustrates a normal modes analysis SOL 103 using the Lanczos method EIGRL entry All frequencies below 100 Hz are requested The MODES Case Control command is used to specify the number of times a subcase 1s repeated and therefore enables different output requests for each mode The output requests for this problem are eigenvectors for all modes DISPLACEMENT ALL above the subcase level corner stresses for the first two modes STRESS CORNER ALL and MODES 2 in Subcase 1 and element strain energies for the third mode ESE ALL An abridged version of the input file 1s shown in Figure 3 15 FILE bd03bkt dat
112. 01 1 278503E 02 1002 5 884620E 02 1003 8 020268E 01 1011 1 278420E 02 1012 5 883779E 02 1013 8 022697E 01 1021 7 525866E 01 1022 4 885996E 02 1023 2 255234E 02 LO 7 528390E 01 1032 4 896509E 02 1033 24299399 ET0Z2 TYPE ELAS2 SUBTOTAL 3 172818E 03 GENERALIZED MASS 1 000000E 00 PRP RPP EE 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 ENERGIES 99 PERCENT OF TOTAL 2 3116 0035 ZA 8929 0028 0068 24 1506 0338 0067 2 33 7076 0305 94 1469 ENERGIES 99 PERCENT OF TOTAL 9114 4 1950 wo ed e914 1944 5719 i NO K w rco Figure 3 24 Abridged Output from the Car Model NX Nastran Basic Dynamic Analysis User s Guide 4831 6071 93617 4906 6078 4 5192 0 000000E 00 LANCZOS ITERATION GENERALIZ STIFFNES 3464 T9E 60654886F 71769821E 633242 F 078395 48535758F 805541E 350976 940912F 416198E 413452 TTE 726959 F XO XO OO1OTN O1 4S WN DN 1 173240E 03 1 104569E 03 STRAIN ENERGY DE 1 402770E 04 3 172818E 03 STRAIN ENERGY DE 3 33 Chapter 3 Real Eigenvalue Analysis Mode shapes for modes 7 8 9 and 10 are shown in Figure 3 25 Mode 7 is an overall twisting mode mode 8 is a roof collapse mode mode 9 is a local front roof mode and mode 10 is a local rear mode Plots s
113. 1 0 0 0 0 2 G 0 0 4 176756E 01 0 0 0 0 3 G 0 0 4 176756E 01 0 0 0 0 4 G 0 0 4 176756E 01 0 0 0 0 5 G 0 0 4 176756E 01 0 0 0 0 6 G 0 0 4 176756E 01 0 0 0 0 7 G 0 0 4 176756E 01 0 0 0 0 8 G 0 0 4 176756E 01 0 0 0 0 9 G 0 0 4 176756E 01 0 0 0 0 10 G 0 0 4 176756E 01 0 0 0 0 ct G 0 0 4 176756E 01 0 0 0 0 EIGENVALUE 0 000000E 00 CYCLES 0 000000E 00 REAL EIGENVECTOR N O POINT ID TYPE T1 T2 T3 R1 1 G 0 0 7 163078E 01 0 0 0 0 2 G 0 0 95 730462E 01 0 0 0 0 3 G 0 0 4 297847E 01 0 0 0 0 4 G 0 0 2 865231E 01 0 0 0 0 5 G 0 0 1 432615E 01 0 0 0 0 6 G 0 0 1 508516E 14 0 0 0 0 T G 0 0 1 432615E5 01 0 0 0 0 8 G 0 0 2 865231E 01 0 0 0 0 9 G 0 0 4 297847E 01 0 0 0 0 10 G 0 0 5 730463E 01 0 0 0 0 11 G 0 0 7 163078E 01 0 0 0 0 Method GENERALIZED MASS 1 000000E 00 PRR ep OCDODDOOCCO00 C OO CCCo CcoCco Cocco OOO OO OOO C2 CO CO CO OCC cC5Cc5o C00 cC CO CO Co CoCoCoCcoCcoCoCcoco Oi OO OOO CO CO CO CO 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 R2 R2 R2 CO CO OC C5CoCoCcoCoCocCo ia ou ms 1 i Sia ag oL 1 i PAPA HHP AAAAYH AD Table 4 7 shows the epsilon and strain energy printed in UIM 3035 for the three SUPORT cases statically determinate overdetermined and underdetermined 4 12 NX Nastran Basic Dynamic Analysis User s Guide C CO OCC cC5oCcoCco Cocco a GENERALIZE STIFFNESS 0 D D 483918E4 732272E4 751285E4 616299E4
114. 11E 01 4 276701E 01 0 C OCC C5CoCcoCcoCco C OC C0cC5 05000 cC C OC CC Coco CCCo C OCC cC5CoCcoCcoCcco OOOO CO CO C2 CO CO CD Figure 4 5 Unconstrained Beam Modes Without SUPORT SINV Method USER INFORMATION MESSAGE 3035 FOR DATA BLOCK SUPPORT PT NO EPSILON KLR STRAIN ENERGY o 3 3 3 3 3 3 3 3 3 291096E 01 291096E 01 291096E 01 291096E 01 291095E 01 291095E 01 291095E 01 291095E 01 291095E 01 291095E 01 EPSILONS LARGER THAN 0 001 ARE FLAGGED WITH AS 1 7 7496606E 17 5 5879354E 09 2 7 7496606E 17 0 0000000E 00 3 7 7496606E 17 7 1622708E 11 REAL EIGENVALUES MODE EXTRACTION EIGENVALUE RADIANS CYCLES NO ORDER 1 1 0 0 0 0 0 0 2 2 0 0 0 0 0 0 3 3 0 0 0 0 0 0 4 4 6 483918E 03 8 052278E 01 1 281560E 01 S 5 4 732272E 04 2 175379E 02 3 462222E 01 6 6 1 751285E 05 4 184836E 02 6 660372E 01 7 7 4 616299E 05 6 794335E 02 1 081352E 02 EIGENVALUE 0 000000E 00 CYCLES 0 000000E 00 REAL EIGENVECTOR N O POINT ID TYPE T1 T2 T3 R1 1 G 4 176756E 01 0 0 0 0 0 0 2 G 4 176756E 01 0 0 0 0 0 0 3 G 4 176756E 01 0 0 0 0 0 0 4 G 4 176756 E 01 0 0 0 0 0 0 5 G 4 176756 E 01 0 0 0 0 0 0 6 G 4 176756 E 01 0 0 0 0 0 0 7 G 4 176756 E 01 0 0 0 0 0 0 8 G 4 176756E 01 0 0 0 0 0 0 9 G 4 176756E 01 0 0 0 0 0 0 10 G 4 l17T6756E 01 0 0 0 0 0 0 11 G 4 176756E 01 0 0 0 0 0 0 EIGENVALUE 0 000000E 00 CYCLES 0 000000E 00 REAL EIGENVECTOR N O POINT ID TYPE T1 T2 T3 R1 1 G 0 0 4 176756E 0
115. 170818E 02 159040E 01 124720E 01 Real Eigenvalue Analysis 0 0 0 0 O R N O R1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O R N O R1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O R N O R1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Now consider the second model for which I1 and 12 are identical Printed output is shown in Figure 3 12 Note that modes 1 and 2 3 and 4 5 and 6 etc have identical frequencies this 1s a case of repeated roots Also note that the eigenvectors are not pure y or pure z translation as they were in the first model the eigenvectors are linear combinations of the y and z modes since this model has repeated roots MODE EXTRACTION NO ORDER 1 1 2 3 3 2 4 5 5 4 6 6 T T 8 8 EIGENVALUE CYCLES POINT ID TYPE G 2 G 3 G 4 G 5 G EIGENVALUE ANALYSIS NUMBER OF EIGENVALUES EXTRACTED NUMBER OF TRIANGULAR DECOMPOSITIONS TOTAL NUMBER OF VECTOR ITERATIONS REASON FOR TERMINATION EIGENVALUE 1 685851E 02 PES BOAO r2 pmppmoOosc 685851E 02 474471E 03 474471E 03 974941E 04 974941E 04 870792E 05 870792E 05 1 685851E 02 2 066473E 00 T1 0 198658E 20 293447E 20 218317E 19 577188E 19 r2 1C0to cC E 109908E 03 469681E 02 416008E 02 249444E 01 0 REAL BiB DYN COOH EH E T2 RADIANS 298403E 01 298403E 01 046410E 01 046410E 01 230458E 02 230458E 02 3252606E 02 3252606E 02 E
116. 33 Chapter 6 Transient Response Analysis E T E Me a l 00 e 0 02 Displacement 11 m Time sec Figure 6 13 Displacements at Grid Points 6 and 11 6 34 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis Acceleration 6 msec Acceleration 11 m sec Time sec Figure 6 14 Accelerations at Grid Points 6 and 11 Bending Moment Al Nim Time sec Figure 6 15 Bending Moment A1 for Element 6 NX Nastran Basic Dynamic Analysis User s Guide 6 35 Chapter 6 Transient Response Analysis SDisplacementl 0 0015 mm eL isplacement 0 0 2 0 Time sec Figure 6 16 Modal Displacements for Modes 1 and 2 Bracket Model Consider the bracket model shown in Figure 6 17 A pressure load of 3 psi is applied to the elements in the top face in the z direction with the time history shown in Figure 6 18 The modal transient analysis 1s run for 4 seconds with a time step size of 0 005 second Modal damping of 2 critical damping is used for all modes Modes up to 3000 Hz are computed with the Lanczos method The model 1s constrained near the base 6 36 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis me I Figure 6 17 Bracket Model Pressure 3 psi o 0 46 0 15 a Time ser Figure 6 18 Time Variation for Applied Load Figure 6 19 shows the abridged input file The LSEQ entry is used to apply the pre
117. 4 and FREQ5 Bulk Data entries FREQ Defines discrete excitation frequencies 5 20 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis FREQI Defines a starting frequency F4 a frequency incitement Af and the number of frequency increments to solve NDF FREQ2 Defines a starting frequency F444 and ending frequency Feng and the number of logarithmic intervals NF to be used in the frequency range FREQ3 Defines the number of excitation frequencies used between modal pairs in a given range FREQ4 Defines excitation frequencies using a spread about each normal mode within a range FREQ5 Defines excitation frequencies as all frequencies in a given range as a defined fraction of the normal modes 1Used for modal solution only The FREQUENCY Case Control command selects FREQi Bulk Data entries All FREQi entries with the same selected Set ID are applied in the analysis therefore you can use any combination of FREQ FREQ1 FREQ2 FREQ3 FREQ4 and FREQ5 entries The examples that follow show the formats of the FREQi entries Notice that the six sets of excitation frequencies shown in the examples will be combined in a single analysis if the Set IDs are identical FREQ This FREQ entry specifies ten specific unequally spaced loading frequencies to be analyzed Field Contents SID Set ID specified by a FREQUENCY Case Control command F Frequency value cycles per unit time FREQ1 The FREQ1 example
118. 402994 L9 05 020 BEA TBL4 ENDT ENDDATA Figure 8 8 Input File for an Additional Transient Load FILE bdOSbar9 dat THIS IS RESTART RUN TO PERFORM FREQUENCY RESPONSE RESTART ASSIGN MASTER bd08barl MASTER ID CANT BEAM SOL 111 TIME 10 CEND TITLE CANTILEVER BEAM FREQUENCY RESPONSE RESTART SPC 1 METHOD 10 SET 1 11 DISP PHASE 1 SUBCASE 1 S S A TWO PERCENT CRITICAL DAMPING IS gt APPLIED TO TIBIS RUN AS OPPOSED TO S ONE PERCENT CRITICAL DAMPING IN S THE TRANSIENT ANALYSIS S SDAMP 1000 DLOAD 1000 FREQ 1000 PLOT RESULTS X Y plot commands EGIN BULK B ADDITIONAL ENTRIES FOR FREQUENCY RESPONSE SID DARFA M N TC TD RLOAD1 1000 1001 1002 DAREA 1001 11 3 0 1 T ABLED1 1002 Duy Lepa 00g ler ENDT FORCING FREQUENCIES S RESONANT FREQUENCIES F REOGIDOSOI2w0SIT4 2 1000252 12 59101 15 01795 NX Nastran Basic Dynamic Analysis User s Guide Restarts in Dynamic Analysis PREO 1000 34 902 1 736 08563 SPREAD THROUGHOUT FREQUENCY RANGE OF INTEREST WITH BIAS BETWEEN HALF POWER POINTS UY UY UY Xo NM EREOIO000 1 249 1 000 440 79 12 795 159 13 EREO J1000 2 0404 2 0594 2 0125 2 097 EREO I000 2 2242 2 9204 P 2 V TIPZ O92 2 1D6 EREO 10007 9 90349 04 1 LOU S78 biel tog A T2853 BRE DOHO gL OT O72 1 OL Ze pA Fy Ae OOS EREO 1000 13 1017 14 5439 154306 16 0638 16 634 EREO 1000 24 0904 26224 72941095 3
119. 5E 03 7 287524E 18 5 949959E 01 G 1 986670E 19 1 304284E 17 4 027668E 03 0 2 010369E 03 4 506177E 18 5 999959F 01 G 2 106813E 19 1 285776E 17 4 244778E 03 m 2 079488E 03 4 219749E 18 ene es PARTIAL OUTPUT FROM bdO08bar6 06 KAERRA Xx Y OUTPUT SUMMARY RESPONSE SUBCASE CURVE FRAME XMIN FRAME XMAX FRAME YMIN FRAME X FOR YMAX FRAME ID TYPE NO CURVE ID ALL DATA ALL DATA ALL DATA YMIN ALL DATA 1 DISP i 11 5 0 000000E 00 5 999959F 01 0 000000E 00 0 000000E 00 7 886210E 03 2 0 000000E 00 5 999959F 01 0 000000E 00 0 000000E 00 7 886210F 03 2 1 ACCE 2 10 5 0 000000E 00 5 999959F 01 8 511892E 01 2 650001E 01 9 618800E 01 5 0 000000E 00 5 999959F 01 8 511892E 01 2 650001E 01 9 618800E 01 5 Figure 8 11 Partial Output from Transient Analysis with Unit Step Function Input kKkKKKK kKkKeKKK PARTIAL OUTPUT FROM bd08bar7 f06 NX Nastran Basic Dynamic Analysis User s Guide 8 15 Chapter 8 8 16 NM N N N N SUBCASE POINT ID TIME 5 000000E 03 1 000000E 02 4050002E 01 700002E 01 750002 E 01 800002E 01 850002E 01 900002E 01 950002E 01 PRP REE ER 5 949959E 01 599 OO OE SUBCASE CURVE ID TYPE 1 DISP POINT ID FREQUENCY 0 000000E 01 073000E 00 087000E 00 100632E 00 224000E 00 347000E 00 950000E 01 000000E 02 CURVE ID TYPE 1 DISP 1 DISP OMAAMNAMA QQ FRAME NO 1 KkKKK K TYPE G G Q QAQA QAN QAQA Q FRAME NO 1 1
120. 6 UFM 4391 UFM 4392 Diagnostic Messages for Dynamic Analysis SYSTEM FATAL MESSAGE 4276 ERROR CODE This message occurs when NX Nastran encounters errors that are not otherwise trapped including system errors There are various error codes EC each of which has a different meaning In nearly every case the log file contains further information about the problem so you should look there for further clues In addition because these are errors that most likely should be caught 1n another manner and with a more explicit error message you should look at the recent Error Reports search for 42 76 In many cases increasing memory BUFFSIZE or disk space resolves the problem especially when attempting to run large models on workstations This error often indicates machine underflow or overflow although 1t 1s impossible to list specific reasons for this error code Observed problems include e Modeling problems This condition is usually accompanied by an arithmetic fault floating overflow type message in the log file on some machines Perform a static analysis and verify that the value for the maximum factor diagonal ratio is acceptable e When SFM 4276 is followed by an access violation then it is often due to a lack of memory or disk space or due to a coding error in NX Nastran USER WARNING MESSAGE 4312 CONM2 HAS NONPOSITIVE DEFINITE INERTIA MATRIX Most dynamic analysis methods req
121. 6 Using the continuation entry is the only way to specify the three new options ALPH NUMS and Fi The number of segments that a frequency range will be broken into for parallel processing You must define a value greater than 1 to take advantage of parallel NUMS processing You may also specify NUMS using the NUMSEG keyword on the NASTRAN statement If you specify both then NUMS takes precedence Fi Directly specifies the upper frequencies of each segment such that V1 lt F1 lt F2 lt F15 lt V2 ALPH Automatically generates the Fi values based on the following formula Fi V2 VI 1 0 ALPH 10 ALPH MS If you specify both ALPH and Fi then Fi takes precedence over ALPH as long as they are consistent If ALPH is multiplied by 100 it may be specified on the FRQSEQ keyword of the NASTRAN statement For a detailed description of the EIGRL input see the NX Nastran Numerical Methods User s Guide User Interface for the Other Methods The data entered on the EIGR entry selects the eigenvalue method and the frequency range or number of required roots The basic format of the Bulk Data entry is as follows Ls s S S S T3 The METHOD field selects the eigenvalue method from the following list AHOU Automatic Householder method HOU Householder method MHOU Modified Householder method SINV Sturm modified inverse power method The F1 field specifies the lowest frequency of interest in the eigenvalue ext
122. 6 4744715 1 Q000000E 00 6 4744715 1 000000E 00 4 97494 LE 1 000000E 00 4 97494 F 1 000000E 00 168707925 1 000000E 00 Leo lO POZE 1 R2 R3 0 0 0 0 6 847622E 02 5 927882E 02 1 268971E 01 1 098529E 01 1 753660E 01 1 518116E 01 2 L4 1397E 01 1 853772E 01 3 25 Chapter 3 Real Eigenvalue Analysis 6 G 14097125919 1 845877E 01 7 G 2 170278E 19 2 507827E 01 8 G 2 389961E 19 3 214496E 01 9 G 20590381 3E T9 3 948168E 01 10 G 2 648916E 19 4 695067E 01 11 G 2 681884E 19 5 446261E 01 EIGENVALUE 1 685851E 02 CYCLES 2 066473E 00 REAL E I POINT ID TYPE T1 T2 1 G 0 0 0 0 2 G 1 219015E 33 1 052334E 02 3 G 2 407892E 33 4 008016E 02 4 G 3 537263E 33 8 566635E 02 5 G 4 579275E 33 1 443302E 01 6 G 5 508284E 33 2 132276E 01 7 G 6 301480E 33 2 896932E 01 8 G 6 939436E 33 3 713246E 01 9 G 7 406566E 33 4 560753E 01 10 G 7 691474E 33 5 423541E 01 LT G 7 787220E 33 6 291289E 01 EIGENVALUE 6 474471E 03 CYCLES 1 280626E 01 REAL E I POINT ID TYPE T1 T2 1 G Ds 0 0 G 1 606174E 26 6 893317E 02 3 G 3 172614E 26 2 244652E 01 4 G 4 660607E 26 3 933468E 01 5 G 6 033448E 26 5 129929E 01 6 G 7 257351E 26 5 389377E 01 7 G 8 302282E 26 4 501138E 01 8 G 9 142668E 26 2 499085E 01 9 G 9 757999E 26 3 798927B 02 10 G 1 013329E 25 3 789206E U1 LX G 1 025940E 25 T 400293E 01 EIGENVALUE 6 474471E 03 CYCLES 1 280026E 01 REAL E I POINT ID TYPE T1 T2 1 G 0 0 0 0 2 G 6 181717E 19 3 123822E 02 3 G 1 221121E 18 1 017205
123. 629657E 02 CYCLES 2 031740E 00 REAL EIGENVECTOR N O 1 POINT ID TYPE T1 T2 T3 R1 R2 R3 I G 0 0 0 0 0 0 0 0 0 0 0 0 2 G 0 0 1 391872E 02 2 259793E 10 0 0 1 470464E 09 9 057010E 02 3 G 0 0 5 301210E 02 8 606855E 10 0 0 2 725000E 09 1 678406E 01 4 G 0 0 1 133067E 01 1 839608E 09 0 0 3 76582 6E 09 2 319480E 01 5 G 0 0 1 908986E 01 3 099362E 09 0 0 4 598456E 09 2 832321E 01 6 G 0 0 2 820258E 01 4 578870E 09 0 0 54232973E 09 3 223138E 01 7 G 0 0 3 831632E 01 6 220901E 09 0 0 5 685052E 09 3 501587E 01 8 G 0 0 4 911331E 01 7 973862E 09 0 0 5 976744E 09 3 681249E 01 9 G 0 0 6 032288E 01 9 793808E 09 gu 6 137029E 09 3 779972E 01 3 24 EIGENVALUE ANALYSIS NUMBER OF EIGENVALUES EXTRACTED NUMBER OF TRIANGULAR DECOMPOSITIONS TOTAL NUMBER OF VECTOR ITERATIONS REASON FOR TERMINATION NX Nastran Basic Dynamic Analysis User s Guide SUMMARY STURM INVERSE POWER 6 9 59 ALL EIGENVALUES FOUND IN RANGE 10 11 EIGENVALUE CYCLES POINT ID 1 F3 Co 00 10Y014 W h2 pa EIGENVALUE CYCLES POINT ID 1 F3 Co 00 10Y014 WN pnmo EIGENVALUE CYCLES POINT ID 1 F3 CO o 00 10Y014 W h2 pa G G 0 0 O O 1 742047E 02 2 100632E 00 TYPE OQMAAMNANMNAMNAMMA 0 l zr 3 E w J or O us 6 s T1 0 363453E 33 693333E 33 930893E 33 123021E 33 163003E 33 051232E 33 765834E 33 289217E 33 608492E 33 7195798E 33 6 258656E 03 1 259101E 01 TYPE QAMNAAMNAANAAAA
124. 9221EF04 The deformed shape resulting from the first mode is illustrated in Figure 3 17 and is overlaid on the undeformed shape Figure3 18 illustrates the stress contours plotted on the deformed shape of the second mode The element strain energy contour plot for the third mode is shown in Figure 3 19 NX Nastran Basic Dynamic Analysis User s Guide 3 29 Chapter 3 Real Eigenvalue Analysis oe Figure 3 17 Deformed Shape of the First Mode Vara Y Figure 3 19 Element Strain Energy Contours for the Third Mode 3 30 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis Car Frame Model Figure 3 20 shows a model of an aluminum car frame The frame model is comprised of plate elements CQUAD4 and CTRIA3 with springs CELAS2 representing the suspension Spring stiffnesses are input in the three translational directions a stiffness of 500 lb in is used in the vertical direction T2 and stiffnesses of 1000 lb in are used in the other translational directions T1 and T3 When using CELASi elements to connect two grid points it is recommended that the coordinates of the two grid points be identical in order to represent coaxial springs noncoincident coordinates can lead to errors The goal of the analysis is to compute resonant frequencies up to 50 Hz using the Lanczos method Element strain energies are computed for the springs in order to help characterize the resulting modes Figure 3 21 shows
125. 983 Blakely Ken Dynamic Analysis Application and Modeling Considerations J of Engineering Computing and Applications Fall 1987 Bramante A Paolozzi A Peroni I Effective Mass Sensitivity A DMAP Procedure MSC 1995 World Users Conf Proc Paper No 39 May 1995 Brutti C Conte M Linari M Reduction of Dynamic Environment to Equivalent Static Loads by a NASTRAN DMAP Procedure MSC 1995 European Users Conf Proc Italian Session September 1995 Butler Thomas G Dynamic Structural Responses to Rigid Base Acceleration Proc of the Conf on Finite Element Methods and Technology Paper No 8 March 1981 Butler Thomas G Telescoping Robot Arms MSC NASTRAN Users Conf Proc Paper No 10 March 1984 Butler T G Experience with Free Bodies Thirteenth NASTRAN Users Colloq pp 378 388 May 1985 NASA CP 2373 Butler Thomas G Mass Modeling for Bars Fifteenth NASTRAN Users Colloq pp 136 165 August 1987 NASA CP 2481 Butler T G Coupled Mass for Prismatical Bars Sixteenth NASTRAN Users Colloq pp 44 63 April 1988 NASA CP 2505 Caldwell Steve P Wang B P An Improved Approximate Method for Computing Eigenvector Derivatives in MSC NASTRAN The MSC 1992 World Users Conf Proc Vol I Paper No 22 May 1992 Case William R Dynamic Substructure Analysis of the International Ultraviolet Explorer IUE Spacecraft NASTRAN Users Exper pp 221 248 September 1975
126. 988 Burroughs John W An Enhancement of NASTRAN for the Seismic Analysis of Structures Ninth NASTRAN Users Colloq pp 79 96 October 1980 NASA CP 2151 Chen J T Chyuan S W Yeh C S Hong H K Comparisons of Analytical Solution and MSC NASTRAN Results on Multiple Support Motion of Long Bridge During Earthquake The 4th MSC Taiwan Users Conf Paper No 20 November 1992 Chen J T Hong H K Yen C S Chyuan S W Integral Representations and Regularizations for a Divergent Series Solution of a Beam Subjected to Support Motions Earthquake Engineering and Structural Dynamics Vol 25 pp 909 925 1996 I 30 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Chen Yohchia Nonlinear Seismic Analysis of Bridges Practical Approach and Comparative Study The MSC 1993 World Users Conf Proc Paper No 57 May 1993 Chen Yohchia Refined Analysis for Soil Pipe Systems MSC 1994 World Users Conf Proc Paper No 38 June 1994 Dahlgren F Citrolo J Knutson D Kalish M Dynamic Analysis of the BPX Machine Structure Proc of the 14th IEEE NPSS Symp on Fusion Engineering Vol 1 pp 47 49 1992 Fallet P Derivery J C MSC NASTRAN Earthquake Analysis NASTRAN User s Conf May 1979 Hill Ronald G Nonlinear Seismic Analysis of a Reactor Structure with Impact Between Core Components NASTRAN Users Exper pp 397 418 September 1975 NASA TM X 3278 Hi
127. A COCODODOOOCOCCOO CO C CO C5 C5oCoCcoCco Co Coco T 6 690287E 03 1 301795ET01 TYPE QAOAAAMNAMNAMMA Figure 3 11 Printed Results from the First Model MMNNFRER m pP C9 TL 0 698388E 22 305710E 22 073314E 21 389628E 21 671725E 21 912658E 21 106496E 21 248464E 21 335068E 21 364175E 21 7 173455E8 01 8 321185E 01 REAL E I rFROAIA AWE ONO T2 0 249974E 10 574880E 10 834005E 09 4092054E 09 571193E 09 214489E 09 970303E 09 794348E 09 165196E 08 3o2052E5 08 REAL E I T2 0 0 568120E 02 464387E 01 318525E 01 m T 941767E 01 743728E 01 170797E 02 159041E 01 124724E 01 7 2 4 4 2 4 4 8 632111E 01 916957E 01 REAL E I T2 0 0 207686E 08 2029794E 08 866785E 07 mas A09781E 07 8 6 5912 79E 07 6 1 1 2 1 7 ex 615435E 07 602044E 07 796384E 07 217935E 07 520816E 06 pnmo 1 1 l a 7 8 BMA OUI O14 DN 1c 4 8 164657E 08 350998E 08 N V E C T T3 0 391872E 02 x 133067E 01 908986E 01 820258E 01 3 4 EE 6 173455E 01 321185E 01 301210E 02 831632E 01 911331E 01 032288E 01 NOME GO T3 lt 0 88200 998 06 200556E 07 608564E 07 314543E 07 684467E 07 417950E 07 56328 7E 07 417504E 08 A01546E 07 055190E 06 N VECT T3 0 568131E 02 464390E 01 318528E 01 632114E 01 916957E 01 941765E 01 743725E 01
128. AEdIqAAI da A 1 Nomenclature for Dynamic Analysis ccce tmn B 1 too l ESERE ere eee eee ae ee AN E ee a ena ae E eee ee eee eee ae ee eee B 1 Structural Properties ee rss B 2 Multiple Degree of Freedom System 0 0 0 ee eee B 3 The Set Notation System Used in Dynamic Analysis enr C 1 Displacement Vector Sets 0 0 eee ees C 1 Common Commands for Dynamic Analysis cere ntn D 1 Solution Sequences for Dynamic Analysis cens D 1 Case Control Commands for Dynamic Analysis llle D 1 Bulk Data Entries for Dynamic Analysis eee D 2 Parameters for Dynamic Analysis ce eel D 4 File Management Section 6 4 644 5 4 4 6054045 640044 6 64 ROS COE REOR ea e ee ea E 1 dol AMTTCPC E 1 lb gs rrr E 1 NA Nasiran DalaDane as acp ak E hr eee EL Soe FEES EERE HESS ORE TR PER EOS E 2 Fue Management Commands 66 lt 4406460ecc 00 eee eee enced TRO X ROCA RO OX X RERO ER E 2 Numerical Accuracy Considerations cce eee t mt F 1 LII Suus eee REA E E eee E MA EOS AR A eee KOREA RUE eee REO XC RA F 1 Linear Equation Solution usada ded d dor hE ARR EROR EO REA E RR REGE RERREARexREZEZa F 1 Eigenvalue Analysis eee Res F 2 be ee 2253944 9 45 5 2 X 14 4S 3 PR dE I C gra w dad o9 d qd d 39g ad XR 3 F 3 Definiteness of Matrices 20 nue Reel F 3 Numerical Accuracy Issues 2 ces F 4 So
129. AG 6 YBTITLE LOAD PHASE 6 XYPLOT OLOAD 6 T2RM T2IP YTMAX 8 0 YTMIN 0 0 YTTITLE LOAD MAG 11 YBTITLE LOAD PHASE 11 XYPLOT OLOAD 11 T2RM T2IP S BEGIN BULK Bulk Data 5 ENDDATA Plotted Output Figure 9 11 X Y Plot Commands for the Bar Transient Response Analysis NX Nastran Basic Dynamic Analysis User s Guide 9 13 Chapter 9 Plotted Output Displ E Displ 11 0 0 lime sec Figure 9 12 X Y Plots for the Bar Transient Response Analysis 9 14 NX Nastran Basic Dynamic Analysis User s Guide Plotted Output 4 0 Accel 6 ANN nats 6 0 Acoel 11 Time sec 20 Figure 9 13 X Y Plots for the Bar Transient Response Analysis NX Nastran Basic Dynamic Analysis User s Guide 9 15 Chapter 9 Plotted Output Bend Moment Al El 6 2 0 lime sec Figure 9 14 X Y Plots for the Bar Transient Response Analysis 9 16 NX Nastran Basic Dynamic Analysis User s Guide Plotted Output Sdisp 1 0 10 Sdisp 2 Time sec Figure 9 15 X Y Plots for the Bar Transient Response Analysis NX Nastran Basic Dynamic Analysis User s Guide 9 17 Chapter 9 Plotted Output Load 6 Load 11 2 0 Time sec Figure 9 16 X Y Plots for the Bar Transient Response Analysis 9 18 NX Nastran Basic Dynamic Analysis User s Guide Chapter 10 Guidelines for Effective Dynamic Analysis e Overview e Overall Analysis Strategy e Un
130. AOA NX Nastran Basic Dynamic Analysis User s Guide RADIANS 111741E 04 903 5005 05 426423E 05 822883E 05 125174E 04 313996E 04 627861E 03 068686E 03 C9 NO ho r0 I5 IS oy EIGENVALUES CYCLES 544039E 05 576196E 05 181952E 05 267405E 06 790770E 05 091289E 05 590821E 02 292416E 02 Figure 4 9 Unconstrained Bracket Frequencies GENERALIZED pbBbmpBmbpmpmpmpmpb MASS 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 000000E 00 GENERALIZED STIFFNESS es eg ci es Es 690642E 07 807991E 09 515176E 09 390596E 09 266017E 08 1 726585E 08 Zs 4 2794603E 06 649932E 06 Chapter 5 Frequency Response Analysis e Overview e Direct Frequency Response Analysis e Modal Frequency Response Analysis e Modal Versus Direct Frequency Response e Frequency Dependent Excitation Definition e Solution Frequencies e Frequency Response Considerations e Solution Control for Frequency Response Analysis e Examples NX Nastran Basic Dynamic Analysis User s Guide 5 1 Chapter 5 Frequency Response Analysis 5 1 Overview Frequency response analysis is a method used to compute structural response to steady state oscillatory excitation Examples of oscillatory excitation include rotating machinery unbalanced tires and helicopter blades In frequency response analysis the excitation is explicitly defined in the frequency domain All of the
131. AREA entries To accommodate more complicated loadings conveniently the LSEQ entry is used to define static load entries that define the spatial distribution of dynamic loads o3 2 83 4 5 ee s w The LSEQ Bulk Data entry contains a reference to a DAREA Set ID and a static Load Set ID The static loads are combined with any DAREA entry in the referenced set The DAREA Set ID does not need to be defined with a DAREA Bulk Data entry The DAREA Set ID is referenced by a TLOADi entry This reference defines the temporal distribution of the dynamic loading The Load Set ID may refer to one or more static load entries FORCE PLOADi GRAV etc All static loads with the Set ID referenced on the LSEQ entry define the spatial distribution of the dynamic loading NX Nastran converts this information to equivalent dynamic loading 6 20 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis Figure 6 5 demonstrates the relationships of these entries To activate a load set defined in this manner the DLOAD Case Control command refers to the Set ID of the selected DLOAD or TLOADoi entry and the LOADSET Case Control command refers to the Set ID of the selected LSEQ entries The LSEQ entries point to the static loading entries that are used to define dynamic loadings with DAREA Set ID references Together this relationship defines a complete dynamic loading To apply dynamic loadings in this manner the DLOAD and LOADSET Cas
132. ATE TABLE ID All tables must have unique numbers Check for uniqueness USER FATAL MESSAGE 2101A GRID POINT COMPONENT ILLEGALLY DEFINED IN SETS The above grid point and component are defined in each of the above independent subsets A point may belong to a maximum of one independent subset This error occurs when a DOF is defined as belonging to two mutually exclusive sets see NX Nastran User s Guide A common example of this occurs when a DOF is defined as dependent on an MPC M set as well as being constrained s set on an SPC entry The message for this states that the component is illegally defined in the um user defined m set and us user defined s set sets These two sets are mutually exclusive because all MPC equations are processed before the SPCs are applied and the m set DOFs are removed from the matrix When the program attempts to apply the SPC the DOF is no longer available and the fatal message 1s issued The normal correction for this 1s to modify the MPC so that the DOF in question is independent n set Then there 1s no conflict USER FATAL MESSAGE 2107 EIGR CARD FROM SET REFERENCES DEPENDENT COORDINATE OR GRID POINT When the point option is used on an EIGR entry the referenced point and component must be in the analysis set a set for use in normalization USER FATAL MESSAGE 2109 NO GRID SCALAR OR EXTRA POINTS DEFINED Dynamics problems must have at least one g
133. AXIS LINEAR LINEAR LOG LINEAR OA yi AELE yj In xjZxiy In xj xiy wo E EE LINEAR NX Nastran Basic Dynamic Analysis User s Guide 5 15 Chapter 5 Frequency Response Analysis BOD anys In x xi vi In xj xi nGiZxiy Field Contents TID Table identification number X1 Table parameter Xl yl Tabular values Values of x are frequency in cycles per unit time The TABLED2 entry uses the algorithm yY yy x XI Equation 5 24 ENDT ends the table input The TABLEDS entry has the following format Field Contents TID Table identification number X1 X2 Table parameters X2z 0 0 Xl yl Tabular values Values of x are frequency in cycles per unit time The TABLEDS entry uses the algorithm EE eun y YT gt Equation 5 25 ENDT ends the table input The TABLED4 entry has the following format o3 2 83 4 55 e 7 es e w 5 16 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis Field Contents TID Table identification number Xi Table parameters X2 40 0 X3 lt X4 Ai Coefficients The TABLED4 entry uses the algorithm i IN E Aj ED Equation 5 26 N is the degree of the power series When x X3 X3 is used for x when x gt X4 X4 is used for x This condition has the effect of placing bounds on the table there 1s no extrapolation outside of the table boundaries ENDT ends the table input DAREA Example Suppose the following co
134. Apoc R3 R3 593777E 15 723840E 15 575675E 15 220145E 14 439249E 14 596912E 14 698929E 14 745155E 14 770949E 14 758923E 14 R3 doo 775385E 01 775385 E 01 io395E 01 775385E 01 775385E 01 775385 E 01 775385E 01 775385 E 01 775385 E 01 775385 E 01 Rigid Body Modes It can be seen from this example that aside from clean rigid body vectors there is no advantage to using a SUPORT entry to compute rigid body modes Statically determinate SUPORT USER INFORMATION MESSAGE 3035 FOR DATA BLOCK KLR SUPPORT PT NO EPSILON STRAIN ENERGY EPSILONS LARGER THAN 0 001 ARE FLAGGED WITH ASTER 1 747496606E 17 5 53879354E 09 2 7 7496606E 17 0 0000000E 00 3 7 171496606E 17 7 1622708E 11 Overdetermined SUPORT xxx USER INFORMATION MESSAGE 3035 FOR DATA BLOCK KLR SUPPORT PT NO EPSILON STRAIN ENERGY EPSILONS LARGER THAN 0 001 ARE FLAGGED WITH ASTER 1 1 9913979E 01 7 2869660E 06 kk KK 2 1 9913979E 01 0 0000000E 00 kk KK 3 1 9913979E 01 7 1850081E 11 KKK 4 1 9913979E 01 7 2869660E 06 kk KK Underdetermined SUPORT USER INFORMATION MESSAGE 4158 STATISTICS FOR SYMMETRIC DECOMPOSITION OF DATA BLOCK KLL FOLLOW MAXIMUM RATIO OF MATRIX DIAGONAL TO FACTOR DIAGONAL 9 1EF 13 AT ROW NUMBER 31 xxx USER WARNING MESSAGE 4698 STATISTICS FOR DECOMPOSITION OF MATRIX KLL THE FOLLOWING DEGREES OF FREEDOM HAVE FACTOR DIAGONAL RATIOS GREATER THAN 1 00000E 05 OR HAVE NEGATIVE TERMS ON THE FACTOR DIAGONAL GRID P
135. BSF element is now available This element acts as a thin layer of acoustic absorbing material along the fluid structure interface Version 69 introduced several features which are parallel to those available for structural analysis such as direct damping modal damping and the ability to control the modes in a response analysis through the use of parameter You can define panels to provide integrated response data Effects of gravity large motions and static pressures are ignored Complex eigenvalues frequency response and transient response are the available solution sequences Design sensitivity and optimization processes may reference the acoustic outputs as responses with appropriate design constraints Applications for the coupled fluid structure option are automotive and truck interiors aircraft cabins and acoustic devices such as loudspeakers and microphones Uncoupled Acoustics Several methods are available in NX Nastran for the analysis of normal modes of compressible fluids bounded by rigid containers and or free surfaces One method is the acoustic cavity capability which uses two dimensional slot elements and axisymmetric ring elements to define the fluid region This method was specifically developed for the acoustic analysis of solid rocket motor cavities A better method is to use the three dimensional fluid elements for the coupled acoustics described above and provide the appropriate boundary conditions 11 8 Non
136. CQUAD4 CQUADS CROD CTETRA CTRIA3 CTRIA6 CTRIAX6 CTUBE A negative value the default causes the generation of lumped mass matrices translational components only for all of the above elements Default 1 0 The load vectors are generated from the equation Pj CP1 iP e CP2 P where P2 is selected via the Case Control command P2G and P comes from Bulk Data static load entries Default 1 PARAM CURVPLOT 1 requests that X Y or curve plots be made for displacements loads SPC forces or grid point stresses or strains The y values are response values the x values are related to grid point locations through the parameter DOPT PARAM CURVPLOT 1 suppresses SORT2 type processing in superelement dynamic analysis SORT 1 requests will be honored To obtain stress or strain plots set the CURV parameter to 1 DOPT controls the x spacing of curves over grid points for the CURVPLOT module The default for DOPT is the length between grid points Default 0 By default the matrix method of data recovery is used in the modal solutions DDRMM 1 will force calculation of complete g set solution vectors by the mode displacement method which is needed for SORT1 output SORT1 output is required for deformed structure plots grid point force balance output the mode acceleration technique and postprocessing with PARAM POST 1 or 2 Default NEW Structured SOLs only PARAM DYNSPCFE NEW requests that mass and damping cou
137. Combination DLOAD One of the requirements of transient loads is that all TLOAD1s and TLOAD2s must have unique SIDs If they are to be applied in the same analysis they must be combined using the DLOAD Bulk Data entry The total applied load 1s constructed from a combination of component load sets as follows PT SY S IP Equation 6 31 where S overall scale factor S scale factor for i th load set P i th set of loads P total applied load The DLOAD Bulk Data entry has the following format 1 2 3 4 5 6 7 8 j 9 10 DLOAD SID SS 2 fpet Field Contents SID Load set ID S Overall scale factor Si Individual scale factors Li Load set ID number for TLOAD1 and TLOAD2 entries As an example in the following DLOAD entry DLOAD SID Abbe a dynamic Load Set ID of 33 is created by taking 0 5 times the loads in Load Set ID of 14 adding to it 2 0 times the loads in Load Set ID of 27 and multiplying that sum by an overall scale factor of 3 25 As with other transient loads a dynamic load combination defined by the DLOAD Bulk Data entry is selected by the DLOAD Case Control command 6 22 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis 6 6 Integration Time Step The TSTEP Bulk Data entry is used to select the integration time step for direct and modal transient response analysis This entry also controls the duration of the solution and which
138. D1 TABD1 0 0 0 02 1000 0 0 02 ENDT LOAD DEFINITION SRLOAD1 SID DAREA DELAY DPHASE TC TD RLOAD1 2 999 22 SLSEQ SID DAREA LID TID LSEQ 3 999 ii STABLED1 TID TABL1 S TABL1 X1 Yl X2 Y2 ETC TABLED1 22 TABL1 TABL1 0 0 1 0 1000 0 1 0 ENDT PRESURE LOAD OF 3 PSI PER ELEMENT SPLOADA SID EID P1 NX Nastran Basic Dynamic Analysis User s Guide 5 37 Chapter 5 Frequency Response Analysis PLOAD4 1 171 a PLOAD4 1 172 Em PLOAD4 1 160 ET etc basic model ENDDATA Figure 5 22 Abridged Input File for the Bracket Model Table 5 10 Relationship Between Case Control Commands and Bulk Data Entries for the Bracket Model Case Control METHOD DAMPING po PLOAD4 LSEQ DAREA ID gt DAREA ID RLOALD1 x TABLEDI Figure 5 23 shows a logarithmic plot of the z displacement magnitude of grid point 999 which 1s the concentrated mass at the center of the cutout 10 1 000 amp 0 100 0 010 Ba 0 001 0 0001 0 Frequency Hz 100 Figure 5 23 Displacement Magnitude Log 5 38 NX Nastran Basic Dynamic Analysis User s Guide Chapter 6 Transient Response Analysis e Overview e Direct Transient Response Analysis e Modal Transient Response Analysis e Modal Versus Direct Transient Response e Transient Excitation Definition e Integration Time Step e Transient Excitation Considerations e Solution Control for Transient Response Analysis
139. DATA TABD1 TABD1 TABLI TABLI 6 TABL2 Figure 6 19 Input File Abridged for the Bracket Model Table 6 10 Relationship Between Case Control Commands and Bulk Data Entries for the Bracket Model Case Control METHOD FREQUENCY SDAMPING LOADSET DLOAD Bulk Data EIGRL FREQ1 TABDMPI aid LSEQ Le DAREA ID gt DAREA ID RLOADT TABLED1 Figure 6 20 shows a plot of the z displacement of grid point 999 which is the concentrated mass at the center of the cutout 6 38 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis ove HMA UN Ww W wey Displacement eri 0 08 0 lime sec 4 Figure 6 20 Displacement Time History for Grid Point 999 NX Nastran Basic Dynamic Analysis User s Guide 6 39 Chapter 7 Enforced Motion e Overview e The Large Mass Method in Direct Transient and Direct Frequency Response e The Large Mass Method in Modal Transient and Modal Frequency Response e User Interface for the Large Mass Method e Examples NX Nastran Basic Dynamic Analysis User s Guide 7 1 Chapter 7 Enforced Motion 7 1 Overview Enforced motion specifies the displacement velocity and or acceleration at a set of grid points for frequency and transient response Enforced motion is used when base motion is specified instead of or in conjunction with applied loads A common application is an earthquake excitation applied to a building In this cas
140. E 0 0 field 7 of the RLOAD2 entry is blank q phase lead of 45 degrees for grid point 6 entered on the DPHASE entry t 0 0 field 4 of the RLOAD2 entry is blank Logarithmic plots of the output are shown in the following figures Figure 5 18 shows the magnitude of the displacements for grid points 6 and 11 Figure 5 19 shows the magnitude of the modal displacements for modes 1 and 2 Figure 5 20 shows the magnitude of the bending moment at end A in plane 1 for element 6 Logarithmic plots are especially useful for displaying frequency response results since there can be several orders of magnitude between the maximum and minimum response values 5 34 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis m c Displacement 6 m i oq placement 11 m Dis 0 Frequency Hz 20 Figure 5 18 Displacement Magnitude Log NX Nastran Basic Dynamic Analysis User s Guide 5 35 Chapter 5 Frequency Response Analysis SDispla cement 1 m E m m Fd SDisplacement 7 0 Frequency Hz 20 Figure 5 19 Modal Displacement Magnitude Log 1000 Moment Al N m 0 Frequency Hz 20 Figure 5 20 Bending Moment Magnitude at End A Plane 1 Log Bracket Model Consider the bracket model shown in Figure 5 21 An oscillating pressure load of 3 psi is applied to the elements on the top face in the z direction The model is constrained at
141. E 01 4 G 1 794002E 18 1 782531E 01 5 G 2 322707E 18 2 324743E 01 6 G 2 vss OBS 2 442331E 01 7 G 196 9Z6E 15 2 039817E 01 8 G 3 520915E 18 1 132542E 01 9 G 3 758207E 18 1 721460E 02 10 G 3 902959E 18 1 716725E 01 11 G 3 951610E 18 3 353654E 01 Figure 3 12 Printed Results from the Second Model zi OY O1 43 WN PN Q FA OBS CO CO NO IS S 1 CO XO COD PN PN PKNPDPOC 132276E 01 896933E 01 713246E 01 560753E 01 423540E 01 291288E 01 N VECTOR T3 0 109882E 03 469673E 02 415994E 02 249442E 01 845875E 01 5007825E 01 214495E 01 948168E 01 695069E 01 446264E 01 N V E cT OE T3 0 123881E 02 017221E 01 782550E 01 324757E 01 442332E 01 039804E 01 132523E 01 721591E 02 716723E 01 353632E 01 N VECTOR T3 x 40932 79E 02 244643E 01 933455E 01 129921E 01 389376E 01 501146E 01 499097E 01 798841E 02 188207E 01 400307E 01 C OC C0 c0 C0 C2 C5 C9 OOO C5 C CO CO CO CO OC C5CoCoCco Co Cc OOOO OC CJ C C2 CO OO OOOO C CO OOO OO CO C OC C5oCoCcoCco Cc Cc CO CO CO C5C5oCoCoCco Co Cc C OC 0 c0 C0 N O R1 N O R1 N O R1 Z s T 2 x a2 a a a ed 2 I ot tol O1 014 CO 2 S ES SD SO ES CD Id o d gd tol PrRrRPoOPSRFRPNOOABO 436876E 01 647398E 01 783232E 01 857873E 01 888212E 01 894634E 01 2 R2 0 eO Pb 518114E 01 alz moor x 2 ea 227866E 02 0985206E 01 853771E 01 109563E
142. E IS GREATER THAN 600 More than 600 roots are in the desired frequency range which is greater than the maximum allowed using SINV Decrease the size of the frequency range USER INFORMATION MESSAGE 5239 BISECTIONING IN THE ere kk INTERVAL The frequency subregion encompassing eigenvalues xx yy is cut in half in order to find the remaining roots USER INFORMATION MESSAGE 5240 THE BISECTION VALUE IS NEG The selected value is midway between the lowest and highest frequencies in the frequency subregion USER INFORMATION MESSAGE 5241 MISSING ROOT S IN THE er kk INTERVAL The Sturm sequence check has indicated that roots are missing in the frequency range and they cannot be found by further bisectioning If the run terminates with missing roots decrease the frequency range H 10 NX Nastran Basic Dynamic Analysis User s Guide UIM 5242 UIM 5274 UFM 5288 SFM 5299 UFM 5400 Diagnostic Messages for Dynamic Analysis USER INFORMATION MESSAGE 5242 THE ROOT FOUND IS NOT THE LOWEST ONE ABOVE FMIN The Sturm sequence check indicates that at least one unfounded root exists between FMIN and the lowest frequency root found Set FMAX close to the lowest frequency found so that the lower roots can be found USER INFORMATION MESSAGE 5274 THE ACTUAL TIME OF TRIDIAGONALIZATION IS THE ACTUAL TIME OF EIGENVALUE ITERATION IS THE ACTUAL TIME OF EIGENVECTOR GENERATION IS The
143. EL 6 MAG YBTITLE BEND MOMENT A1 EL 6 PHASE XYPLOT ELFORCE 6 2 10 S YTLOG NO YBMAX 90 0 YBMIN 0 0 CURVELINESYMBOL 2 YTMAX 4 0 YTMIN 0 0 YTTITLE LOAD MAG 6 YBTITLE LOAD PHASE 6 XYPLOT OLOAD 6 T2RM T2IP Ow YTMAX 8 0 YTMIN 0 0 YTTITLE LOAD MAG 11 YBTITLE LOAD PHASE 11 XY PLOT OLORAD 711 TZ RM 0212 S BEGIN BULK S Bulk Data S ENDDATA Plotted Output Figure 9 9 X Y Plot Commands for the Bar Frequency Response Analysis NX Nastran Basic Dynamic Analysis User s Guide 9 9 Chapter 9 Plotted Output Displ Mag 6 1 QE 5 Displ Phase 6 Displ Mag 11 2 Ss L Disp Phase 11 i Frequency Hz 20 9 10 NX Nastran Basic Dynamic Analysis User s Guide Bend Moment Al El Mag Rend Moment Al Fl 6 Phase Plotted Output Sdisp Mag Model a l F C C disp Phase Medel LOE 2 sdisp Mag Mode 2 Fu 1 0E 4 360 Sdisp Phase Mode 2 160 L OES Frequency Hz 20 NX Nastran Basic Dynamic Analysis User s Guide 9 11 Chapter 9 Plotted Output feel bh n fa 6 100 5 5 f g __ fa 6 0 8 0 as EE E g E 3 d isl 20 Frequency Hz Figure 9 10 X Y Plots for the Bar Frequency Response Analysis Figure 9 11 shows X Y plot commands for a modal transient response analysis of the cantilever beam model Plots are made for the appli
144. ESPONSE YMIN FRAME ALL DATA 4 039956E 03 4 039956E 03 MAGNITUDE PHASE T3 4 085192E 04 0 4 323836E 04 359 4344 8 402211E 03 303 53720 9 514135E 03 288 0963 9 936970E 03 270 0652 3 091950E 03 199 3742 1 564160E 03 190 2192 5 272466E 07 180 4391 5 216914E 07 180 4361 ARY RE XMAX FRAME ALL DATA 000000E 02 000000E 02 000000E 02 000000E 02 S Ohe UUI R1 oO O O O O O O O O O 0 0 PONSE YMIN FRAME ALL DATA 216914E 07 216914E 07 804361E 02 000000E 00 4 4 R2 0 2 5 zs l 2 A 2 mm 2 A 984776E 05 102005E 04 833254E 03 908739E 03 000815E 03 072399E 703 097317E 03 081293E 03 048310E 03 2039099503 e X FOR YMIN 199981E 01 E9998 TE 01 Figure 8 12 Partial Output from Transient Analysis with a Triangular Pulse VECTOR R2 2 024146E 04 180 0000 2 134119E 04 179 4676 3 874130E 03 12337533 4 382166E 03 108 2796 4 572148E 03 90 2504 1 408677E 03 19 5776 7 050781E 04 10 5024 8 710860E 07 6610 8 615909E 07 6566 X FOR YMIN 000000E 02 000000E 02 000000E 02 000000E 00 Figure 8 13 Partial Output from Frequency Response Analysis E RO Bou T PROJECT ID VER S I ON BLANK kkxk xx xx PARTIAL OUTPUT FROM bd08bar9 f06 DEREC TIT O R E EI MT ASSIGNED INT VALUE NX Nastran Basic Dynamic Analysis User s Guide KkKKKK VERSION ID CREATION TIME 249621E 03 W
145. FERS TO A NONEXISTENT STATIC LOAD MATRIX COLUMN NCOLS The most likely cause occurs when changing an LSEQ entry on a restart without regenerating and assembling the static load matrix NX Nastran Basic Dynamic Analysis User s Guide H 7 Appendix H UFM 4603 UFM 4645 UFM 4646 UFM 4647 UWM 4648 UFM 4671 Diagnostic Messages for Dynamic Analysis USER FATAL MESSAGE 4603 THE LSEQ SET ID I NOT UNIQUE WITH RESPECT TO OTHER STATIC LOAD IDS LSEQ set IDs must be unique with respect to all other static load set IDs USER FATAL MESSAGE 4645 THE SHIFTED STIFFNESS MATRIX IS NOT POSITIVE DEFINITE The matrix sum K i M is decomposed by the Cholesky method at the start of the MGIV method of eigensolution This decomposition requires that the matrix be positive definite A condition that prevents this is a massless mechanism for example a point mass on an offset with no rotational stiffness USER FATAL MESSAGE 4646 THE MASS MATRIX IS NOT POSITIVE DEFINITE USING THE HOU METHOD USE MHOU INSTEAD The reduced mass matrix has columns that are not linearly independent Common causes are rotation degrees of freedom whose only inertia terms result from point masses on offsets Use the MHOU method instead since 1t does not require a positive definite mass matrix USER FATAL MESSAGE 4647 INSUFFICIENT TIME TO COMPLETE HK ROK OK CPU ESTIMATE SEC CPU REMAINING SEC I O ESTIMATE
146. FREQ Default 1 E5 The ratios of terms on the diagonal of the stiffness matrix to the corresponding terms on the diagonal of the triangular factor are computed If for any row this ratio is greater than MAXRATIO the matrix will be considered to be nearly singular having mechanisms If any diagonal terms of the factor are negative the stiffness matrix is considered implausible non positive definite The ratios greater than MAXRATIO and less than zero and their associated external grid identities will be printed out The program will then take appropriate action as directed by the parameter BAILOUT By default in the superelement solution sequences the program will terminate processing for that superelement A negative value for BAILOUT directs the program to continue processing the superelement Although forcing the program to continue with near singularities is a useful modeling checkout technique it may lead to solutions of poor quality or fatal messages later in the run It is recommended that the default values be used for production runs A related parameter is ERROR In nonsuperelement solution sequences the default value 1 of BAILOUT causes the program to continue processing with near singularities and a zero value will cause the program to exit if near singularities are detected In SOLs 101 200 when PARAM CHECKOUT YES is specified PARAM MAXRATIO sets the tolerance for detecting multipoint constraint equations with poor
147. Form D 4 Parameters for Dynamic Analysis This section lists some of the parameters that are often used for dynamic analysis These parameters are listed alphabetically beginning below See the NX Nastran Quick Reference Guide for a description of all parameters ASING Default 0 ASING specifies the action to take when singularities null rows and columns exist in the dynamic matrices or Ky in statics If ASING 1 then a User Fatal Message will result If ASING 0 the default singularities are removed by appropriate techniques depending on the type of solution being performed AUTOSPC Default YES Gin SOLutions 101 through 200 except 106 and 129 Default NO in all other SOLutions AUTOSPC specifies the action to take when singularities exist in the stiffness matrix K AUTOSPC YES means that singularities will be constrained automatically AUTOSPC NO means that singularities will not be constrained Singularity ratios smaller than PARAM EPPRT default 1 E 8 are listed as potentially singular If PARAM AUTOSPC has the value YES identified singularities with a ratio smaller than PARAM EPZERO default 1 E 8 will be automatically constrained with single point constraints If PARAM EPPRT has the same value as PARAM EPZERO the default case all singularities are listed If PARAM EPPRT is larger than PARAM EPZERO the printout of singularity ratios equal to exactly zero is suppressed If PARAM PRGPST is set to NO
148. France September 1995 Brughmans M Lembregts F Ph D Furini F Ph D Modal Test on the Pininfarina Concept Car Body ETHOS 1 MSC 1995 World Users Conf Proc Paper No 5 May 1995 Budynas R Kolhatkar S Modal Analysis of a Robot Arm Using Finite Element Analysis and Modal Testing Proc of the 8th Int Modal Analysis Conf Vol I pp 67 70 January 1990 Budynas R G Krebs D Modal Correlation of Test and Finite Element Results Using Cross Orthogonality with a Reduced Mass Matrix Obtained by Modal Reduction and NASTRAN s Generalized Dynamic Reduction Solution Proc of the 9th Int Modal Analysis Conf Vol I pp 549 554 April 1991 Butler Thomas G Test vs Analysis A Discussion of Methods Fourteenth NASTRAN Users Colloq pp 173 186 May 1986 NASA CP 2419 Call V Mason D Space Shuttle Redesigned Solid Rocket Booster Structural Dynamic Predictions and Correlations of Liftoff AIAA SAE ASME ASEE 26th Joint Propulsion Conf Paper No AIAA 90 2081 July 1990 Chung Y T Model Reduction and Model Correlation Using MSC NASTRAN MSC 1995 World Users Conf Proc Paper No 8 May 1995 Coladonato Robert J Development of Structural Dynamic Test Evnironments for Subsystems and Components Seventh NASTRAN Users Colloq pp 85 110 October 1978 NASA CP 2062 Coppolino Robert N Integrated Dynamic Test Analysis Processor Overview MSC NASTRAN Users Conf Proc Paper No 5 March
149. GENVALUE APPROACHING INFINITY AT TH MODE EIGENVECTORS WILL NOT BE COMPUTED BEYOND THIS POINT The MHOU and AHOU methods substitute a very large number for eigenvalues that approach machine infinity If eigenvectors are computed for these artificial values they may be numerical noise or they may cause overflows Eigenvector computation is halted at the first machine infinity instead even if you requested eigenvectors in this range USER INFORMATION MESSAGE 5222 COUPLED UNCOUPLED SOLUTION ALGORITHM USED The modal methods use uncoupled solution algorithms if possible The uncoupled algorithms are considerably more economical than the coupled algorithms Coupled algorithms are required when any of the following effects are present transfer functions DMIG requests of the p type element damping and PARAM G Consider the use of modal damping TABDMP 1 entry to reduce the cost of your analysis in modal solutions USER FATAL MESSAGE 5225 ATTEMPT TO OPERATE ON THE SINGULAR MATRIX IN SUBROUTINE DCMP This message is preceded by the listing of the grid point ID and degrees of freedom for any null columns USER INFORMATION MESSAGE 5236 THE FREQUENCY RANGE HAS BEEN SPLIT INTO SUBREGIONS The overall frequency range for eigenanalysis is split 1nto several smaller ranges when using the SINV option to calculate modes and frequencies USER FATAL MESSAGE 5238 THE NUMBER OF ROOTS IN THE DEFINED FREQUENCY RANG
150. GO OCA RR Y dn 10 8 moo rrr 10 8 IET DG a a ee eee a ee ee re ee ee Se 10 8 Eigenvalue A alysis 66 46 6665 REOR Hees hee Y RUE e Hee E SORGE AUR E XO XC GREE b ESS 10 9 Frequency Response Analysis ce es 10 9 Transient Response Analysis eres 10 11 Results Interpretation and Verification cen 10 12 Computer Resource Requirements eee ees 10 14 Advanced Dynamic Analysis Capabilities cce enn 11 1 Bes g s usa 4 X ERA WUEXUERORAGCA XR RR ae RR Rd d RA e 3 4 dq e rex RiqE S3 Eu 11 2 Lronamus Pedut du us dob 3o do REESE GEOYR HE ORL o4 EDS Robo ob a OR ok EERE EROS 11 2 Complex Eigenvalue Analysis see es 11 3 Response Spectrum Analysis eee rs 11 3 Random Vibration Analysis 66 uc degen Rd Oe EEO ESSERE EEE ES SE REESE ORE SS 11 5 Mode Acceleration Method 0 0 0 ee eee eens 11 5 4 NX Nastran Basic Dynamic Analysis User s Guide Contents Flvid Siructure nera kia amp xcd ede Eee EERE EERE EEE OHS HEE dC e d 11 5 Nonlinear Transient Response Analysis 0 eee ee ee ene 11 6 PCO Ano DEDE nc ee bee ee ke hihiri E SEEK mA REP Kee SEO OES 11 9 Design Optimization and Sensitivity 0 0 ee ee 11 10 Control System Analysis ee ess 11 12 Aeroelastic Analysis 2e rs 11 12 DADA Gah eek eek oS eae DEES ES ES SOS EOS EERE OETA EES 224923323 11 14 a Ps bo oe oe RE X q4PEqETAMmEGQESG RIGQAR
151. Gimbaled Antennas for a Communications Satellite System MSC 1996 World Users Conf Proc Vol IV Paper No 33 June 1996 Subrahmanyam K B Kaza K R V Brown G V Lawrence C Nonlinear Vibration and Stability of Rotating Pretwisted Preconed Blades Including Coriolis Effects J of Aircraft Vol 24 No 5 pp 342 352 May 1987 Sundaram S V Hohman Richard L Richards Timothy R Vibration Modes of a Tire Using MSC NASTRAN MSC NASTRAN Users Conf Proc Paper No 26 March 1985 Tamba Richard Mowbray Graham Rao Ananda An Effective Method to Increase the Natural Frequencies of a Transmission Assembly The Sixth Australasian MSC Users Conf Proc November 1992 Tawekal Ricky Budiyanto M Agus Finite Element Model Correlation for Structures The MSC 1993 World Users Conf Proc Paper No 73 May 19938 Tawekal Ricky L Miharjana N P Validation of 3650 DWT Semi Containe Ship Finite Element Model by Full Scale Measurements MSC 1994 World Users Conf Proc Paper No 19 June 1994 Thornton Earl A A NASTRAN Correlation Study for Vibrations of a Cross Stiffened Ship s Deck NASTRAN Users Exper pp 145 160 September 1972 NASA TM X 2637 Ting Tienko Chen Timothy L C Twomey William A Practical Solution to Mode Crossing Problem in Continuous Iterative Procedure The 1989 MSC World Users Conf Proc Vol I Paper No 14 March 1989 Ting Tienko Chen T Twomey W Correla
152. HOU method or the AHOU method is the preferred methods to use when nearly singular mass matrices are expected because these methods decompose the matrix K M instead of the mass matrix The shift parameter is automatically set to be large enough to control rigid body modes Better modeling practices also reduce the costs and increase the reliability for the two examples cited above If an offset point mass is significant in any mode it is better to attach it to an extra grid point at its center of gravity and model the offset with a rigid element The auto omit feature then eliminates the rotational degrees of freedom Similarly if only a few interior points of a superelement have mass it may be more economical to convert them to exterior points which also eliminates the singular boundary mass matrix It is possible to input negative terms into a mass matrix directly with DMIG terms or scalar mass elements This class of problem causes fatal errors due to nonpositive definite mass matrices for the transformation methods fatal errors with the Lanczos method The complex eigenvalue methods should be used for this type of problem which infers that modal or dynamic reduction methods may not be used A similar but quite different problem arises because Cholesky decomposition is used on the generalized mass matrix named MI in the diagnostics when orthogonalizing the eigenvectors with respect to the mass matrix The existence of negative term
153. HS 25th Structures Structural Dynamics and Materials Conf AIAA Paper 84 0942 CP May 1984 Ghosh Tarun MSC NASTRAN Based Component Mode Synthesis Analysis Without the Use of DMAPS MSC 1996 World Users Conf Proc Vol II Paper No 18 June 1996 Gieseke R K Analysis of Nonlinear Structures via Mode Synthesis NASTRAN Users Exper pp 341 360 September 1975 NASA TM X 3278 Graves Roger W Interfacing MSC NASTRAN with SDRC IDEAS to Perform Component Mode Synthesis Combining Test Analytical and F E Data The MSC 1988 World Users Conf Proc Vol II Paper No 58 March 1988 Halcomb J R Application of Component Modes to the Analysis of a Helicopter Proc of the MSC NASTRAN Users Conf March 1979 Hambric Stephen A Power Flow and Mechanical Intensity Calculations in Structural Finite Element Analysis ASME J of Vibration and Acoustics Vol 112 pp 542 549 October 1990 Herting David N Hoesly R L Development of an Automated Multi Stage Modal Synthesis System for NASTRAN Sixth NASTRAN Users Colloq pp 485 448 October 1977 NASA CP 2018 Herting David N Accuracy of Results with NASTRAN Modal Synthesis Seventh NASTRAN Users Collog pp 389 404 October 1978 NASA CP 2062 Herting D N A General Purpose Multi Stage Component Modal Synthesis Method Finite Elements in Analysis and Design Vol 1 No 2 1985 Hill R G Merckx K R Seismic Response Evaluation of a Re
154. June 1996 Chiang C K Robinson J H Rizzi S A Equivalent Linearization Solution Sequence for MSC NASTRAN Winter Annual Meeting of the American Society of Mechanical Engineers pp 133 138 November 1992 Ciuti Gianluca Avionic Equipment Dynamic Analysis MSC 1995 European Users Conf Proc Italian Session September 1995 Coyette J P Lecomte C von Estorff O Evaluation of the Response of a Coupled Elastic Structure Subjected to Random Mechanical or Acoustical Excitations Using MSC NASTRAN and SYSNOISE MSC European Users Conf Paper No 21 September 1996 Crispino Maurizio A 3 D Model for the Evaluation through Random Analysis of Vertical Dynamic Overloads in High Speed Railway Lines MSC 1995 European Users Conf Proc Italian Session September 1995 Galletly Robert Wagner R J Wang G J Zins John Random Vibration and Acoustic Analysis Using ARI RANDOM a NASTRAN Post Processor MSC NASTRAN Users Conf Proc Paper No 26 March 1984 Hatheway A Random Vibrations in Complex Electronic Structures MSC NASTRAN Users Conf Proc Paper No 13 March 1983 Hatheway Alson E Evaluation of Ceramic Substrates for Packaging of Leadless Chip Carriers MSC NASTRAN Users Conf Proc Paper No 16 March 1982 Michels Gregory J Vibroacoustics Random Response Analysis Methodology MSC 1995 World Users Conf Proc Paper No 9 May 1995 Palmieri F W Example Problems Illustra
155. Larkin Paul A Miller Michael W STS Coupled Loads Analysis Using MSC NASTRAN MSC NASTRAN Users Conf Proc Paper No 18 March 1985 Lee J H Tang J H K Dynamic Response of Containments Due to Shock Wave Proc of the Int Conf on Containment Design pp 25 32 June 1984 Lee Sang H Bock Tim L Hsieh Steve S Adaptive Time Stepping Algorithm for Nonlinear Transient Analysis The MSC 1988 World Users Conf Proc Vol II Paper No 54 March 1988 Leifer Joel Gross Michael Non Linear Shipboard Shock Analysis of the Tomahawk Missile Shock Isolation System 58th Shock and Vibration Symp Vol 1 pp 97 117 October 1978 NASA CP 2488 Lipman Robert R Computer Animation of Modal and Transient Vibrations Fifteenth NASTRAN Users Colloq pp 111 117 August 1987 NASA CP 2481 Mattana G Miranda D MSC NASTRAN Applications in P 180 Analysis Proc of the MSC NASTRAN First Italian Users Conf October 1987 McMeekin Michael Kirchman Paul An Advanced Post Processing Methodology for Viewing MSC NASTRAN Generated Analyses Results MSC 1994 World Users Conf Proc Paper No 21 June 1994 McNamee Martin J Zavareh Parviz Nonlinear Transient Analysis of a Shock Isolated Mechanical Fuse The MSC 1990 World Users Conf Proc Vol I Paper No 21 March 1990 I 32 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Neilson H C Everstine G C Wang Y F Transi
156. M 5405 USER WARNING MESSAGE 5405 ERROR OCCURRED DURING ITERATION ERROR NUMBER IS Y SEE DESCRIPTION FOR VALUES OF Y AND USER ACTION This message marks the breakdown of the inverse iteration process 1n the Lanczos method See the NX Nastran Numerical Methods User s Guide for additional values and actions 41 File open error in interface see This error should not occur GINO error message report error to UGS E um a GINO This error should not occur possp 8 gt report error to UGS error w s e cao er message report error to UGS a cl NR 2 1 ncrease memory H 12 NX Nastran Basic Dynamic Analysis User s Guide UWM 5406 UWM 5407 UWM 5408 UWM 5411 Diagnostic Messages for Dynamic Analysis 99 Three consecutive factorizations Possible ill conditioning check failed at a shift model Lanczos internal table overflow Specify smaller internal may 23 due to enormous number of be necessary to have several shifts runs 31 Internal error in Lanczos This error should not occur REIGL module report error to UGS No convergence in solving the Possible ill conditioning check tridiagonal problem model Too many eigenvalues were found inconsistency between the roots found and Sturm Check the orthogonality of the eigenvectors if it is good then ignore this warning USER WARNING MESSAGE 5406 NO CONVERGENCE IN SOLVING THE TRIDIAGONAL PROBLEM This message signals eigensolution problems
157. MP1 table is activated by selecting the Table ID with the SDAMPING Case Control command Field Contents TID Table identification number TYPE Type of damping units G default CRIT Q fi Frequency value cycles per unit time gi Damping value in the units specified At resonance the three types of damping are related by the following equations b G Ga l u l wg CF CF Equation 5 19 Note that the z subscript is for the i th mode and not the i th excitation frequency The values of f and gi define pairs of frequencies and dampings Note that gi can be entered as one of the following structural damping default critical damping or quality factor The entered damping is converted to structural damping internally using Equation 5 19 Straight line interpolation 1s used for modal frequencies between consecutive f values Linear extrapolation is used at the ends of the table ENDT ends the table input 5 8 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis For example if modal damping is entered using Table 5 1 and modes exist at 1 0 2 5 3 6 and 5 5 Hz NX Nastran interpolates and extrapolates as shown in Figure 5 3 and in the table Note that there is no table entry at 1 0 Hz NX Nastran uses the first two table entries at f 2 0 and f 3 0 to extrapolate the value for f 1 0 0 20 entered value e computed value 0 0 20 4 0 6 0 f Hz Figure 5 3 Example TABDM
158. MSC 1991 World Users Conf Proc Vol I Paper No 18 March 1991 Rose Ted Some Sugsestions for Evaluating Modal Solutions The MSC 1992 World Users Conf Proc Vol I Paper No 10 May 1992 Rose Ted Using Optimization in MSC NASTRAN to Minimize Response to a Rotating Imbalance MSC 1994 Korea Users Conf Proc December 1994 Rose Ted Using Dynamic Optimization to Minimize Driver Response to a Tire Out of Balance MSC 1994 Korea Users Conf Proc December 1994 Rose Ted Using Optimization in MSC NASTRAN to Minimize Response to a Rotating Imbalance 1994 MSC Japan Users Conf Proc Paper No 28 December 1994 Rose Ted L Using Optimization in MSC NASTRAN to Minimize Response to a Rotating Imbalance The Sixth Annual MSC Tarwan Users Conf Proc Paper No D November 1994 Saito Hiroshi Watanabe Masaaki Modal Analysis of Coupled Fluid Structure Response MSC NASTRAN Users Conf Proc March 1982 Salvestro Livio Sirocco Howden Currie Andrew Cyclic Symmetry Analysis of an Air Blower Fan Seventh Australasian Users Conf Proc Sydney October 1993 Scanlon Jack Swan Jim A Stand Alone DMAP Program for Modal Cross Correlation MSC 1995 World Users Conf Proc Paper No 40 May 1995 Schiavello D V Sinkiewicz J E DMAP for Determining Modal Participation MSC NASTRAN Users Conf Proc Paper No 15 March 1983 Schwering W Shulze A DMAP for Identification of Modeshapes Pr
159. MSC NASTRAN Users Conf Proc Paper No 6 March 1986 Pamidi M R Pamidi P R Modal Seismic Analysis of a Nuclear Power Plant Control Panel and Comparison with SAP IV NASTRAN Users Exper pp 515 530 October 1976 NASA TM X 3428 Pamidi P R On the Append and Continue Features in NASTRAN Seventh NASTRAN Users Colloq pp 405 418 October 1978 NASA CP 2062 Paolozzi A Interfacing MSC NASTRAN with a Structural Modification Code Proc of the 18th MSC Eur Users Conf Paper No 30 June 1991 NX Nastran Basic Dynamic Analysis User s Guide l 25 Appendix References and Bibliography Park H B Suh J K Cho H G Jung G S A Study on Idle Vibration Analysis Technique Using Total Vehicle Model MSC 1995 World Users Conf Proc Paper No 6 May 1995 Parker G R Brown J J Kinetic Energy DMAP for Mode Identification MSC NASTRAN Users Conf Proc Paper No 8 March 1982 Parker G R Brown J J Evaluating Modal Contributors in a NASTRAN Frequency Response Analysis MSC NASTRAN Users Conf Proc Paper No 14 March 1983 Pulgrano Louis J Masters Steven G Self Excited Oscillation of a 165 Foot Water Tower MSC 1995 World Users Conf Proc Paper No 32 May 1995 Reyer H Modal Synthesis with External Superelements in MSC NASTRAN Proc of the MSC NASTRAN Eur Users Conf May 1984 Rose Ted A Method to Apply Initial Conditions in Modal Transient Solutions The
160. N USER ACTION DELETE THIS FILE AND RESUBMIT THE JOB DELETE is not a suggested option if you are using RESTART since you can delete your database inadvertently Manual deletion of unwanted databases is a safer approach Example ASSIGN DBl sample DBl INIT DBALL LOGICAL DB1 50000 These statements create a physical file called sample DB1 for the logical name DB1 in the current directory Without the ASSIGN statement the physical file name created is called dyn1 DB1 assuming once again that your input file is called dyn1 dat ASSIGN DB1 mydiskl se sample DBl ASSIGN DB2 mydisk2 sample DB2 INIT DBALL LOGICAL DB1 50000 DB2 40000 Two logical names DB1 and DB2 are created for the DBset DBALL DB1 points to a physical file called sample DB1 that resides in the file system directory mydisk1 se DB2 points to a physical file called sample DB2 that resides in the file system directory mydisk2 Format Simplified to Assign FORTRAN Files ASSIGN DB1 mydiskl se sample DBl ASSIGN DB2 mydisk2 sample DB2 INIT DBALL LOGICAL DB1 50000 DB2 40000 E 4 NX Nastran Basic Dynamic Analysis User s Guide File Management Section This is the logical keyword for the FORTRAN file being created The default values depend on the keyword Acceptable keywords are log ke BUSEY DBC DBMIG INPUTT2 INPUTT4 OUTPUT2 OUTPUT4 DBUNLOAD DBLOAD and USERFILE You should reference the NX Nastran Quick Reference G
161. NING INFORMATION MESSAGE ID text where ID is a unique message identification number and text is the message as indicated in capital letters for each of the diagnostic messages Four asterisks in the message text indicates information that 1s filled in for a specific use of the message such as the number of a grid point or the name of a Bulk Data entry Some of the messages are followed by additional explanatory material including suggestions for remedial action Fatal messages cause the termination of the execution following the printing of the message text These messages always appear at the end of the NX Nastran output Warning and information messages appear at various places in the output stream Such messages only convey warnings or information to the user Consequently the execution continues in a normal manner following the printing of the message text As an example consider message number 2025 which appears in the printed output as follows USER FATAL MESSAGE 2025 UNDEFINED COORDINATE SYSTEM 102 The three leading asterisks are always present in numbered user and system diagnostic messages The word USER indicates that this is a user problem rather than a system problem The word FATAL indicates that this 1s a fatal message rather than a warning or information message The number 2025 1s the identification number for this message The text of the message follows the comma The number 102 replaces the aster
162. NORMAL MODES ANALYSIS Executive Case Control 9 2 NX Nastran Basic Dynamic Analysis User s Guide Plotted Output S 9 OUTPUT REQUESTS DISPLACEMENT PLOT ALL S STRUCTURE PLOTS OUTPUT PLOT CSCALE 3 0 SET 333 ALL AXES MX MY Z VIEW 20 20 20 FIND SCALE ORIGIN 5 SET 333 S PLOT UNDEFORMED SHAPE PLOT SET 333 ORIGIN 5 S PLOT DEFORMED UNDEFORMED SHAPES PLOT MODAL DEFORMATION 0 1 PLOT MODAL DEFORMATION 0 2 BEGIN BULK S Bulk Data S ENDDATA Figure 9 1 Normal Modes Structure Plot Commands for the Bracket Model Undeformed Shape Max Def 3 82 Mode Max Def 506 Mode 2 Figure 9 2 Normal Modes Structure Plots for the Bracket Model Figure 9 3 shows the structure plotting commands applied to a modal frequency response analysis of the cantilever beam model The displacements are computed in magnitude phase NX Nastran Basic Dynamic Analysis User s Guide 9 3 Chapter 9 Plotted Output form PARAM DDRMM 1 and PARAM CURVPLOT 1 are required in the Bulk Data to create structure plots at specified frequencies Note that PARAM DDRMM 1 generally increases the amount of computer time and is not recommended unless otherwise required Figure 9 4 shows the resulting plots The first plot shows the undeformed shape and the next plot shows the magnitude of response at 2 05 Hz which is overlaid on the undeformed shape The default is chosen such that the maximum plotted deformation is 5 of t
163. NX Nastran Basic Dynamic Analysis User s Guide Proprietary amp Restricted Rights Notice 2008 Siemens Product Lifecycle Management Software Inc All Rights Reserved This software and related documentation are proprietary to Siemens Product Lifecycle Management Software Inc NASTRAN is a registered trademark of the National Aeronautics and Space Administration NX Nastran is an enhanced proprietary version developed and maintained by Siemens Product Lifecycle Management Software Inc MSC is a registered trademark of MSC Software Corporation MSC Nastran and MSC Patran are trademarks of MSC Software Corporation All other trademarks are the property of their respective owners TAUCS Copyright and License TAUCS Version 2 0 November 29 2001 Copyright c 2001 2002 2003 by Sivan Toledo Tel Aviv Univesity stoledo tau ac il All Rights Reserved TAUCS License Your use or distribution of TAUCS or any derivative code implies that you agree to this License THIS MATERIAL IS PROVIDED AS IS WITH ABSOLUTELY NO WARRANTY EXPRESSED OR IMPLIED ANY USE IS AT YOUR OWN RISK Permission is hereby granted to use or copy this program provided that the Copyright this License and the Availability of the original version is retained on all copies User documentation of any code that uses this code or any derivative code must cite the Copyright this License the Availability note and Used by permission If this code or any derivative c
164. OINT ID DEGREE OF FREEDOM MATRIX FACTOR DIAGONAL RATIO MATRIX DIAGONAL 11 R3 9 49483E 13 2 84000E 04 xxx USER INFORMATION MESSAGE 3035 FOR DATA BLOCK KLR SUPPORT PT NO EPSILON STRAIN ENERGY EPSILONS LARGER THAN 0 001 ARE FLAGGED WITH AS 1 7 6288287E 17 5 53879354E 09 2 7 6288287E 17 s T595 Ona Figure 4 7 UIM 3035 Results Unconstrained Bracket Example The constraints SPCs on the example bracket model from Real Eigenvalue Analysis are removed to create an unconstrained model see Examples for a description of the model Figure 4 8 shows the bracket model The model is a three dimensional model and therefore produces six rigid body modes The NX Nastran results are shown in Figure 4 9 for the first eight modes The Lanczos method is used NX Nastran Basic Dynamic Analysis User s Guide 4 13 ge ts Chapter 4 T ar MODE EXTRACTION NO ORDER 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 The six rigid body modes have computational zero frequencies on the order of 10 5 Hz Note that the magnitudes of the rigid body modes may be different when the same problem is run on a different computer type Also note that the output is sorted by the value of the eigenvalue in ascending order 4 14 Rigid Body Modes Figure 4 8 Unconstrained Bracket Model EIGENVALUE 1s E xm xor la 690642E 07 807991E 09 515176E 09 390596E 09 266017E 08 1 726585E 08 Za 4 279463E 06 649932E 06 REAL NMNRRRPON
165. OLLOWING DEGREES OF FREEDOM HAVE FACTOR DIAGONAL RATIOS GREATER THAN OR HAVE NEGATIVE TERMS ON THE FACTOR DIAGONAL During decomposition the degrees of freedom listed have pivot ratios that are greater than maxratio or are negative Verify that the degrees of freedom are not part of a mechanism and that elements do not have excessive stiffness In SOLs 100 and higher this condition causes run termination PARAM BAILOUT may be used to continue the run to obtain messages issued by subsequent modules See the NX Nastran Numerical Methods User s Guide USER INFORMATION MESSAGE 5010 STURM SEQUENCE DATA FOR EIGENVALUE EXTRACTION TRIAL EIGENVALUE real CYCLES real NUMBER OF EIGENVALUES BELOW THIS VALUE integer This message is automatic output during eigenvalue extraction using the Lanczos and SINV methods This message can be used along with the list of eigenvalues to identify the modes found See the NX Nastran Numerical Methods User s Guide USER FATAL MESSAGE 5025 LAMA PURGED DSTA MODULE TERMINATED The LAMA data block contains a list of natural frequencies and may be purged because no eigenvalues were computed or the data block was not properly recovered on restart NX Nastran Basic Dynamic Analysis User s Guide H 9 Appendix H UIM 5218 UIM 5222 UFM 5225 UIM 5236 UFM 5238 UIM 5239 UIM 5240 UIM 5241 Diagnostic Messages for Dynamic Analysis USER INFORMATION MESSAGE 5218 EI
166. OTS X Y plot commands S BEGIN BULK S ENTRIES FOR TRANSIENT RESPONSE INITIAL CONDITION STI SID G C UO VO TIT 777 2 2 Duo S TIME STEP TSTEP SID N1 DEL NO1 TSTEP 888 1000 0 01 1 S basic model ENDDATA Transient Response Analysis Figure 6 7 Input File Abridged for the Two DOF Example Table 6 8 shows the relationship between the Case Control commands and the Bulk Data entries This example represents the simplest form of dynamic response input The only required entries are those that define the time step and the initial conditions Note that the unspecified initial NX Nastran Basic Dynamic Analysis User s Guide 6 27 Chapter 6 Transient Response Analysis conditions are assumed to be zero Note too that the initial conditions are available only for direct transient response analysis Table 6 8 Relationship Between Case Control Commands and Bulk Data Entries for the Two DOF Model Case Control Bulk Data Figure 6 8 shows the plots of the resulting displacements for grid points 1 and 2 Note that there are two frequencies of response a higher frequency of about 5 Hz and a lower frequency of about 0 25 Hz The energy and hence response appears to be transferred repetitively between grid points 1 and 2 as represented by the lower frequency response This energy transfer is called beating Beating occurs when there are closely spaced modes in this case 4 79 Hz and 5 29 Hz in which energy transfe
167. P1 Table 5 1 Example TABDMPI Interpolation Extrapolation Computed TABDMP1 C TAB2 ENDT Modal damping is processed as a complex stiffness when PARAM KDAMP is entered as 1 The uncoupled equation of motion becomes 2 1 m S 1 iG w k 5 w p w Equation 5 20 The default for PARAM KDAMP is 1 which processes modal damping as a damping matrix as shown in Equation 5 17 NX Nastran Basic Dynamic Analysis User s Guide 5 9 Chapter 5 Frequency Response Analysis The decoupled solution procedure used in modal frequency response can be used only if either no damping is present or modal damping alone via TABDMP1 is used Otherwise the modal method uses the coupled solution method on the smaller modal coordinate matrices if nonmodal damping i e CVISC CDAMPi GE on the MAT entry or PARAM G is present Mode Truncation in Modal Frequency Response Analysis It is possible that not all of the computed modes are required in the frequency response solution You need to retain at a minimum all the modes whose resonant frequencies lie within the range of forcing frequencies For example if the frequency response analysis must be between 200 and 2000 Hz all modes whose resonant frequencies are in this range should be retained This guideline is only a minimum requirement however For better accuracy all modes up to at least two to three times the highest forcing frequency should be retained In the example wher
168. Proc Vol II Paper No 51 March 1990 Rose Ted Using Residual Vectors in MSC NASTRAN Dynamic Analysis to Improve Accuracy The MSC 1991 World Users Conf Proc Vol I Paper No 12 March 1991 Rose Ted DMAP Alters to Apply Modal Damping and Obtain Dynamic Loading Output for Superelements The MSC 1993 World Users Conf Proc Paper No 24 May 1993 Rose Ted McNamee Martin A DMAP Alter to Allow Amplitude Dependent Modal Damping in a Transient Solution MSC 1996 World Users Conf Proc Vol V Paper No 50 June 1996 Ross Robert W Prediction and Elimination of Resonance in Structural Steel Frames The MSC 1988 World Users Conf Proc Vol II Paper No 45 March 1988 Russo A Mocchetti R Dynamic Analysis of Loaded Structures in the Helicopter Field Proc of the MSC NASTRAN Eur Users Conf May 1984 Salus W L Jones R E Ice M W Dynamic Analysis of a Long Span Cable Stayed Freeway Bridge Using NASTRAN NASTRAN Users Exper pp 143 168 September 1973 NASA TM X 2893 Sauer G Wolf M Gyroscopic Effects in the Dynamic Response of Rotating Structures Proc of the MSC NASTRAN Eur Users Conf Paper No 11 May 1986 Schips C Aero Engine Turbine Dynamic Analysis Proc of the 18th MSC Eur Users Conf Paper No 8 June 1991 Schmitz Ronald P Structural Dynamic Analysis of Electronic Assemblies Using NASTRAN Restart Format Change Capability NASTRAN Users Exper
169. RA 250000 SCRB 300000 This statement creates the SCRATCH DBset with logical names of SCR1 SCR2 SCRA and SCRB Two physical files dyn1 SCR1 and dyn1 SCR2 are created with a maximum size of NX Nastran Basic Dynamic Analysis User s Guide E 3 Appendix E File Management Section 150000 and 100000 blocks respectively These two files are regular scratch files Two additional physical files dyn1 SCRA and dyn1 SCRB are created with a maximum size of 250000 and 300000 blocks respectively These two files are SCR300 type files ASSIGN Purpose Assigns physical filenames to logical filenames or special FORTRAN files that are used by other FMS statements or DMAP modules Format Simplified to Assign Logical Files ASSIGN log namei filenamei TEMP DELETE log namei The i th logical name for the DBset created by the INIT statement TEMP Requests that filenamei be deleted at the end of the job This is optional and is often used for USRSOU and USROBJ Requests that filenamei be deleted if it exists before the start of the run This is optional however if this option is not used and the FORTRAN file exists prior to the current run then the job may fail with the following messages USER FATAL MESSAGE 773 DBDEF IHE FOLLOWING PHYSICAL FILE ALREADY EXISTS LOGICAL NAME XXXX DELETE PHYSICAL FILE YYYY USER INFORMATION NO ASSOCIATED DEFAULT FILES OR ASSIGNED DBSETS CAN EXIST PRIOR TO THE DATA BASE INITIALIZATION RU
170. REA SID P1 CA Al DAREA 997 3 2 1 0 TABLED4 TID X1 X2 X3 x4 TABLED4 901 Oa ee 100 S TAB4 AO Al A2 A3 A4 AS TAB901 1 0 ENDT MODAL EXTRACTION SEIGRL SID V1 V2 ND MSGLVL EIGRL 10 L 30 0 9 S FREQUENCY RANGE 2 10 HZ FREQ1 SID F1 DF NDF FREQ1 888 Z2 0 05 160 S MODAL DAMPING OF 5 CRITICAL STABDMP1 TID TYPE TAB1 F1 G1 F2 G2 ETC TABDMP1 777 CRIT TABD7 0 0 05 100 0 05 ENDT NX Nastran Basic Dynamic Analysis User s Guide TAB4 TAB901 TABD7 Enforced Motion 7 9 Chapter 7 Enforced Motion basic model ENDDATA Figure 7 3 Input File for Enforced Constant Acceleration The large mass value is chosen as 1 0E7 kilograms and is input via the CONM2 entry The scale factor for the load 1 0E7 is input on the DLOAD Bulk Data entry The factor of 1 0E7 is approximately six orders of magnitude greater than the overall structural mass 10 1 kg The TABLED4 entry defines the constant acceleration input One of the other TABLEDi entries can also be used but the TABLED4 entry is chosen to show how to use it for enforced constant velocity and displacement later in this example Figure 7 4 shows the X Y plots resulting from the input point grid point 3 and an output point grid point 1 The plots show acceleration and displacement magnitudes Note that the acceleration input is not precisely 1 0m sec there is a very slight variation between 0 9999 and 1 0000 due to the large mass approximation
171. Rucker Carl E Modal Analysis of a Nine Bay Skin Stringer Panel NASTRAN Users Exper pp 343 362 September 1971 NASA TM X 2378 Gupta Viney K Zillmer Scott D Allison Robert E Solving Large Scale Dynamic Systems Using Band Lanczos Method in Rockwell NASTRAN on Cray X MP Fourteenth NASTRAN Users Colloq pp 236 246 May 1986 NASA CP 2419 Hardman E S Static and Normal Modes Analysis of an Aircraft Structure Using the NASTRAN External Superelement Method Proc of the MSC NASTRAN Eur Users Conf May 1986 Harn Wen Ren Hwang Chi Ching Evaluation of Direct Model Modification Methods via MSC NASTRAN DMAP Procedures The MSC 1990 World Users Conf Proc Vol II Paper No 43 March 1990 l 22 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Hayashida Mirihiro Application of Design Sensitivity Analysis to Reduction of Vibration of Ship s Deck Structure The Sixth MSC NASTRAN User s Conf in Japan October 1988 in Japanese Herting D N Joseph J A Kuusinen L R MacNeal R H Acoustic Analysis of Solid Rocket Motor Cavities by a Finite Element Method National Aeronautics and Space Administration pp 285 324 September 1971 NASA TM X 2378 Herting David N Accuracy of Results with NASTRAN Modal Synthesis Seventh NASTRAN Users Collog pp 389 404 October 1978 NASA CP 2062 Hill R G The Use of MSC NASTRAN to Determine the Impact Response of
172. SEC I O REMAINING SEC CPU and I O limits are supplied on the Executive Control statement TIME in minutes The module where the terminated program is listed If the time to completion appears reasonable you should increase the estimates on the TIME statement and resubmit the run For large models an increase in the system memory request should also be considered USER WARNING MESSAGE 4648 THE MODAL MASS MATRIX IS NOT POSITIVE DEFINITE The modal mass matrix cannot be decomposed by the Cholesky algorithm after merging elastic and free body modes Cholesky decomposition 1s used to orthogonalize the eigenvectors with respect to the mass matrix The causes include the input of negative masses and the calculation of eigenvectors for eigenvalues approaching machine infinity Inspect the model or ask for fewer eigenvectors using the F2 option When this condition occurs the eigenvectors are not orthogonalized or normalized The second parameter of the READ or REIGL module is given a negative sign This parameter is used in the solution sequences to branch to an error exit after printing the real eigenvalue table You may use a DMAP Alter to print these eigenvectors if the cause of the problem 1s not apparent in the eigenvalues The solution can be forced to completion by changing the sign of this parameter You should be aware that a poor quality solution is provided for this case This poor solution may be useful for diagnosing the prob
173. SO is NO but the C D E and F points are entered in error negative mass terms can result if either E1 or E2 entries are entered The offending DOF can be traced using the USET tables The Lanczos method gives wrong answers for indefinite matrices The existence of negative diagonal terms indicates a subclass of indefinite matrix See the NX Nastran Numerical Methods User s Guide for more information NX Nastran Basic Dynamic Analysis User s Guide H 13 Appendix H Diagnostic Messages for Dynamic Analysis UIM 5458 USER INFORMATION MESSAGE 5458 METHOD IS SELECTED or METHOD IS The exact text of this message depends on the METHOD field on the selected EIGR Bulk Data entry This message indicates the eigensolution status all eigenvalues found not all found etc UFM 6133 USER FATAL MESSAGE 6133 DFMSDD SINGULAR MATRIX IN SPARSE DECOMPOSITION USER ACTION CHECK MODEL This message is often followed by UFM 4645 UFM 4646 or UWM 4648 UFM 6134 USER FATAL MESSAGE 6134 DFMSDD MATRIX IS NOT POSITIVE DEFINITE IN SPARSE DECOMPOSITION USER ACTION CHECK MODEL This message is often followed by UFM 4645 UFM 4646 or UWM 4648 SFM 6135 SYSTEM FATAL MESSAGE 6135 ERROR IN READING SYMBOLIC FACTOR IN SPARSE FBS This message may be issued if the FBS module is using a sparse method to solve factors which are not decomposed by the sparse method This message can also be caused by a compatib
174. STRAN and Empirical Data to Verify a Design MSC NASTRAN Users Conf Proc Paper No 11 March 1984 Scapinello F Colombo E An Approach for Detailed Analysis of Complex Structures Avoiding Complete Models Proc of the MSC NASTRAN Eur Users Conf May 1987 Sok chu Park Ishii Tetsu Honda Shigeki Nagamatsu Akio Vibration Analysis and Optimum Design of Press Machines 1994 MSC Japan Users Conf Proc Stack Charles P Cunningham Timothy J Design and Analysis of Coriolis Mass Flowmeters Using MSC NASTRAN The MSC 1993 World Users Conf Proc Paper No 54 May 1993 Su Hong Structural Analysis of Ka BAND Gimbaled Antennas for a Communications Satellite System MSC 1996 World Users Conf Proc Vol IV Paper No 33 June 1996 Tawekal Ricky Budiyanto M Agus Finite Element Model Correlation for Structures The MSC 1993 World Users Conf Proc Paper No 73 May 1993 Ting T Ojalvo I U Dynamic Structural Correlation via Nonlinear Programming Techniques The MSC 1988 World Users Conf Proc Vol II Paper No 57 March 1988 Ting Tienko Chen Timothy L C FE Model Refinement with Actual Forced Responses of Aerospace Structures The MSC 1991 World Users Conf Proc Vol II Paper No 51 March 1991 Ting Tienko Test Analysis Correlation for Multiple Configurations The MSC 1993 World Users Conf Proc Paper No 74 May 1993 Ujihara B H Dosoky M M Tong E T Improving a NASTRAN
175. Shape Natural Frequency Phase Angle Positive Definite Positive Semi Definite Repeated Roots Resonance Component mode synthesis The lowest value of damping for which oscillation does not occur when the structure is displaced from its rest position Values of damping less than the critical damping value create an underdamped system for which oscillatory motion occurs Energy dissipation in vibrating structures Degree of freedom Ratio of dynamic response to static response which is a function of the forcing frequency natural frequency and damping Vibration response due to applied time varying forces Vibration response when there is no applied force Normal modes analysis and transient response to initial conditions are examples of free vibration analysis Computation of the steady state response to simple harmonic excitation Lagrange multiplier technique Stress free zero frequency motions of a portion of the structure A mechanism can be caused by an internal hinge The deformed shape of a structure when vibrating at one of its natural frequencies The frequency with which a structure vibrates during free vibration response Structures have multiple natural frequencies The angle between the applied force and the response In NX Nastran this angle is a phase lead whereby the response leads the force A matrix whose eigenvalues are all greater than zero A matrix whose eigenvalues are greater than or
176. So C VU wm o gs II velocity of mass acceleration of mass Figure 1 1 Single Degree of Freedom SDOF System Dynamic and Static Degrees of Freedom Mass and damping are associated with the motion of a dynamic system Degrees of freedom with mass or damping are often called dynamic degrees of freedom degrees of freedom with stiffness are called static degrees of freedom It is possible and often desirable in models of complex systems to have fewer dynamic degrees of freedom than static degrees of freedom The four basic components of a dynamic system are mass energy dissipation damper resistance spring and applied load As the structure moves in response to an applied load forces are induced that are a function of both the applied load and the motion in the individual components The equilibrium equation representing the dynamic motion of the system is known as the equation of motion Equation of Motion This equation which defines the equilibrium condition of the system at each point in time is represented as NX Nastran Basic Dynamic Analysis User s Guide 1 3 Chapter 1 Fundamentals of Dynamic Analysis mii t b t kult p t Equation 1 2 The equation of motion accounts for the forces acting on the structure at each instant in time Typically these forces are separated into internal forces and external forces Internal forces are found on the left hand side of the equation and external forces ar
177. T 1 126 MAKE 2D MODEL GRDSET 345 SEIGRL SID V1 V2 EIGRL 10 9041 50 S basic model ENDDATA Figure 4 4 Input File for Cantilever Beam Model Table 4 2 lists the computed frequencies The overdetermined run for the Lanczos method works well the same run for the SINV method gives an extra zero frequency mode that does not really exist The overdetermined runs have redundant SUPORTs in the x direction therefore two rigid body modes are computed in this direction when using the SINV method In all cases the flexible greater than 0 frequencies are correct 4 10 NX Nastran Basic Dynamic Analysis User s Guide Rigid Body Modes Table 4 2 Frequencies for the Unconstrained Beam Models SINV Method Frequencies Hz Stat Det Over Det No SUPORT SUPORT SUPORT Lanczos Method Frequencies Hz No SUPORT Under Det Stat Det Over Det SUPORT SUPORT 8 07E 6 3 07 E 5 Figure 4 5 shows the output for the rigid body modes computed for the SINV method when using no SUPORT The rigid body frequencies are denoted by computational zeroes on the order of 10 5 Hz or less Note that the magnitude may be different when the same problem is run on a different computer type Figure 4 6 shows the output for the rigid body modes computed for the SINV method when using the statically determinate SUPORT The accuracy of the statically determinate SUPORT DOFs is verified by the computational zeroes for epsilon and the str
178. TRAN The MSC 1993 World Users Conf Proc Paper No 36 May 1993 Patel Jayant S Seltzer S M Complex Eigenvalue Solution to a Spinning Skylab Problem NASTRAN Users Exper pp 439 450 September 1971 NASA TM X 2378 Patel Jayant S Seltzer S M Complex Eigenvalue Analysis of Rotating Structures NASTRAN Users Exper pp 197 234 September 1972 NASA TM X 2637 Patel Kirit V Stress Analysis of Hybrid Pins in a Warped Printed Wiring Board Using MSC NASTRAN MSC 1995 World Users Conf Proc Paper No 20 May 1995 Paxson Ernest B Jr Simulation of Small Structures Optics Controls Systems with MSC NASTRAN The 1989 MSC World Users Conf Proc Vol II Paper No 39 March 1989 Pinnament Murthy Mode Acceleration Data Recovery in MSC NASTRAN Dynamic Analysis with Generalized Dynamic Reduction MSC NASTRAN Users Conf Proc Paper No 24 March 1985 Raney John P Kaszubowski M Ayers J Kirk Analysis of Space Station Dynamics Using MSC NASTRAN The MSC 1987 World Users Conf Proc Vol I Paper No 11 March 1987 Reyer H A Crash Down Calculated with NASTRAN Proc of the MSC NASTRAN Eur Users Conf April 1982 Rose Ted L Using Superelements to Identify the Dynamic Properties of a Structure The MSC 1988 World Users Conf Proc Vol I Paper No 41 March 1988 Rose Ted L Creation of and Use of Craig Bampton Models Using MSC NASTRAN The MSC 1990 World Users Conf
179. TRAN Eur Users Conf Paper No 4 May 1984 DYNAMICS REDUCTION METHODS Abdallah Ayman A Barnett Alan R Widrick Timothy W Manella Richard T Miller Robert P Stiffness Generated Rigid Body Mode Shapes for Lanczos Eigensolution with Support DOF Via a MSC NASTRAN DMAP Alter MSC 1994 World Users Conf Proc Paper No 10 June 1994 Flanigan Christopher C Implementation of the IRS Dynamic Reduction Method in MSC NASTRAN The MSC 1990 World Users Conf Proc Vol I Paper No 13 March 1990 Fox Gary L Evaluation and Reduction of Errors Induced by the Guyan Transformation Tenth NASTRAN Users Colloq pp 233 248 May 1982 NASA CP 2249 Komzsik L Dilley G Practical Experiences with the Lanczos Method Proc of the MSC NASTRAN Users Conf Paper No 18 March 1985 Kuang Jao Hwa Lee Chung Ying On a Guyan Reduction Recycled Eigen Solution Technique The 2nd Annual MSC Taiwan Users Conf Paper No 13 October 1990 Levy Roy Guyan Reduction Solutions Recycled for Improved Accuracy NASTRAN Users Exper pp 201 220 September 1971 NASA TM X 2378 Maekawa Seiyou Effect of Guyan Reduction and Generalized Dynamic Reduction The Second MSC NASTRAN User s Conf in Japan October 1984 in Japanese Mera A MSC NASTRAN Normal Mode Analysis with GDR An Evaluation of Limitations MSC NASTRAN Users Conf Proc Paper No 27 March 1985 Mera Andrew Static Reduction and Symmetry Trans
180. Td 0 w CO No No No ho NO ho DO OOO CUR AZZ 317352E 21 077055E 19 104969E 19 131340E 19 146708E 19 144943E 19 129652E 19 109444E 19 lt pLOUGZE 19 pao 410901E 19 X Y O UT CURVE ID 11 5 PARTIAL OUTPUT FROM bd08bar8 f06 T1 2 016639E 20 0 u E36 733E 20 359 4255 4 228285E 19 QUUD dure doll 288 0493 5 003335E 19 270 0177 1 560747E 19 199 3224 ILS LI 9E 20 190 2228 0 0 20 0 X Y eae Sy oT CURVE ID LIEG gss boom 11 C C Er Restarts in Dynamic Analysis DISP GAC T2 0 CO rn 3 WWNNND h2 606407E 21 430443E 21 232167E 18 2175425E 18 401124E 18 724639E 18 204978E 18 684523E 18 053196E 18 196586E 17 de LA Oe P U T XMIN FRAME ALL DATA 000000E 00 000000E 00 OMPLEX T2 4 838324E 19 0 5 467976E 19 359 0918 1 831657E 16 169 4034 1 747242E 16 145 7774 1 561973E 16 122 0074 aby 943312E 17 32 8670 Owe T1202E 19 19 2229 0 0 9 0 PUT SUM XMIN FRAME ALL DATA 000000E 01 000000E 00 000000E 01 000000E 00 SUMMARY 6 5 M PRE EMENT T3 491364 75 02 7 628838E 05 ARARARARARARA 099007E 03 180374E 03 255632E 03 308840E 03 328179E 03 313660E 03 212623E 03 2 607416E 03 2 775622E 03 XMAX FRAME ALL DATA QOODODE 01 999959E 01 kKkKKKK DISPLACEMENT VECTOR R1 C OC C OO ccc C0 CoO R
181. Vibration Characteristics of a Steering Wheel According to Geometric Variations MSC 1994 Korea Users Conf Proc December 1994 in Korean Korean A Study on Idle Vibration Analysis Technique Using Total Vehicle Model MSC 1994 Korea Users Conf Proc December 1994 in Korean NX Nastran Basic Dynamic Analysis User s Guide I 19 Appendix References and Bibliography Korean Vibration Analysis for Outercase in Drum Washer and Floor MSC 1994 Korea Users Conf Proc December 1994 in Korean Ahmad M Fouad Guile Carl W Analysis of Coupled Natural Frequencies of Thin Walled Beams with Open Cross Sections Using MSC NASTRAN The MSC 1990 World Users Conf Proc Vol I Paper No 15 March 1990 Allen James J Martinez David R Techniques for Implementing Structural Model Identification Using Test Data Sandia National Laboratories June 1990 SAND90 1185 Arakawa H Murakami T Ito H Vibration Analysis of the Turbine Generator Stator Frame The MSC 1988 World Users Conf Proc Vol II Paper No 43 March 1988 Armand Sasan Lin Paul Influence of Mass Moment of Inertia on Normal Modes of Preloaded Solar Array Mast The MSC 1992 World Users Conf Proc Vol I Paper No 12 May 1992 Arora Tejbir Birmingham Lily Application of MSC NASTRAN Superelement Dynamic Reduction Techniques for the Vertical Launching System The MSC 1988 World Users Conf Proc Vol I Paper No 39 March 1988 Barne
182. Vol I Paper No 11 March 1988 Yang Jackson C S Frederick Diana L Application of NASTRAN in Nonlinear Analysis of a Cartridge Case Neck Separation Malfunction NASTRAN Users Exper pp 389 396 September 1975 NASA TM X 3278 Young K J Mitchell L D On the Performance of Various Kinds of Rod and Beam Mass Matrices on a Plane Frame Structure Proc of IMAC IX Vol I pp 1057 1065 April 1991 DYNAMICS ANALYSIS TEST CORRELATION Allen James J Martinez David R Techniques for Implementing Structural Model Identification Using Test Data Sandia National Laboratories June 1990 SAND90 1185 Anker J C Checks that Pay Proc of the MSC NASTRAN Eur Users Conf May 1984 Blakely Ken Howard G E Walton W B Johnson B A Chitty D E Comparison of a Nonlinear Dynamic Model of a Piping System to Test Data Tth Int Conf on Struct Mech in Reactor Tech August 1983 Blakely Ken Walton W B Selection of Measurement and Parameter Uncertainties for Finite Element Model Revision 2nd Int Modal Analysis Conf February 1984 I 10 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Blakely Ken Updating MSC NASTRAN Models to Match Test Data The MSC 1991 World Users Conf Proc Vol II Paper No 50 March 1991 Blakely Ken Revising MSC NASTRAN Models to Match Test Data Proc of the 9th Int Modal Analysis Conf April 1991 Blakely Ken Get the M
183. a a a ee ee PPP P P Pe ee ee at aana et a a a gt an utut uut utut uut a aM MM a a i a MM SS a a a a a Figure 3 5 Two DOF Model The masses are constrained to deflect in only the y direction The example illustrates normal modes analysis SOL 103 using automatic selection of the Householder or modified Householder method METHOD AHOU on the EIGR entry The eigenvectors are normalized to the unit value of the largest displacement component NORM MAX on the EIGR entry The input file is shown in Figure 3 6 3 20 TIME 5 N FILE bd03two dat IWO DOF SYSTEM S CHAPTER 3 ORMAL MODES SOL 103 NORMAL MODES ANALYSIS CEND 2 TITLE TWO DOF SYSTEM SUBTITLE S SELECT SPC 10 SELECT METHOD S SELECT DISPLACEMENT 3 SET 2 SGECFORCE SET 3 ELFORCE S SPC EIGR 99 NORMAL MODES ANALYSIS ENTRY OUTPUT SET 1 1 2 2 11 12 3 BEGIN BULK 1 SEIGR SID METHOD Fl F2 NE ND EIG EIG NORM G EIGR 99 AHOU 0 EIG1 MAX S GRID 1 0 GRID 2 0 GRID 3 0 C 2 La 0 GRDSET 13456 CONM2 1 1 0 1 CONM2 2 2 10 0 200 EIG1 ooo NX Nastran Basic Dynamic Analysis User s Guide CELASZ ll 100 0 CELAS2 12 1 0E4 SPC 10 3 2 S ENDDATA 1 2 22 2232 Real Eigenvalue Analysis Figure 3 6 Input File for the Two DOF Model The printed output is shown in Figure 3 7 The eigenvalue summary lists the eigenvalue W2 circular frequency W radians
184. a DLOAD Case Control command or a DLOAD Bulk Data entry DAREA Identification number of DAREA entry that defines A Integer gt 0 DELAY Identification number of DELAY entry that defines t Integer 0 Excitation function as defined below Additional information is in Enforced Motion Integer Excitstion Function 0 or blank TYPE p Enforced Displacement B Enforced Velocity B JEnforced Acceleration Values 1 2 and 3 apply only to the large mass method for enforced motion TID TABLEDi entry that defines F t Time Dependent Loads TLOAD2 Entry The TLOAD2 entry is a general analytical form with which to define a time dependent load The value of the force at a particular instant in time is determined by evaluating the analytic function at the specific time You enter the appropriate constants in the function The TLOAD2 entry defines dynamic excitation in the form t lt T1 t ort gt 124 T P t Pa At e cos 2mFi P Tl t st lt J24 T Equation 6 26 where DAREA DELAY TYPE NX Nastran Basic Dynamic Analysis User s Guide 6 15 Chapter 6 Transient Response Analysis Field Contents SID Set ID defined by a DLOAD Case Control command DAREA Identification number of DAREA entry that defines A Integer gt 0 DELAY Identification number of DAREA entry that defines t Integer gt 0 TYPE Defined as on the TLOAD1 entry T1 T2 Time constants F Frequency cyc
185. a Reactor Core Due to Seismic Loading The MSC 1987 World Users Conf Proc Vol I Paper No 26 March 1987 Hirano Tohru Visual Evaluation Method for the Vibration Analysis Utilizing a Super Intelligent Color Graphic Display The First MSC NASTRAN User s Conf in Japan October 1983 in Japanese Hsueh W c Hsui T C Yen K Z Y Modal and Frequency Response Analyses of Vertical Machining Center Structures VC65 The Fifth Annual MSC Taiwan Users Conf Proc November 1993 Huang Jieh Shan Detect the Variety of Structural System by the Vibration Test The 2nd Annual MSC Taiwan Users Conf Paper No 11 October 1990 in Chinese Igarashi Mitsuo Eigenvalue Analysis of Shaft Supported by Anti Isotropic Bearing The Fifth MSC NASTRAN User s Conf in Japan October 1987 in Japanese Ito Hiroyuki Application of Modal Analysis Technique for Cars The Fourth MSC NASTRAN User s Conf in Japan October 1986 in Japanese Jabbour K N Normal Mode Analysis of the Radio Astronomy Explorer RAE Booms and Spacecraft NASTRAN Users Exper pp 237 250 September 1971 NASA TM X 2378 Jasuja S C Borowski V J Anderson D H Finite Element Modeling Techniques for the Simulation of Automotive Powertrain Dynamics Proc of the 5th Int Modal Analysis Conf Vol II pp 1520 1530 April 1987 Jiang K C Gahart R Analysis and Modal Survey Test of Intelsat VITA Deployed Solar Array MSC 1994 World Users
186. a synchronous manner The structural configuration does not change its basic shape during motion only its amplitude changes If differentiation of the assumed harmonic solution is performed and substituted into the equation of motion the following is obtained wW M b sin t K o sinwt 0 Equation 3 3 which after simplifying becomes 3 4 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis K w M o 0 Equation 3 4 This equation is called the eigenequation which is a set of homogeneous algebraic equations for the components of the eigenvector and forms the basis for the eigenvalue problem An eigenvalue problem is a specific equation form that has many applications in linear matrix algebra The basic form of an eigenvalue problem is A AlI x 0 Equation 3 5 where A square matrix eigenvalues I identity matrix X eigenvector In structural analysis the representations of stiffness and mass in the eigenequation result in the physical representations of natural frequencies and mode shapes Therefore the eigenequation is written in terms of K w and M as shown in Equation 3 4 with W l There are two possible solution forms for Equation 3 4 1 Ifdet ll e M 0 the only possible solution is id 0 Equation 3 6 This is the trivial solution which does not provide any valuable information from a physical point of view since it represents the case o
187. able 2 2 lists consistent units for common variables There are several ways to verify units For mass you can print the results from the grid point weight generator and verify that the mass is correct For stiffness you can apply a simple load and verify that the resulting static displacements seem reasonable For both you can verify that the natural frequencies are reasonable These checks assume that you have enough knowledge about your structure to know when the results are reasonable and when a mistake has been made In other words running small models and or proceeding through dynamic analysis via the steps outlined in the previous section are necessary in order to be confident that the correct units are specified 10 4 Mass Mistakes with mass primarily involve mistakes in mass units as described in the previous section A common mistake is to mix mass and weight units Using PARAM WTMASS does not solve this problem because it scales all mass and weight input except certain types of direct input matrices and still leaves the mixture of units Also the use of PARAM WTMASS can have unwanted effects as well because it also scales the large mass used in enforced motion thereby scaling the value of the enforced motion input In order to reduce the chances for error it is recommended that only mass units be used everywhere Therefore avoid the use of weight input wherever possible as well as the use of PARAM WTMASS One way to verify mas
188. acteristic frequencies of the structure 6 12 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis Dynamic Data Recovery in Modal Transient Response Analysis In modal transient response analysis two options are available for recovering displacements and stresses mode displacement method and matrix method Both methods give the same answers although with cost differences The mode displacement method computes the total physical displacements for each time step from the modal displacements and then computes element stresses from the total physical displacements The number of operations is proportional to the number of time steps The matrix method computes displacements per mode and element stresses per mode and then computes physical displacements and element stresses as the summation of modal displacements and element stresses Costly operations are proportional to the number of modes Since the number of modes is usually much less that the number of time steps the matrix method is usually more efficient and is the default The mode displacement method can be selected by using PARAM DDRMM 1 in the Bulk Data The mode displacement method is required when time frozen deformed structure plots are requested see Plotted Output The mode acceleration method Advanced Dynamic Analysis Capabilities is another form of data recovery for modal transient response analysis This method can provide better
189. actor Core Using Modal Synthesis Proc of the 3rd Int Modal Analysis Conf Vol 2 pp 996 1000 June 1985 Hodgetts P A Maitimo F M Wijker J J Dynamic Analysis of the Polar Platform Solar Array Using a Multilevel Component Mode Synthesis Technique Proc of the 19th MSC European Users Conf Paper No 15 September 1992 NX Nastran Basic Dynamic Analysis User s Guide I 15 Appendix References and Bibliography Ichikawa Tetsuji Hagiwara Ichiro Frequency Response Analysis of Large Scale Damped Structures Using Component Mode Synthesis Nippon Kikai Gakkai Ronbunshu C Hen Transactions of the Japan Society of Mechanical Engineers Part C v 60 n 569 Jan 1994 Jasuja S C Borowski V J Anderson D H Finite Element Modeling Techniques for the Simulation of Automotive Powertrain Dynamics Proc of the 5th Int Modal Analysis Conf Vol II pp 1520 1530 April 1987 Jay Andrew Lewis Bryan Stakolich Ed Effect of Time Dependent Flight Loads on Turbofan Engine Performance Deterioration ASME J of Engineering for Power Vol 104 No 3 July 1982 Kammer Daniel C Jensen Brent M Mason Donald R Test Analysis Correlation of the Space Shuttle Solid Rocket Motor Center Segment J of Spacecraft Vol 26 No 4 pp 266 273 March 1988 Kasai Manabu Generalized CMS Employing External Superelements The Fourth MSC NASTRAN User s Conf in Japan October 1986 in Japanese Kasai Manabu Representation
190. ad they form the following complex stiffness matrix 5 4 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis K 1 iG K 1 G Kz Equation 5 7 where K global stiffness matrix G overall structural damping coefficient PARAM G Kr element stiffness matrix Gg element structural damping coefficient GE on the MATi entry When the above parameters and or coefficients are specified they are automatically incorporated into the stiffness matrix and therefore into the equation of motion for the solution All of the forms of damping can be used in the same analysis and their effects are added together In frequency response analysis it is not necessary to assume an equivalent viscous form for structural damping since the solution is complex Therefore a complex stiffness matrix is allowed 5 3 Modal Frequency Response Analysis Modal frequency response analysis 1s an alternate approach to computing the frequency response of a structure This method uses the mode shapes of the structure to reduce the size uncouple the equations of motion when modal or no damping is used and make the numerical solution more efficient Since the mode shapes are typically computed as part of the characterization of the structure modal frequency response is a natural extension of a normal modes analysis As a first step in the formulation transform the variables from physical coordinates u w to modal
191. ain energy printed in UIM 3035 Note that the three rigid body modes have frequencies of 0 0 Hz The SUPORT entry provides cleaner mode shapes than those shown in Figure 4 5 as illustrated by the purely x translation y translation and z rotation eigenvectors shown in Figure 4 6 REAL EIGENVALUES MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZ NO ORDER MASS STIFFNES 1 1 1 866121E 11 4 319862E 06 6 875275E 07 1 000000E 00 1 866121F 2 2 1 819082E 09 4 265070E 05 6 788069E 06 1 000000E 00 1 819082 F 3 3 2 000299E 09 4 472470E 05 7 118156E 06 1 000000E 00 220002995 4 4 6 483918E 03 8 052278E 01 1 281560E 01 1 000000E 00 6 483918R 5 5 AcT3227 2ETU04 2 175379E 02 3 462222E 01 1 000000E 00 4 132272 6 6 1 751285E 05 4 184836E 02 6 660372E 01 1 000000E 00 1 751285 F EIGENVALUE 1 866121E 11 CYCLES 6 875275E 07 REAL EIGENVECTOR NO 1 POINT ID TYPE T1 T2 T3 R1 R2 R3 1 G 4 273806E 34 2 470432E 01 0 0 0 0 0 0 1 067134E 01 2 G 4 273806E 34 2 790573E 01 0 0 0 0 0 0 1 067134E 01 3 G 4 273806E 34 3 110713E 01 0 0 0 0 0 0 1 067134E 01 4 G 4 273806E 34 3 430853E 01 0 0 0 0 0 0 1 067134E 01 5 G 4 273806E 34 3 750993E 01 0 0 0 0 0 0 1 067134E 01 6 G 4 273806E 34 4 071134E 01 0 0 0 0 0 0 1 067 1342 01 7 G 4 273806E 34 4 391274E 01 0 0 0 0 0 0 1 067134E 01 8 G 4 273806E 34 4 711414E 01 0 0 0 0 0 0 1 067134E 01 9 G 4 273806E 34 5 031555E 01 0 0 0 0 0 0 1 067134E 01 10 G 4 273806E 34 5 351695E 01 0 0 0 0
192. al modes is in general the most expensive operation Therefore a common application of restart is the performance of a transient or frequency response analysis by restarting from the normal modes calculation which was saved in the database from a previous run This restart process avoids the recalculation of the normal modes The cost of restarting is measured in the disk space required to store data blocks for subsequent use Judging whether to not save data blocks and simply rerun the analysis or to save data blocks for restarting is determined by several factors such as the amount of available disk space and your computer s solution speed Note that the database can be copied to tape which then provides you with more free disk space When you are ready to perform a restart this database can then be copied from the tape back to your disk 8 2 Automatic Restarts NX Nastran s Executive System effectively uses modern database technology Among its many features the Executive System implements the NASTRAN Data Definition Language NDDL With NDDL NX Nastran is able to use automatic restart logic with the superelement solution sequences For more information on the NDDL refer to the NX Nastran DMAP Programmer s Guide In order to maintain upward compatibility we retained the old solution sequences and added a new series of superelement solution sequences These solution sequences are also known as the Structured Solution Sequences soluti
193. all of the reduction methods The basis of the method is to attach artificial masses to the structure at the degrees of freedom where the motion is to be enforced These large masses should be orders of magnitude larger than the total mass or the moment of inertia of the structure A survey of the literature shows recommendations for mass ratios ranging from 10 to 108 with a value of 109 as the most common recommendation The mass ratio affects both the accuracy and numerical conditioning and must be adjusted in a compromise that meets both criteria With regard to load accuracy the error in the approximation is inversely proportional to the ratio A ratio of 10 causes an error of ten percent at resonance for a mode with one half percent of damping which represents an extreme case Off resonance excitation or higher damping ratios result in lower errors Numerical conditioning problems are much more difficult to predict The Lagrange Multiplier Method Another method to enforce motion is the Lagrange multiplier method In this method the input motion function is described by a constraint equation This method provides better accuracy than the large mass method where the numerical error introduced 1s proportional to the large mass The formulation introduces an indefinite system of linear equations where some numerical problems may arise from the fact that the system matrix contains terms that have dimensions of stiffness as well as nondimensiona
194. ame modes 3 32 OUTPUT FROM G RID POINT REFERENCE POINT M O 8 027376E 01 0 000000E 00 0 000000E 00 0 000000E 00 0 000000E 00 8 027376E 01 0 000000E 00 2 808118E 01 0 000000E 00 0 000000E 00 8 027376 E 01 2 179473E 01 0 000000E 00 2 808118E 01 2 179473E 01 2 325008E 03 2 808118E 01 0 000000E 00 7 610537E 01 2 153940E 03 2 179473E 01 7 610537E 01 0 000000E 00 2 662697E 03 S 1 000000E 00 0 000000E 00 0 000000E 00 1 000000E 00 0 000000E 00 0 000000E 00 DIRECTION NX Nastran Basic Dynamic Analysis User s Guide WEIGHT 0 c 0 aa zx l Ta 808118E 01 2 7 610537E 01 000000E 00 610537E 01 153940E 03 020870E 04 626398E 02 0 000000E 00 0 000000E 00 1 000000E 00 ONNO GENERATOR 179473E 01 000000E 00 662697E 03 626398E 02 437676E 03 X MASS AXIS SYSTEM X Y Z S 8 027376E 01 8 027376E 01 8 027376E 01 7 8 3 2 6 9 4 MASS 9509408E 02 764180E 01 962963E 01 017097E 03 905332E 02 976128E 01 891269E 04 Real Eigenvalue Analysis ze ess 0 Q000000E 00 9 480728E 01 9 480728E 01 peer G Zi zs 2 715050E 01 3 498177E 01 0 000000E 00 3 498177E 01 2 715050E 01 I S 8 764180E 01 3 962963E 01 2 011031E 03 2 217236E 01 2 217236E 01 1 630595E 03 I Q 7 448741E 02 1 630595E 03 Q 9 976128E 01 5 012719E 04 6 905355E 02 4 555999 E 04 4 686146E 04 9 999998E 01 Fig
195. ampanile P Pisino E Testi R Manzilli G Minen D Flexible Structures in Adams Using Modal Data from NASTRAN Proc of the 21st MSC European Users Conf Italian Session September 1994 Carlson Mark Applications of Finite Element Analysis for an Improved Musical Instrument Design MSC 1996 World Users Conf Proc Vol I Paper No 8 June 1996 Carneiro S H S Duarte J A A Mendonca C B Theoretical and Experimental Modal Analysis of the VLS Satellite Launcher Vehicle Bent Proc of the 2nd MSC NASTRAN Users Conf in Brazil Paper No 3 March 1993 in Portuguese Case William R Jr NASTRAN DMAP Alter for Determining a Local Stiffness Modification to Obtain a Specified Eigenvalue NASTRAN Users Exper pp 269 284 September 1973 NASA TM X 2893 Case William R A NASTRAN DMAP Procedure for Calculation of Base Excitation Modal Participation Factors Eleventh NASTRAN Users Colloq pp 113 140 May 1983 Cattani E Micelli D Sereni L Cocordano S Cylinder Block Eigenfrequencies and Eigenvectors Prediction with a Linear Brick and Wedge Finite Element Model Proc of the 19th MSC European Users Conf Paper No 16 September 1992 Chang Cuann yeu Chang Yuan bing Using MSC NASTRAN to Obtain Modal Parameters The MSC 1988 World Users Conf Proc Vol I Paper No 21 March 1988 Chargin M L Dunne L W Herting D N Nonlinear Dynamics of Brake Squeal MSC 1996 World Users
196. amping since the peak response occurs during the first cycle of response Damping in a long duration transient excitation such as an earthquake can make a difference in the peak response on the order of 10 to 20 or so but this difference is small when compared to the other modeling uncertainties Therefore it is often conservative to ignore damping in a transient response analysis For frequency response analysis however the value of damping is critical to the value of the computed response at resonance since the dynamic magnification factor is inversely proportional to the damping value One way to verify the accuracy of the modal damping ratio input is to run the modal frequency response across the half power bandwidth of the modal frequencies of interest as shown in Figure 10 2 Peak Response Peak Halt Power Point m Response ye f fy Frequency Halt Power Bandwidth Figure 10 2 Half Power Bandwidth For lightly damped structures Z lt 0 1 the approximate relationship between the critical damping ratio the half power bandwidth f f1 and the resonant frequency f is 10 6 NX Nastran Basic Dynamic Analysis User s Guide Guidelines for Effective Dynamic Analysis Edw 2 OF wee Equation 10 1 Another approximate way to verify damping is to run transient response analysis and look at the successive peak values of the free vibration response as shown in Figure 10 3 In direct transient
197. ample TABDMP1 Table 6 1 Example TABDMPI Interpolation Extrapolation Computed With the modal equations in the form of Equation 6 22 an efficient uncoupled analytical integration algorithm is used to solve for modal response as decoupled SDOF systems Each of the modal responses is computed using NX Nastran Basic Dynamic Analysis User s Guide 6 11 Chapter 6 Transient Response Analysis 0 No initial conditions for modal transient response p b 2m S Wy bt 2m E COS af E t sin wt bt 2m I bt 2m te E p t sinw t t dt ntu 0 Equation 6 24 In a modal transient analysis you may add nonmodal damping CVISC CDAMPi GE on the MAT entry or PARAM G With nonmodal damping there is a computational penalty due to the coupled B matrix causing the coupled solution algorithm to be used In modal transient response analysis it is recommended that you use only modal damping TABDMP1 If discrete damping is desired direct transient response analysis is recommended Note that there are no nonzero initial conditions for modal transient response analysis Mode Truncation in Modal Transient Response Analysis It is possible that not all of the computed modes are required in the transient response solution Often only the lowest few suffice for dynamic response calculation It is quite common to evaluate the frequency content of transient loads and determine a frequency above which
198. ample is NX Nastran Basic Dynamic Analysis User s Guide G 9 Appendix G Grid Point Weight Generator 707 7070 0 0 0100000 5 866 0 0 0 010 0000 707 7070 0 0 0010000 86 5 0 0 0 001 0000 D 0 0 10 0 000 1 000 0 0 1 0 0 00 0 1 000 0 0 0 707 707000 0100 0 0 1 5 86600 10 100 0 0 0 707 707 000 1010 0 0 5 866 5 01 0 5010 0 0 O0 0 0 101000106 1116 0 0 0 es 6 poi Grid 1 Grid 2 Grid 3 Grid 4 Equation G 9 Using the global transformation matrix D the rigid body mass matrix about the reference point in the basic coordinate system MO is obtained by Equation G 10 M0 D MJJ D Equation G 10 For the example MO is determined to be 925 933 0 0 2 2967 933 10 75 0 3 0 6 058 M0 0 0 20 5 10 0 3 5 8 25 15 Z 0 10 2 5 95 0 296 6 0058 Q0 15 0 7 496 Equation G 11 Comparing the results shown in Figure G 11 to MO generated by the GPWG module Figure G 2 shows the matrices to be numerically the same 3 The next step is to inspect the MO to determine whether the basic coordinate system can be used as the principal mass directions The principal mass axes are axes that have no coupling between the translational mass components For real structures there is no coupling in the translational mass terms in the inertia matrix However with inconsistent scalar masses CONM1 CMASSi or DMIG you may define any type of mass matrix you desire To determine whether coupling exis
199. amplitude and phase parts of a matrix element If the matrix is real TIN 1 or 2 then Bi must be blank DMIG Case Control User Interface In order to include these matrices the Case Control must contain the appropriate K2GG M2GG B2GG or K42GG command Once again only the g type DMIG input matrices are included in this guide Examples 1 K2GG mystiff The above Case Control command adds terms that are defined by the DMIG Bulk Data entries with the name mystiff to the g set stiffness matrix 2 M2GG yourmass The above Case Control command adds terms that are defined by the DMIG Bulk Data entries with the name yourmass to the g set mass matrix 3 B2GG ourdamp The above Case Control command adds terms that are defined by the DMIG Bulk Data entries with the name ourdamp to the g set viscous damping matrix 4 K42GG strdamp The above Case Control command adds terms that are defined by the DMIG Bulk Data entries with the name strdamp to the g set structural damping matrix Use of the DMIG entry for inputting mass and stiffness 1s illustrated in one of the examples in Real Eigenvalue Analysis 2 16 NX Nastran Basic Dynamic Analysis User s Guide Chapter 3 Real Eigenvalue Analysis e Overview e Reasons to Compute Normal Modes e Overview of Normal Modes Analysis e Methods of Computation e Comparison of Methods e User Interface for Real Eigenvalue Analysis e Solution Control for Norma
200. and equilibrium iterations and convergence checks are required at each load step The new CBUSH element introduced in Version 69 adds some capabilities in this area also In addition gap elements CGAP can be used in conjunction with elastic elements to produce systems with piece wise linear force deflection curves This process also requires the additional computations of nonlinear element stiffness matrix generation equilibrium iteration and convergence testing Nonlinear analyses requiring these additional computations can be substantially more costly than an equivalent linear analysis even if the nonlinearities are relatively few in number An efficient technique called the pseudoforce method exists in NX Nastran in which the localized nonlinearities are treated so that they require no additional computer time when compared to a purely linear analysis In this method which is available only for transient response solutions SOLs 109 and 112 for example deviations from linearity are treated as additional applied loads The dynamic equations of motion are written as M a t LBJ att Kies iPr 0 1NGOO Equation 11 2 11 8 NX Nastran Basic Dynamic Analysis User s Guide Advanced Dynamic Analysis Capabilities where M B and K denote the system mass damping and stiffness matrices respectively The vectors and u denote applied nodal loads and system displacements respectively as functions of time The vec
201. and used in aeroelastic analysis The modal coordinate set X is separated into zero frequency modes x and elastic finite frequency modes X For dynamic analysis by the modal method the extra points u are added to the modal coordinate set X to form the h set as shown in Figure C 2 C 2 NX Nastran Basic Dynamic Analysis User s Guide The Set Notation System Used in Dynamic Analysis The parameter PARAM USETPRT can be used to print of lists of degrees of freedom and the sets to which they belong Different values of the PARAM create various tables in the printed output The supersets formed by the union of other sets have the following definitions Mutually Exclusive Sets Combined Sets 1 Figure C 1 Combined Sets Formed from Mutually Exclusive Sets The set names have the definitions described 1n Table C 2 Table C 2 Sets in NX Nastran Mutually Exclusive Sets Points eliminated by multipoint constraints Points eliminated by single point constraints that are included in boundary condition changes and by the automatic SPC feature Points eliminated by single point constraints that are listed on grid point Bulk Data entries NEP NN Points omitted by structural matrix partitioning Generalized coordinates for dynamic reduction or component mode synthesis Reference points used to determine free body motion The free boundary set for component mode synthesis or dynamic reduction b Coordinates f
202. ang Bo Ping Minimum Weight Design of Structures with Natural Frequency Constraints Using MSC NASTRAN The MSC 1988 World Users Conf Proc Vol II Paper No 60 March 1988 Welte Y Vibration Analysis of an 8MW Diesel Engine Proc of the MSC NASTRAN Eur Users Conf May 1986 West Timothy S Approximate Dynamic Model Sensitivity Analysis For Large Complex Space Structures MSC 1996 World Users Conf Proc Vol I Paper No 6 June 1996 Wijker J J Substructuring Technique Using the Modal Constraint Method Proc of the MSC NASTRAN Eur Users Conf June 1983 Wijker J J MSC NASTRAN Normal Mode Analysis on CRAY Computers Proc of the MSC NASTRAN Eur Users Conf June 1983 Yang Howard J Sorted Output in MSC NASTRAN Proc of the Conf on Finite Element Methods and Technology Paper No 4 March 1981 Yen K Z Y Hsueh W C Hsui T C Chatter Suppression of a CNC Lathe in Inside Diameter Cutting The Sixth Annual MSC Taiwan Users Conf Proc Paper No 4 November 1994 Zhu H Knight D Finite Element Forced Response Analysis on the Mondeo Front End Accessory Drive System Proc of the 20th MSC European Users Conf September 1993 DYNAMICS RANDOM RESPONSE Barnett Alan R Widrick Timothy W Ludwiczak Damian R Combining Acceleration and Displacement Dependent Modal Frequency Responses Using An MSC NASTRAN DMAP Alter MSC 1996 World Users Conf Proc Vol II Paper No 17
203. ar to that for normal modes analysis see Real Eigenvalue Analysis except that damping is added and the eigenvalue is now complex In addition the mass damping and stiffness matrices may be unsymmetrical and they may contain complex coefficients Complex eigenvalue analysis is controlled with the EIGC Bulk Data entry similar to the EIGRL or EIGR Bulk Data entries for normal modes analysis There are four methods of solution upper Hessenberg complex Lanczos determinant search and inverse power Complex eigenvalue analysis is available as a direct method SOL 107 in which the equations are of the same size as the number of physical variables Complex eigenvalue analysis is also available as a modal method SOL 110 in which undamped modes are first computed and then are used to transform the matrices from physical to modal variables 11 4 Response Spectrum Analysis Response spectrum analysis is an approximate method of computing the peak response of a transient excitation applied to a simple structure or component This method is used in civil engineering to predict the peak response of a component on a building that is subjected to earthquake excitation it is also used in aerospace engineering to predict the peak response of equipment in a spacecraft that is subjected to an impulsive load due to stage separation Because NX Nastran Basic Dynamic Analysis User s Guide 11 3 Chapter 11 Advanced Dynamic Analysis Capabilities it
204. as a function of time e This time varying load application induces time varying response displacements velocities accelerations forces and stresses These time varying characteristics make dynamic analysis more complicated and more realistic than static analysis 1 2 Equations of Motion The basic types of motion in a dynamic system are displacement u and the first and second derivatives of displacement with respect to time These derivatives are velocity and acceleration respectively given below l du l u v velocity dt i a acceleration du d di Equation 1 1 1 2 NX Nastran Basic Dynamic Analysis User s Guide Fundamentals of Dynamic Analysis Velocity and Acceleration Velocity is the rate of change in the displacement with respect to time Velocity can also be described as the slope of the displacement curve Similarly acceleration is the rate of change of the velocity with respect to time or the slope of the velocity curve Single Degree of Freedom System The most simple representation of a dynamic system is a single degree of freedom SDOF system see Figure 1 1 In an SDOF system the time varying displacement of the structure a t t is defined by one component of motion u t Velocity and acceleration are derived from the displacement mass inertia damping energy dissipation stiffness restoring u t force applied force p t displacement of mass
205. ase Control output requests Eigenvectors are printed only if a DISPLACEMENT or VECTOR command is included These requests are summarized in Table 3 4 Table 3 4 Eigenvalue Extraction Output Requests Grid Output Requests the eigenvector mode shape for a set of grid DISPLACEMENT or VECTOR onis Requests the grid point force balance table to be computed GPFORCE for each mode for a set of grid points Requests grid point stresses to be computed for a set of grid points This request must be accompanied by the ELSTRESS Case Control re quest and the definition of stress surfaces and or stress volumes in the OUTPUT POST section of the Case Control Requests forces of single point constraint to be computed for a set of grid points for each mode Element Output ELSTRESS or STRESS Requests the computation of modal stresses for a set of elements for each mode Requests the computation of modal element strain energies SE for a set of elements for each mode ELFORCE or FORCE Requests the computation of modal element forces for a set of elements for each mode SPCFORCE Requests the computation of modal element strains for a set of elements Miscellaneous A special Case Control request that permits selective output MODES l requests to be processed on selective modes STRAIN Bulk Data Section In addition to Bulk Data entries required to define the structural model the only other required Bulk Data entry is the eige
206. ass matrices contain uncoupled translational components of mass Coupled mass matrices contain translational components of mass with coupling between the components The CBAR CBEAM and CBEND elements contain rotational masses in their coupled formulations although torsional inertias are not considered for the CBAR element Coupled mass can be more accurate than lumped mass However lumped mass is more efficient and is preferred for its computational speed in dynamic analysis The mass matrix formulation is a user selectable option in NX Nastran The default mass formulation is lumped mass for most NX Nastran finite elements The coupled mass matrix formulation is selected using PARAM COUPMASS 1 in the Bulk Data Table 2 1 shows the mass options available for each element type Table 2 1 Element Mass Types Element Type CONMi CONROD ee ee CONEAX 0X j J 2 2 NX Nastran Basic Dynamic Analysis User s Guide Finite Element Input Data c pi 2 1 Element Mass Types Element Type Lumped Mass Coupled Mass Element Type Lumped Mass Coupled Mass cMAssi TX ICSHEAR X lCouple mass is selected by PARAM COUPMASS 1 The NX Nastran coupled mass formulation is a modified approach to the classical consistent mass formulation found in most finite element texts The NX Nastran lumped mass is identical to the classical lumped mass approach The various formulations of
207. astran Basic Dynamic Analysis User s Guide B 1 Appendix B Nomenclature for Dynamic Analysis b Damping cr Critical Damping M Stiffness Applied Force Circular Frequency ge 8 8 H Circular Natural Frequency Eigenvalue Eigenvalue Frequency lh uu 0 E Lr Natural Frequency e H Period E Y Damped Circular Natural Frequency Damping Ratio Quality Factor Phase Angle L DD KO d Logarithmic Decrement B 2 Structural Properties Geometry i Length A Area B 2 NX Nastran Basic Dynamic Analysis User s Guide Stiffness E G J Damping G Gr Nomenclature for Dynamic Analysis Young s Modulus Shear Modulus Torsional Constant Poisson s Ratio Area Moment of Inertia Mass Density Mass Density Weight Density Polar Moment of Inertia Overall Structural Damping Coefficient Element Structural Damping Coefficient B 3 Multiple Degree of Freedom System u pi ii 61 TA Displacement Vector Velocity Vector Acceleration Vector Mode Shape Vector Rigid Body Modes i th Modal Displacement i th Modal Velocity NX Nastran Basic Dynamic Analysis User s Guide B 3 Appendix B Nomenclature for Dynamic Analysis E i th Modal Acceleration Ht j th Generalized Mass K fi j th Generalized Stiffness A k k th Eigenvalue M Matrix M Rigid Body Mass Matrix A Stiffness Matrix A E Element Stiffness Matrix E Damping Matrix F Force Matrix B 4
208. at only one frequency which should be 0 0 Hz Compare the 0 0 Hz displacement results to the static analysis displacement results The results should be the same if direct frequency response without structural damping is used If the results are not equal then there is probably an error in the specification of the dynamic load and you should check the LSEQ and DAREA entries If modal frequency response without structural damping is used then the 0 0 Hz results should be close to the static results the difference is due to modal truncation Next apply the load across the entire frequency range of interest If you are running modal frequency response then make sure that you have enough modes to ensure accurate results for even the highest forcing frequency Also be sure to have a small enough Af in order to accurately capture the peak response Verify these results for reasonableness it may be easier to look at magnitude and phase results instead of real and imaginary results which are the default values If your ultimate goal is a transient response analysis for which damping 1s to be neglected then the frequency response analysis can also omit damping However if damping is to be included then use the correct damping in your frequency response analysis The proper specification of damping can be verified by looking at the half power bandwidth Plots are important at this stage to assist in results interpretation X Y plots are necessary
209. ation analysis frequency range of interest For buckling analysis eigenvalue range of interest Real or blank 5 x 1016 lt V1 V2 x5 x 1016 ND Number of eigenvalues and eigenvectors desired Integer gt 0 or blank MSGLVL Diagnostic level 0 lt Integer lt 4 Default 0 MAXSET Number of vectors in block or set 1 Integer lt 15 Default 7 SHFSCL Estimate of the first flexible mode natural frequency Real or blank NORM Method for normalizing eigenvectors Character MASS or MAX NX Nastran Basic Dynamic Analysis User s Guide 3 13 Chapter 3 Real Eigenvalue Analysis Field Contents MASS Normalize to unit value of the generalized mass Not available for buckling analysis Default for normal modes analysis Normalize to unit value of the largest displacement in the analysis MAX set Displacements not in the analysis set may be larger than unity Default for buckling analysis Examples of the results of using explicit or default values for the V1 V2 and ND fields are shown in Table 3 2 The defaults on the EIGRL entry are designed to provide the minimum number of roots in cases where the input is ambiguous Alternatively you can write the entry above using the new free field format You must specify certain new parameters such as ALPH NUMS and Fi when using the free field format See the NX Nastran Quick Reference Guide for details Table 3 2 Number and Type of Roots Found with the EIGRL Entry Numbe
210. ation in the loading is the characteristic that differentiates a dynamic load from a static load This time variation is called the temporal distribution of the load A complete dynamic loading is a product of spatial and temporal distributions Using Table IDs and Set IDs in NX Nastran makes it possible to apply many complicated and temporally similar loadings with a minimum of input Combining simple loadings to create complicated loading distributions that vary in position as well as time is also a straightforward task The remainder of this section describes the Bulk Data entries for transient excitation The description is given in terms of the coefficients that define the dynamic load See the NX Nastran Quick Reference Guide for more complete Bulk Data descriptions Time Dependent Loads TLOAD1 Entry The TLOAD1 entry is the most general form in which to define a time dependent load It defines a dynamic loading of the form VP iA F t 1 T Equation 6 25 6 14 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis The coefficients of the force are defined in tabular format You need not explicitly define a force at every instant in time for which the transient solution is evaluated Only those values which describe the character of the loading are required NX Nastran interpolates linearly for intermediate values oa o2 8 4 sj ee 7 s eo j m Field Contents SID Set ID defined by
211. ations NASTRAN Users Exper pp 707 734 September 1973 NASA TM X 2893 Yang Jackson C S Goeller Jack E Messick William T Transient Analysis Using Conical Shell Elements NASTRAN Users Exper pp 125 142 September 1973 NASA TM X 2893 NX Nastran Basic Dynamic Analysis User s Guide I 33
212. atrices because of the computational cost of extracting all of the eigenvalues However other operations particularly linear equation solution and dynamic reduction may detect nonpositive definite matrices and provide diagnostics using these terms as described later in this appendix F 6 Numerical Accuracy Issues The numerical operations of NX Nastran are executed in a finite 64 bit floating point arithmetic Depending on the specific computer s word structure number of bits for mantissa versus exponent different roundoff errors may occur The sophistication level of the actual hardware or software arithmetic units also has an influence on the numerical accuracy To attain the most numerical accuracy possible the following strategies are used in NX Nastran In the decomposition of positive definite matrices the Gaussian elimination process which is the basis of all decomposition algorithms in NX Nastran does not require numerical pivots Since some of the matrices are not positive definite sparse decomposition both symmetric and unsymmetric employs a numerical pivoting row column interchange algorithm These methods consider a pivot term suitable if ay gt 10 Equation F 13 which means that a diagonal term is accepted as a pivot if it is greater than the maximum term in that row multiplied by 10THRESH the default for THRESH is 6 To ensure numerical accuracy in eigenvalue calculations most NX Nastran methods use a s
213. atrix is similar in form to the stiffness matrix because it has both translational and rotational masses Translational masses may be coupled to other translational masses and rotational masses may be coupled to other rotational masses However translational masses may not be coupled to rotational masses CROD Coupled Mass Matrix The CROD element NX Nastran coupled mass matrix is M pAL 0 j 9 Blv D o bla o Rl c o c 0 0 Equation 2 4 The axial terms in the CROD element coupled mass matrix represent the average of lumped mass and classical consistent mass This average 1s found to yield the best results for the CROD element as described below The mass matrix terms in the directions transverse to the element axes are lumped mass even when the coupled mass option 1s selected Note that the torsional inertia is not included in the CROD element mass matrix Lumped Mass Versus Coupled Mass Example The difference in the axial mass formulations can be demonstrated by considering a fixed free rod modeled with a single CROD element Figure 2 1 The exact quarter wave natural frequency for the first axial mode 1s NX Nastran Basic Dynamic Analysis User s Guide 2 5 Chapter 2 Finite Element Input Data 15708 i TA Using the lumped mass formulation for the CROD element the first frequency is predicted to be 1414 EZP F which underestimates the frequency by 10 Using a classical consistent mass approach the pr
214. be evaluated by using natural frequencies and normal modes Does a particular design modification cause an increase in dynamic response Normal modes analysis can often provide an indication In summary there are many reasons to compute the natural frequencies and mode shapes of a structure All of these reasons are based on the fact that real eigenvalue analysis is the basis for many types of dynamic response analyses Therefore an overall understanding of normal modes analysis as well as knowledge of the natural frequencies and mode shapes for your particular structure is important for all types of dynamic analysis 3 3 Overview of Normal Modes Analysis The solution of the equation of motion for natural frequencies and normal modes requires a special reduced form of the equation of motion If there is no damping and no applied loading the equation of motion in matrix form reduces to M K u 0 Equation 3 1 where M mass matrix K E stiffness matrix This 1s the equation of motion for undamped free vibration To solve Equation 3 1 assume a harmonic solution of the form iu 7 O sSiNwe Equation 3 2 where f the eigenvector or mode shape W is the circular natural frequency Aside from this harmonic form being the key to the numerical solution of the problem this form also has a physical importance The harmonic form of the solution means that all the degrees of freedom of the vibrating structure move in
215. be simplified as X D Kj D K cyl Equation 4 12 When r set DOFs exist the printed strain energies are the diagonal elements of LX divided by 2 and should be approximately zero Note that X is the transformation of the stiffness matrix K to r set coordinates which by definition of rigid body 1 e zero frequency vector properties should be null If this is not the case the equilibrium may be violated by the r set choice or other modeling errors may exist The matrix X 1s also called the rigid body check matrix NX Nastran also calculates a rigid body error ratio Jte uu r1 Z m Equation 4 13 One value of c is calculated using Equation 4 13 based on all SUPORT DOFs Therefore in UIM 3035 the same c is printed for every supported DOF where Euclidean norm of the matrix The rigid body error ratio and the strain energy should be zero if a set of statically determinate SUPORT DOFs is chosen Roundoff error may lead to computational zero values for these quantities Computational zero is a small number 10 for example that normally is 0 0 except for numerical roundoff The rigid body error ratio and strain energy may be significantly nonzero for any of the following reasons e houndoff error accumulation e The u set is overdetermined leading to redundant supports The condition gives high strain energy e The u set is underspecified leading to a singular reduced stiffness
216. blem in terms of the behavior of the modes as opposed to the behavior of the grid points Equation 6 13 represents an equality if all modes are used however because all modes are rarely used the equation usually represents an approximation To proceed temporarily ignore the damping resulting in the equation of motion M a t amp iutt iP iti Equation 6 14 If the physical coordinates in terms of the modal coordinates Equation 6 13 is substituted into Equation 6 14 the following equation is obtained M O S t EHHE UPCOJ Equation 6 15 This is now the equation of motion in terms of the modal coordinates At this point however the equations remain coupled To uncouple the equations premultiply by f 7 to obtain 6 M 6 E 6 KXTT6H EY ol P t Equation 6 16 where modal generalized mass matrix 6 M 6 61 K1 6 O tr P h modal force vector modal generalized stiffness matrix The final step uses the orthogonality property of the mode shapes to formulate the equation of motion in terms of the generalized mass and stiffness matrices that are diagonal matrices These matrices do not have off diagonal terms that couple the equations of motion Therefore in this form the modal equations of motion are uncoupled In this uncoupled form the equations of motion are written as a set on uncoupled SDOF systems as NX Nastran Basic Dynamic Analysis User s Guide 6 7 Chapter 6 Trans
217. bounds explicitly results in better plots include the following situations 9 8 If you expect a variable to be constant or vary only slightly but want to plot it to confirm that it indeed does not vary set the YMIN and YMAX to include the expected value but separate them by at least 10 percent of their average value For this case the automatic bound selection chooses bounds very close to each other to make the data fill up the plot This selection causes the bounds to be nearly equal and magnifies the scale of the plot orders of magnitude larger than other plots made of varying functions The response appears to be erratic when in fact it is smooth within engineering criteria The extreme cases occur when the function varies only in its last digit Then the function appears to be oscillating between the upper and lower limits or it can even cause a fatal error due to numerical overflow when it attempts to divide numbers by the difference YMAX YMIN The automatic bound selector tends to round up the bounds to integer multiples of 100 When plotting phase angles bounds that cause grid lines at 90 degrees are more readable For example for a plot that traverses the range of 0 to 360 degrees the usual selected bounds are 0 to 400 degrees If you prefer to have grid lines drawn at integer multiples of 90 degrees set YMIN to 0 0 and YMAX at 360 0 degrees When plotting log plots any bounds you input may be rounded up or down to a value that th
218. c Vol I Paper No 38 March 1988 Flanigan Christopher C Manella Richard T Advanced Coupled Loads Analysis Using MSC NASTRAN The MSC 1991 World Users Conf Proc Vol I Paper No 14 March 1991 Fox Gary L Solution of Enforced Boundary Motion in Direct Transient and Harmonic Problems Ninth NASTRAN Users Colloq pp 96 105 October 1980 NASA CP 2151 Geyer A Schweiger W Multiple Support Excitation for NASTRAN Piping Analysis Proc of the MSC NASTRAN Eur Users Conf April 1982 Geyer A Schweiger W Aeroelastic and Stress Analysis of the CHIWEC Chinese Wind Energy Converter Using MSC NASTRAN Proc of the MSC NASTRAN Eur Users Conf April 1985 Ghofranian S Dimmagio O D Space Station Dynamic Analysis with Active Control Systems Using MSC NASTRAN The MSC 1988 World Users Conf Proc Vol I Paper No 17 March 1988 Gibson Warren C Experiences with Optimization Using ASD NASOPT and MSC NASTRAN for Structural Dynamics The MSC 1987 World Users Conf Proc Vol I Paper No 13 March 1987 Gibson Warren C Austin Eric Analysis and Design of Damped Structures Using MSC NASTRAN The MSC 1992 World Users Conf Proc Vol I Paper No 25 May 1992 Gielen L Brughmans M Petellat C A Stepwise Approach for Fatigue Evaluation of Engine Accessories Prior to Prototyping Using Hybrid Modelling Technology MSC 1996 World Users Conf Proc Vol III Paper No 29 June 1996 G
219. c interaction between a component and its supporting structure For example if a rotating machine such as an air conditioner fan is to be installed on the roof of a building it is necessary to determine if the operating frequency of the rotating fan is close to one of the natural frequencies of the building If the frequencies are close the operation of the fan may lead to structural damage or failure Decisions regarding subsequent dynamic analyses 1 e transient response frequency response response spectrum analysis etc can be based on the results of a natural frequency analysis The important modes can be evaluated and used to select the appropriate time or frequency step for integrating the equations of motion Similarly the results of the eigenvalue analysis the natural frequencies and mode shapes can be used in modal frequency and modal transient response analyses see Frequency Response Analysis and Transient Response Analysis The results of the dynamic analyses are sometimes compared to the physical test results A normal modes analysis can be used to guide the experiment In the pretest planning stages a normal modes analysis can be used to indicate the best location for the accelerometers After the test a normal modes analysis can be used as a means to correlate the test results to the analysis results NX Nastran Basic Dynamic Analysis User s Guide 3 3 Chapter 3 Real Eigenvalue Analysis Design changes can also
220. calar Damper Connection to Scalar Points Only CDAMP4 Scalar Damper Property and Connection to Scalar Points Only CVISC Viscous Damper Connection PDAMP Scalar Damper Property PVISC Viscous Element Property TABDMP1 Modal Damping Table Normal Modes EIGR Real Eigenvalue Extraction Data EIGRL Real Eigenvalue Extraction Data Lanczos Method Dynamic Loading DAREA Dynamic Load Scale Factor DELAY Dynamic Load Time Delay DLOAD Dynamic Load Combination or Superposition DPHASE Dynamic Load Phase Lead LSEQ Static Load Set Definition TABLED1 Dynamic Load Tabular Function Form 1 TABLED2 Dynamic Load Tabular Function Form 2 TABLED3 Dynamic Load Tabular Function Form 3 TABLED4 Dynamic Load Tabular Function Form 4 Frequency Response FREQ Frequency List FREQ1 Frequency List Alternate Form 1 FREQ2 Frequency List Alternate Form 2 FREQ3 Frequency List Alternate Form 3 FREQ4 Frequency List Alternate Form 4 FREQ5 Frequency List Alternate Form 5 RLOAD1 Frequency Response Dynamic Load Form 1 RLOAD2 Frequency Response Dynamic Load Form 2 NX Nastran Basic Dynamic Analysis User s Guide D 3 Appendix D Common Commands for Dynamic Analysis Transient Response TIC Transient Initial Condition TLOAD1 Transient Response Dynamic Load Form 1 TLOAD2 Transient Response Dynamic Load Form 2 TSTEP Transient Time Step Miscellaneous DMIG Direct Matrix Input at Points SUPORT Fictitious Support SUPORT1 Fictitious Support Alternate
221. cale factor of 0 102 in the S1 field field 4 of the DLOAD entry and a factor of 0 15 in the A1 field field 5 of the DAREA entry The applied load is scaled by 0 102 because the large mass is also scaled by 0 102 due to the PARAM WTMASS entry see Equation 7 5 The time variation is specified with the TABLED1 entry The TLOAD1 entry specifies the type of loading field 5 as 0 applied force this gives the same answers if the type is specified as 3 enforced acceleration Figure 7 9 shows the displacement and acceleration response at grid points 1 base and 11 tip Note that at the end of the acceleration pulse the base has a constant velocity and therefore a linearly increasing displacement 7 16 NX Nastran Basic Dynamic Analysis User s Guide Enforced Motion Figure 7 9 Response for Enforced Acceleration Next consider the same model with a 0 015 meter displacement imposed instead of an acceleration The same ramp time history function is used with a peak enforced displacement of 0 015 meter so that the only change to the input file is to change the excitation type from 0 applied force to 1 enforced displacement on field 5 of the TLOAD1 entry and the amplitude in the DAREA entry from 0 15 to 0 015 Figure 7 10 shows the idealized input displacement time history Figure 7 11 shows the displacement and acceleration response at grid points 1 and 11 0 15 Y m Ideal
222. coordinates x W by assuming fx 6 fE o pe Equation 5 8 The mode shapes f are used to transform the problem in terms of the behavior of the modes as opposed to the behavior of the grid points Equation 5 8 represents an equality if all modes are used however because all modes are rarely used the equation usually represents an approximation To proceed temporarily ignore all damping which results in the undamped equation for harmonic motion w M x K x P w Equation 5 9 at forcing frequency W Substituting the modal coordinates in Equation 5 8 for the physical coordinates in Equation5 9 and dividing by e the following is obtained NX Nastran Basic Dynamic Analysis User s Guide 5 5 Chapter 5 Frequency Response Analysis 2 w M O S K O S m P Equation 5 10 Now this is the equation of motion in terms of the modal coordinates At this point however the equations remain coupled I To uncouple the equations premultiply by o to obtain 7 T e T e T o6 M i5 o 6 amp o i Sto 6 1P o Equation 5 11 where 61 ML 61 K1 6 6 P1 modal generalized mass matrix modal generalized stiffness matrix modal force vector The final step uses the orthogonality property of the mode shapes to formulate the equation of motion in terms of the generalized mass and stiffness matrices which are diagonal matrices These diagonal matrices do
223. craft Vol 26 No 4 pp 266 273 March 1988 Kelley William R Isley L D Using MSC NASTRAN for the Correlation of Experimental Modal Models for Automotive Powertrain Structures The MSC 1993 World Users Conf Proc Paper No 8 May 1993 Kelley William R Isley L Dean Foster Thomas J Dynamic Correlation Study Transfer Case Housings MSC 1996 World Users Conf Proc Vol II Paper No 15 June 1996 l 12 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Kientzy Donald Richardson Mark Blakely Ken Using Finite Element Data to Set Up Modal Tests Sound and Vibration June 1989 Lammens Stefan Brughmans Marc Leuridan Jan Sas Paul Application of a FRF Based Model Updating Technique for the Validation of Finite Element Models of Components of the Automotive Industry MSC 1995 World Users Conf Proc Paper No 7 May 1995 Lee John M Parker Grant R Application of Design Sensitivity Analysis to Improve Correlations Between Analytical and Test Modes The 1989 MSC World Users Conf Proc Vol I Paper No 21 March 1989 Linari M Mancino E Application of the MSC NASTRAN Program to the Study of a Simple Reinforced Concrete Structure in Nonlinear Material Field Proc of the 15th MSC NASTRAN Eur Users Conf October 1988 Lowrey Richard D Calculating Final Mesh Size Before Mesh Completion The MSC 1990 World Users Conf Proc Vol II Paper No 44 March 199
224. cy response and aeroelastic analyses Possible analysis response types include Weight e Volume 11 10 NX Nastran Basic Dynamic Analysis User s Guide Advanced Dynamic Analysis Capabilities Eigenvalues Buckling load factor Static displacement stress strain and element force Composite stress strain and failure criterion Frequency response displacement velocity acceleration stress and force Transient response displacement velocity acceleration stress and force Damping level in a flutter analysis Trim and stability derivative responses for static aeroelastic analysis A frequent task is to minimize the total structural weight while ensuring that the design still satisfies all of the design related and performance related constraints The structural weight is termed the design objective which the optimizer attempts to minimize The design variables are the properties that can be changed to minimize the weight The design variables shown in Figure 11 6 are the height and width of the flange and web Constraints on the design variables may be a minimum allowable flange width w and a maximum allowable beam height A With the tip load shown in the figure one performance constraint on the design may be the maximum allowable transverse displacement at the tip while another constraint may be the maximum allowable bending stress The design related and performance related constraints place limits on the optimizer s ability to
225. d start run The eigenvalue table and the grid point weight generator output are requested in this run For the restart run the eigenvector output is desired furthermore reprinting the grid point weight generator output is not desired One way to accomplish this is to delete the existing PARAM GRDPNT 0 entry from the database Table 8 2 Listing of the Cold Start and Restart Input Files Cold Start Run FILENAME runl dat S S S TYPICAL UNIX SUBMITTAL COMMAND S S nastran runl TITLE COLDSTART RUN METHOD 10 SPC 1 BEGIN BULK GRIDTs0 2025 0 GRID 25 710 400 7570 CROD T 10 1 2 PROD 10 1 1 0 MAT llit pype EIGRL 10 1 CONM2 100 2 10 PARAM WTMASS 00259 S REQUEST FOR GRID POINT WEIGHT GENERATOR OUTPUT S PARAM GRDPNT 0 S Restart Run FILENAME run2 dat TYPICAL UNIX SUBMITTAL COMMAND nastran run2 UY UY XU oXour uud RESTART ASSIGN MASTER runl MASTER SOL 103 TIME 5 CEND TITLE RESTART RUN METHOD 10 SPC 1 REQUEST FOR EIGENVECTOR PRINTOUT DISP ALL BEGIN BULK SKIP GRID POINT WEIGHT GENERATOR OUTPUT S 1 ENDDATA NX Nastran Basic Dynamic Analysis User s Guide 8 5 Chapter 8 Restarts in Dynamic Analysis Table 8 2 Listing of the Cold Start and Restart Input Files Cold Start Run Restart Run OPC ig 1 25456 1 OPC ly 12345052 ENDDATA The format for the delete entry is K1 K2 where K1 and K2
226. d upon restart Therefore you must 8 4 NX Nastran Basic Dynamic Analysis User s Guide Restarts in Dynamic Analysis be very careful with the changes that you make in your restart run Adhering to the following rules will avoid unnecessary reprocessing of previously completed operations e You must include all solution type related Case Control commands which are unchanged as compared to the cold start run in your restart run In other words do not make unnecessary LOAD SPC MPC or METHOD command changes or remove them from the Case Control Section unless these are actual changes This process is clarified later with the example problems e Output requests can be modified A typical example can be a request of the eigenvector printout which was not requested in the cold start run Bulk Data Section As mentioned in the previous section the automatic restart logic compares the changes made in the Bulk Data Section and determines the path that it follows A copy of the Bulk Data is stored for each version The restart run must not contain any Bulk Data entry that was included in the previous runs and saved in the database The Bulk Data Section in the current restart run should contain only new entries changed entries and or the deletion of old entries from the database This philosophy is slightly different than the one used in the Case Control Section Table 8 2 shows an example where a normal modes run is performed in the col
227. described in the sections that follow Two DOF Model Consider the two DOF model first introduced in Real Eigenvalue Analysis and shown below in Figure 7 2 For this example apply a constant magnitude base acceleration of 1 0m sec over the frequency range of 2 to 10 Hz and run modal frequency response with 5 critical damping in all modes The acceleration input is applied to the large mass grid point 3 The input file for this model is shown in Figure 7 3 7 8 NX Nastran Basic Dynamic Analysis User s Guide Grid Point 3 V d Grid Point 1 AN m 01kg Grid Point 2 MN m 1 Large Mass F L 10 K 4 Figure 7 2 Two DOF Model with Large Mass FILE bd07two dat S S TWO DOF SYSTEM CHAPTER 7 S TIME 5 SOL 111 CEND TITLE TWO DOR SYSTEM ENFORCED MOTION SUBTITLE MODAL FREQUENCY RESPONSE LABEL S SPECIFY MODAL EXTRACTION METHOD 10 S SPECIFY DYNAMIC INPUT DLOAD 999 FREQ 888 SDAMPING 777 S SELECT OUTPUT ENFORCED CONSTANT ACCELERATION MAGNITUDE DISPLACEMENT PHASE PLOT ALL ACCELERATION PHASE PLOT ALL o XYPLOTS X Y plot commands 9 BEGIN BULK Die ego ie Zu uox RES Sh qeu es d Lee RTS meee ae D siety Sears prem 8 S LARGE MASS AT BASE GRID POINT CONM2 999 3 1 0E7 S LOAD DEFINITION INCLUDES SCALE FACTORS FOR ENFORCED ACCELERATION SDLOAD SID S S1 RLOAD1 DLOAD 999 de OEY 1 0 998 RLOAD1 SID DAREA TE RLOAD1 998 997 901 SDA
228. dition is a means of determining if all roots in the range have truly been found Eigensolutions Using Transformation Methods If the HOU method and variations are selected one of the first operations performed is a Cholesky decomposition which is used to reduce the problem to a special eigenvalue problem The mass matrix is given this operation for the straight HOU method Columns that are identically null are eliminated by the auto omit operation Poor conditioning can result from several sources One example is a point mass input on a CONM2 entry that uses offsets in three directions The grid point to which it is attached has nonzero mass coefficients for all six degrees of freedom However only three independent mass degrees of freedom exist not six Another example results in a superelement analysis when most of the elements in a superelement do not have mass and all interior masses are restricted to only a few structural or mass elements The boundary matrix produced for the superelement is generally full no matter what its rank i e regardless of the number of independent mass degrees of freedom that it contains The presence of a rank deficient mass matrix when using the HOU method produces fatal messages due to the singularity of the mass matrix or produces solutions with poor numerical stability Poor stability is most commonly detected when making small changes to a model and then observing large changes in the solution Either the M
229. dvanced user the discussion of the GPWG is separated into two sections In Commonly Used Features a basic discussion is given that should satisfy most users If you need additional information read Example with Direction Dependent Masses In both sections a simple model consisting of four concentrated masses is used to demonstrate the GPWG output In the first section the mass is the same in each direction For the second section the mass is different in each of the three directions G 2 Commonly Used Features To demonstrate the typical output generated by the GPWG a small model consisting of four concentrated masses as shown in Figure G 1 is used This model is typical of most models because the mass is the same in each coordinate direction The number of masses has been kept small so you can better understand the physics Concentrated masses are located at four different grid points The displacement coordinate system for each of the grid points is the basic coordinate system NX Nastran Basic Dynamic Analysis User s Guide G 1 Appendix G Grid Point Weight Generator p 4 5 Mass Units 1 0 Yt ud P Tox L0 3 3 Mass Units al 2 3Mass Units 1 2 Mass Units 4 e Xb 0 0 0 5 1 0 Figure G 1 Four Concentrated Mass Model To request the GPWG output you must add parameter GRDPNT in either the Bulk Data Section or the Case Control Section as follows PARAM GRDPNT x If a GPWG
230. dynamic analysis with NX Nastran e Real eigenvalue analysis undamped free vibrations e Linear frequency response analysis steady state response of linear structures to loads that vary as a function of frequency e Linear transient response analysis response of linear structures to loads that vary as a function of time Additionally NX Nastran allows you to perform a number of type of advanced dynamics analysis such as shock response spectrum analysis random response analysis design sensitivity design optimization aeroelasticity and component mode synthesis Overview of Real Eigenvalue Analysis Real eigenvalue analysis is used to determine the basic dynamic characteristics of a structure The results of an eigenvalue analysis indicate the frequencies and shapes at which a structure naturally tends to vibrate Although the results of an eigenvalue analysis are not based on a specific loading they can be used to predict the effects of applying various dynamic loads Real eigenvalue analysis is described in Real Eigenvalue Analysis Overview of Frequency Response Analysis Frequency response analysis is an efficient method for finding the steady state response to sinusoidal excitation In frequency response analysis the loading is a sine wave for which the frequency amplitude and phase are specified Frequency response analysis is limited to linear elastic structures Frequency response analysis is described in Frequency
231. e Control commands and the TLOADi and LSEQ Bulk Data entries must be defined A DAREA Bulk Data entry does not need to be defined since the TLOADi and LSEQ entries reference a common DAREA ID The LSEQ entry can also be interpreted as an internal DAREA entry generator for static load entries DLOAD LOADSET Case Control Bulk Data ILOAD i LSEQ N N Dynamic Load DAREA Static Load Entries Temporal Reference Spatial Distribution Link Distribution Figure 6 5 Relationship of Dynamic and Static Load Entries LSEQ Example Suppose the following commands are in the Case Control Section LOADSET 27 DLOAD 25 in addition to the following entries in the Bulk Data Section TABLED1 290 Er In the above the LOADSET request in Case Control selects the LSEQ Set ID 27 entry The DLOAD request in Case Control selects the TLOAD1 Set ID 25 entry This TLOAD1 entry refers 29 NX Nastran Basic Dynamic Analysis User s Guide 6 21 Chapter 6 Transient Response Analysis to a TABLED1 ID 29 which is used to define the temporal variation in the loading DAREA Set ID 28 links the LSEQ and TLOAD1 entries In addition the LSEQ entry refers to static Load Set ID 26 which is defined by FORCE and PLOAD1 entries The FORCE and PLOAD1 entries define the spatial distribution of the dynamic loading and through the DAREA link refer to the TLOAD1 TABLED1 combination for the time varying characteristics of the load Dynamic Load Set
232. e theoretical results as the model fineness in increased In addition note that the error is greatest in the higher modes This table shows the computed frequencies compared to theory it does not show the computed mode shapes compared to theory However the comparison for mode shapes shows even more error than is shown for the frequencies A general rule is to use at least five to ten grid points per half cycle of response amplitude Figure 10 4 shows the theoretical response shape for the fifth mode Note that there are four half cycles in the mode shape which means that 20 to 40 grid points at a minimum are recommended to 10 8 NX Nastran Basic Dynamic Analysis User s Guide Guidelines for Effective Dynamic Analysis accurately represent that mode shape This modeling guideline is also reflected in Table 10 1 which shows that the 40 element model is much more accurate than the 10 element model Table 10 1 Frequencies for a Cantilever Beam Model Lumped Mass Frequencies Hz a T MNMMM 118 21 112 53 117 65 118 21 117 90 117 95 Four Half C ycles Figure 10 4 Fifth Mode Shape of a Cantilever Beam Another way to verify the accuracy of the mesh density is to apply static loads that give a deformed shape the same as the mode of interest and perform stress discontinuity calculations This process can be laborious and is not recommended as a general checkout procedure 10 9 Eigenvalue Analysis In addition to the meshing g
233. e a structure is excited to between 200 and 2000 Hz all modes from 0 to at least 4000 Hz should be retained The frequency range selected on the eigenvalue entry EIGRL or EIGR is one means to control the modes used in the modal frequency response solution Also three parameters are available to limit the number of modes included in the solution PARAM LFREQ gives the lower limit on the frequency range of retained modes and PARAM HFREQ gives the upper limit on the frequency range of retained modes PARAM LMODES gives the number of lowest modes to be retained These parameters can be used to include the proper set of modes Note that the default is for all computed modes to be retained Dynamic Data Recovery in Modal Frequency Response Analysis In modal frequency response analysis two options are available for recovering displacements and stresses the mode displacement method and the matrix method Both methods give the same answers although with differences in cost The mode displacement method computes the total physical displacements for each excitation frequency from the modal displacements and then computes element stresses from the total physical displacements The number of operations is proportional to the number of excitation frequencies The matrix method computes displacements per mode and element stresses per mode and then computes physical displacements and element stresses as the summation of modal displacements and element
234. e anywhere upstream PARAM GPECT 1 output and undeformed structure plots all provide useful data for detecting missing elements At present there are two major methods of identifying large ratios and nonpositive definite matrices In some solutions the largest matrix diagonal to factor diagonal ratio greater than 105 MAXRATIO default is identified by its internal sequence number and the number of negative factor diagonal terms is output The best method to identify mechanisms here is to apply checkout loads that cause internal loads in all of the elements Then inspect the displacement output for groups of grid points that move together with implausibly large displacements and common values of grid point rotation The only condition that causes a fatal error is a true null column and NASTRAN SYSTEM 69 16 avoids this fatal error by placing a unit spring coefficient on the degrees of freedom with null columns This option is recommended only for diagnostic runs because it may mask modeling errors In other solution sequences all ratios greater than 10 are printed in a matrix format named the MECH table The external sequence number of each large ratio is also printed which is the grid point and degree of freedom number If any such ratios exist the action taken depends on the value of PARAM BAILOUT In the conventional solution sequences its default value causes the program to continue after printing the MECH matrix In the superelement solut
235. e applied to the structure This dynamic load is known as the dynamic environment The dynamic environment governs the solution approach 1 e normal modes transient response frequency response etc This environment also indicates the dominant behavior that must be included in the analysis i e contact large displacements etc Proper assessment of the dynamic environment leads to the creation of a more refined finite element model and more meaningful results 1 12 NX Nastran Basic Dynamic Analysis User s Guide Fundamentals of Dynamic Analysis Dynamic Environment Finite Element Model Modal Yes Results No Analysis Satisfactory No J Yes No Results Forced Response Satisfactory Analvsis pe End Figure 1 6 Overview of Dynamic Analysis Process An overall system design 1s formulated by considering the dynamic environment As part of the evaluation process a finite element model is created This model should take into account the characteristics of the system design and just as importantly the nature of the dynamic loading type and frequency and any interacting media fluids adjacent structures etc At this point the first step in many dynamic analyses 1s a modal analysis to determine the structure s natural frequencies and mode shapes see Real Eigenvalue Analysis In many cases the natural frequencies and mode shapes of a structure provide enough information to make design dec
236. e is a plot or set of plots per mode frequency response analysis for which there is a plot or set of plots per output frequency and transient response analysis for which there is a plot or set of plots per output time Structure plot commands are described in the NX Nastran User s Guide In the NX Nastran input file structure plotting commands are listed in the OUTPUT PLOT section which immediately precedes the Bulk Data Section The structure plotting commands define the set of elements to be plotted SET the viewing axes AXES the viewing angles VIEW as well as the plot type and parameters PLOT Optionally the scale of the plotted deformation MAXIMUM DEFORMATION can be specified if not specified the plotted deformation is scaled such that the maximum deformation is 5 of the maximum dimension of the structure Figure 9 1 shows the structure plotting commands applied to a normal modes analysis of the bracket model Figure 9 2 shows the resulting structure plots The first plot shows the undeformed shape and the next two plots show the undeformed shape overlaid on the deformed shapes for modes 1 and 2 The default is chosen such that the maximum plotted deformation is 5 of the maximum dimension of the bracket the actual maximum deformation is printed at the top of the plot The plots shown in this chapter were converted to PostScript format for printing on a PostScript compatible printer S PLOT COMMANDS FOR BRACKET
237. e matrix Field 2 of this DMIG entry must have the same name EXSTIF as referenced by the Case Control K2GG EXSTIF command Fields 3 and 4 of this entry identify this column in terms of its external grid ID and corresponding degree of freedom respectively In this case it is grid point5 degree of freedom 3 z translation at grid point 5 Once this column 1s defined follow the format description as described in the section for column data entry format and then you can input the four terms in this column row by row These four terms are defined by sets of three fields They are the external grid ID number corresponding degree of freedom and the actual matrix term respectively The first term of column one is defined by external grid ID 5 degree of freedom 3 z translation at grid point 5 with a stiffness value of 500039 The second term of column one is defined by external grid ID 5 degree of freedom 5 y rotation at grid point 5 with a stiffness value of 250019 The third term of column one is defined by external grid ID 6 degree of freedom 3 z translation at grid point 6 with a stiffness value of 500039 The fourth term of column one is defined by external grid ID 6 degree of freedom 5 y rotation at grid point 6 with a stiffness value of 250019 The next DMIG entry defines the second column of the above matrix Fields 3 and 4 of this entry identify this column in terms of its external grid ID and corresponding degree of freedom resp
238. e not adversely affected by a poor choice of SUPORT DOFs Again the results of UIM 3035 should be carefully checked to ensure that a proper choice of SUPORT DOFs is made Lanczos Method In the Lanczos method the SUPORT entry attempts to give 0 0 Hz modes The Lanczos routine compares the values of the calculated modes without the SUPORT entry and determines if the calculated frequencies for the N modes are near 0 0 Hz If the computed frequencies are near 0 0 Hz the computed values are replaced with 0 0 Hz If a computed frequency is not near 0 0 Hz then it is retained Note that this may cause problems in response spectrum analysis where 0 0 Hz is required for the SUPORT frequencies The Lanczos computed rigid body eigenvectors are used 1 e the rigid body eigenvectors computed by the SUPORT entry are not used In the above paragraph near means that the eigenvalues are less than 0 01 times the shift scale the SHFSCL field on the EIGRL entry All computed eigenvalues less than this threshold are candidate rigid body modes There is some logic to determine the relationship of these candidate rigid body modes to the number of DOFs on the SUPORT entry Suppose that there are three eigenvalues less than the threshold of 0 01 times the shift scale If your SUPORT entry defines two DOFs then the first two frequencies become 0 0 Hz and the third becomes something that 1s nonzero but small on the order of 1 0E 6 for example On the othe
239. e plotter considers more reasonable In general changing bounds on log plots sometimes requires experimentation before a reasonable set can be found Producing good quality plots is an interactive process whether the plot is produced by an interactive or batch plotter The restart feature discussed in Restarts In Dynamic Analysis can reduce the computer costs for this iteration since restarts performed to change only plot requests are made efficiently S X Y PLOT COMMANDS FOR BAR MODAL FREQUENCY RESPONSE S MAGNITUDE PHASE Executive Case Control S APPLIED LOAD OUTPUT SEI 15 6 11 OLOAD PHASE PLOT 15 S PHYSICAL OUTPUT REQUEST SET 11 6 11 DISPLACEMENT PHASE PLOT 11 S MODAL SOLUTION SET OUTPUT SET 12 1 2 SDISP PHASE PLOT 12 S ELEMENT FORCE OUTPUT SET 13 6 ELFORCE PHASE PLOT 13 OUTPUT XY PLOT XTGRID YES YTGRID YES XBGRID YES NX Nastran Basic Dynamic Analysis User s Guide YBGRID YES S S PLOT RESULTS XTITLE FREQUENCY S VYTLOG YES YTTITLE DISPL MAG 6 YBTITLE DISPL PHASE 6 XYPLOT DISP 6 T2RM T2IP YTTITLE DISPL MAG 11 YBTITLE DISPL PHASE 11 XAYPLOT DISP jill T2RM T2iP S YTTITLE SDISP MAG MODE 1 YBTITLE SDISP PHASE MODE 1 XYPLOT SDISP mode Tl XYPLOT SDISP 1 T1RM TI1IP YTTITLE SDISP MAG MODE 2 YBTITLE SDISP PHASE MODE 2 XYPLOT SDISP J2 TEIRM TITIP S YTTITLE BEND MOMENT A1
240. e restarting from the database created by runl1 dat the following FMS statements can be used in your current run RESTART ASSIGN M MASTER runl MASTER For UNIX machines the filenames are case sensitive They should be entered exactly as they were created in the cold start run and enclosed with single quotes as shown above An alternate way is to use the DBS statement on the submittal line instead of the ASSIGN statement Assuming the current run is called run2 dat then the equivalent submittal statement is as follows nastramn ruH2 dbs runl The ASSIGN statement is not needed in this case as long as the run1 database files are contained in the submittal directory Again the syntax is for a typical UNIX machine You should refer to the machine dependent documentation for your particular computer for specific details Executive Control Section This section is the same as your normal run with the exception of perhaps the SOL x command For example if you are performing a normal modes analysis in runl dat then the SOL x command in run1 dat should reference SOL 103 In run2 dat if you are performing a modal transient restart from runl1 dat then the SOL x statement in this case should then reference SOL 112 DIAGs can be turned on or off Case Control Section The automatic restart logic compares the modifications made to the Case Control and Bulk Data Sections in determining which operations need to be processe
241. e same null column in both K and M These columns and rows are given an uncoupled unit stiffness by the auto omit operation if the default value 0 for PARAM ASING is used If this value is set to 1 a null column in both matrices is regarded as an undefined degree of freedom and causes a fatal error exit 2 A massless mechanism One commonly encountered example is a straight line pinned rod structure made from CBAR elements with no torsional stiffness J defined The structural mass generated for CBAR elements does not include inertia for the torsion NX Nastran Basic Dynamic Analysis User s Guide F 7 Appendix F Numerical Accuracy Considerations degrees of freedom The natural frequency for this torsion mode approaches the limit of zero torsional stiffness divided by zero mass which is an undefined quantity If the elements lie along a global coordinate axis the mass term is identically zero which leads to very large negative or positive eigenvalues and is usually beyond any reasonable search region If the elements are skewed from the global axes the eigenvalues may be computed at any value including negative because of the indeterminacy caused by numerical truncation The negative terms on factor diagonal message generally occurs for every decomposition performed in the iteration It can be shown from Sturm sequence theory that the number of negative terms is exactly equal to the number of eigenvalues below This con
242. e specified on the right hand side The resulting equation is a second order linear differential equation representing the motion of the system as a function of displacement and higher order derivatives of the displacement Inertia Force An accelerated mass induces a force that is proportional to the mass and the acceleration This force is called the inertia force mi Viscous Damping The energy dissipation mechanism induces a force that 1s a function of a dissipation constant and the velocity This force is known as the viscous damping force bu The damping force transforms the kinetic energy into another form of energy typically heat which tends to reduce the vibration Elastic Force The final induced force in the dynamic system is due to the elastic resistance in the system and is a function of the displacement and stiffness of the system This force is called the elastic force or occasionally the spring force kut Applied Load The applied load p t on the right hand side of Equation 1 2 is defined as a function of time This load is independent of the structure to which it is applied e g an earthquake is the same earthquake whether it 1s applied to a house office building or bridge yet its effect on different structures can be very different Solution of the Equation of Motion The solution of the equation of motion for quantities such as displacements velocities accelerations and or stresses all as a functi
243. e there are no applied loads instead the base of the building undergoes an enforced displacement or acceleration time history NX Nastran does not include a completely automatic method for prescribing enforced motion in dynamics Instead the procedures described in 5 and Transient Response Analysis for specifying applied forces are used in conjunction with techniques that convert applied forces into enforced motion One such method that is applicable to both transient response and frequency response is described in this chapter the large mass method Another method for enforced motion described in the NX Nastran Advanced Dynamic Analysis User s Guide is the Lagrange multiplier technique 7 2 The Large Mass Method in Direct Transient and Direct Frequency Response If a very large mass m which is several orders of magnitude larger than the mass of the entire structure is connected to a degree of freedom and a dynamic load p is applied to the same degree of freedom then the acceleration of the degree of freedom to a close approximation is as follows Equation 7 1 In other words the load that produces a desired acceleration ii is approximately p m it Equation 7 2 The accuracy of this approximation increases as m is made larger in comparison to the mass of the structure The only limit for the size of m is numeric overflow in the computer Generally the value of m should be approximately 106 times the mass of the ent
244. e within it NX Nastran discourages using such elements by giving fatal messages when negative element thicknesses or section properties are input However there are applications where such elements are useful such as when using an element with negative stiffness in parallel with a passive element to model a damaged or thinned down element For this reason negative material property coefficients and negative stiffnesses for scalar elements are allowed Also some incorrect modeling techniques such as the misuse of the membrane bending coupling term on PSHELL entries MID4 can lead to negative eigenvalues of the element stiffness matrix Stiffness matrices with negative eigenvalues cause negative terms in D The number of such terms is automatically output by the standard symmetric decomposition subroutine Their existence again causes various warning and fatal messages depending on the context The most common cause of negative terms in D is true mechanisms whose terms are small negative numbers and are actually computational zeroes Indefinite matrices occur when using the Lagrange multiplier method for constraint processing In this method the constraints are not eliminated from but are concatenated to the g size system of equations The constraint equations have zeroes on the diagonal resulting in indefinite matrices These systems can be solved using the block pivoting scheme of the sparse decomposition F 9 Detection and Avoidance o
245. eEH3EReUES E REN ENS REESE 1 2 Equations of Motion ia 246k dor or dod ROO CROP 44 64D EOE EWE RO RO e de 1 2 Dynamic Analysis FrocesS ok ek HEARD dd dE COR d X 4 os qe acd x RE ed UR 1 12 Dynamic Analysis Types leer 1 14 Finite Element Input Data 545223249 dro CRCRCACACACA ACERO RAO AC 9A 2 1 B 7 1 Arr 2 2 lio Suc EEC m 2 2 Eu Og ht eee he eee he OE SURE RES ER 234 3 21 9 1 33 f Rd d d dq S d 2 8 Units in urea oO PSI RISE TREE TOIT CITTOROOTCLOCCIOOISLOTTT 111 2 DT 2 12 Bee MIS INBUL i459 5 2 R9EX4942575 94353022451 29 9 P 290 299 32 52 04 24 2 13 Real Eigenvalue Analysis ccc ccc cece c ere r ere reser ere sere s s tt 3 1 CPI bw ee eee ee ee ee Oe ee ee ee eee eee 3 2 Reasons to Compute Normal Modes cel 9 9 Overview of Normal Modes Analysis ce el 9 4 Methods of Computation esso CEOX ORE RO RECO de eR OR EROR E ds 3 10 Comparison of Methods caosa x Rude be SOR Se HE OSES EAGER ER ESE ES RARE P3 S 3 12 User Interface for Real Eigenvalue Analysis 2 0 0 0 leen 3 13 Solution Control for Normal Modes Analysis eee eee ee ee 3 17 La inl on oh ee eG Be oe hee ee eee OR SEES Bee SEX SE RS RP E IPS 3 18 He TOY MOUBR uod 4 4 xd ED 4S EK EE ORO OEC NOR GEAR EOE EEE C RC 4 1 do 20 ATCP 4 2 ree te Aa es dE BRUCRE ee eRe bE oe dd qug esu dd S AE ERE EEE 4 3 PEN Lora Rasta ARADAaGE mdeTXRAAes4ZAuz4sT4 Y 34TA4 OES ES 4 9 Frequency Respon
246. eam Model Frequency Response Analysis Transient ins am Results Response Peak cm 00Hz 205Hz Displacement 3 Displacement 6 Y 3 17E 3 17E 3 7 61E 2 6 29E 3 Displacement 11 Y 9 77E 3 9 77E 3 2 25E 1 1 87E 2 NX Nastran Basic Dynamic Analysis User s Guide 10 13 Chapter 10 Guidelines for Effective Dynamic Analysis 10 13 Computer Resource Requirements The efficiency of a dynamic analysis can be measured based on computer resource requirements such as computer runtime disk storage and memory These requirements increase as the problem size increases but they can also vary greatly depending on other factors In general a dynamic analysis uses more computer resources than a static analysis In normal modes analysis the requirements vary depending on the density of the model the eigenvalue extraction method used the number of modes requested and the type of decomposition symmetric or sparse If your model has already been built you can use the ESTIMATE utility to estimate resource requirements See e ESTIMATE in the NX Nastran Installation and Operations Guide If you haven t yet created your model but still want to estimate resource needs then read the following In the past we have established benchmark runs to provide guidelines on performance for normal modes analyses We used a cylindrical plate model scaled to various sizes and solved for ten modes using different solution methods principally the Spar
247. ection is the average of the lumped and classical consistent masses as explained for the CROD element and 2 there is no torsional inertia The CBEAM element coupled mass matrix is also identical to the classical consistent mass formulation except for two terms 1 the mass in the axial direction 1s the lumped mass and 2 the torsional inertia 1s the lumped inertia Another important aspect of defining mass is the units of measure associated with the mass definition NX Nastran assumes that consistent units are used in all contexts You must be careful to specify structural dimensions loads material properties and physical properties in a consistent set of units All mass entries should be entered in mass consistent units Weight units may be input instead of mass units if this 1s more convenient However you must convert the weight to mass by dividing the weight by the acceleration of gravity defined in consistent units P 25 LL 2 Ip Equation 2 5 T I mass or mass density g acceleration of gravity Py weight or weight density The parameter PARAM WTMASS factor performs this conversion The value of the factor should be entered as 1 g The default value for the factor is 1 0 Hence the default value for WTMASS assumes that mass and mass density is entered instead of weight and weight density When using English units if the weight density of steel is entered as RHO 0 3 Ib in using PARAM WTMASS 0
248. ectively In this case it is grid point 5 degree of freedom 5 y rotation at grid point 5 The NX Nastran Basic Dynamic Analysis User s Guide 3 41 Chapter 3 Real Eigenvalue Analysis rest of the procedure is similar to that of column one with the exception that only three terms need to be input due to symmetry The next two DMIG entries defines columns three and four of the stiffness matrix respectively Note that due to symmetry one less row needs to be defined for each additional column The mass matrix is input in a similar manner as the stiffness matrix with the following exceptions e The command M2GG EXMASS instead of K2GG EXSTIF is used in the Case Control Section In this case EXMASS is the name of the mass matrix referenced in field two of the DMIG Bulk Data entries e The matrix defined in the DMIG entries is expressed in the mass matrix terms rather than in stiffness matrix terms e Since there are only two non null columns for the mass matrix only two DMIG data entries are required instead of the four entries needed for the stiffness matrix Mass matrices input using DMIG are not scaled by PARAM WTMASS In this example the small field input format is used and the maximum number of characters that can be input are eight including sign and decimal point Greater input precision can be achieved by using the large field format and by changing the TIN field to 2 for the DMIG entries The first two computed natural
249. ectively and it does not easily show the time variation Plotted output overcomes these problems There are two kinds of plotted output structure plots and X Y plots Structure plots can depict the entire structure or a portion of it Structure plots are useful for verifying proper geometry and connectivity They also can be used to show the deformed shape or stress contours at a specified time or frequency X Y plots on the other hand show how a single response quantity such as a grid point displacement or element stress varies across a portion or all of the time or frequency range There are numerous commercial and in house plotting programs that interface to NX Nastran for structure and or X Y plotting The commercial programs are similar because they operate interactively The NX Nastran plot capabilities on the other hand are performed as a batch operation which means that you predefine your plots when you make your NX Nastran run This chapter briefly describes the kinds of plots available in NX Nastran Detailed information is located in the NX Nastran Reference Manual 9 2 Structure Plotting Structure plotting is performed to verify the model s geometry and element connectivity prior to performing a dynamic analysis After or during the analysis structure plotting is performed to view deformed shapes and contours For dynamic response deformed shape and contour plots can be made for normal modes analysis for which ther
250. ed in the Case Control Section Note that stresses and element forces are not factored by CK1 and must be adjusted manually Default 1 0 0 0 CK41 and CK42 specify factors for the total structural damping matrix The total structural damping matrix is K cKar K CK42 KI where K 5 is selected via the Case Control command K42GG and LK is generated from the stiffness of structural element e g CBAR entries in the Bulk Data times the structural damping coefficient GE on material entries e g MAT1 These are effective only if K42GG is selected in Case Control Note that stresses and element forces are not factored by CK41 and must be adjusted manually Default 1 0 CM1 and CM2 specify factors for the total mass matrix The total mass matrix is M CMI M7 CM2 M7 where M2 1s selected via the Case Control command M2GG and ofl is derived from the mass element entries in the Bulk Data Section These are effective only if M2GG is selected in the Case Control Section Default 1 NX Nastran Basic Dynamic Analysis User s Guide D 5 Appendix D CP1 CP2 CURVPLOT DDRMM DYNSPCF EPZERO G HFREQ Common Commands for Dynamic Analysis COUPMASS gt 0 requests the generation of coupled rather than lumped mass matrices for elements with coupled mass capability This option applies to both structural and nonstructural mass for the following elements CBAR CBEAM CHEXA CONROD CPENTA
251. ed loads OLOAD at grid points 6 and 11 displacements DISP of grid points 6 and 11 accelerations ACCE for grid points 6 and 11 bending moment ELFORCE at end A in plane 1 for element 6 and modal displacements SDISP for modes 1 and 2 Figures 9 12 through 9 16 show the resulting plots S X Y PLOT COMMANDS FOR BAR MODAL FREQUENCY RESPONSE S MAGNITUDE PHASE Executive Case Control S Ur APPLIED LOAD OUTPUT SET 15 6 11 OLOAD PHASE PLOT 15 PHYSICAL OUTPUT REQUEST SET 11 6 11 DISPLACEMENT PHASE PLOT 11 S MODAL SOLUTION SET OUTPUT SET 12 1 2 SDISP PHASE PLOT 12 S ELEMENT FORCE OUTPUT SET 13 6 ELFORCE PHASE PLOT 13 OUTPUT XYPLOT XTGRID YES YTGRID YES XBGRID YES 9 12 NX Nastran Basic Dynamic Analysis User s Guide YBGRID YES S PLOT RESULTS XTITLE FREQUENCY S X duo YES YTTITLE DISPL MAG 6 YBTITLE DISPL PHASE 6 MY PLOT DISP 6 T2RM T2IP YTTITLE DISPL MAG 11 YBTITLE DISPL PHASE 11 XYPLOT DISP Z11 T2RM T2lP S YTTITLE SDISP MAG MODE 1 YBTITLE SDISP PHASE MODE 1 XYPLOT SDISP mode T1 XYPLOT SDISP 1 T1RM T1IP YTTITLE SDISP MAG MODE 2 YBTITLE SDISP PHASE MODE 2 AIPRhOT SDISP 2 T1RM T1IP S YTTITLE BEND MOMENT Al EL 6 MAG YBTITLE BEND MOMENT Al EL 6 PHASE XYPLOT ELFORCE 6 2 10 S YTLOG NO YBMAX 90 0 YBMIN 0 0 CURVELINESYMBOL 2 YTMAX 4 0 YTMIN 0 0 YTTITLE LOAD M
252. edicted frequency 2 S u 1 732 is overestimated by 10 Using the coupled mass formulation in NX Nastran the frequency 1549 EP Es is underestimated by 1 4 The purpose of this example is to demonstrate the possible effects of the different mass formulations on the results of a simple problem Remember that not all dynamics problems have such a dramatic difference Also as the model s mesh becomes finer the difference in mass formulations becomes negligible t 4 7 Single Element Model giat uut ut ut utut utum utu ea a a at wat a at at atat at at atat at atat at atat atat atat atat at ata Theoretical Natural NE d Fip E708 5 Ep Frequency P 1 5 70i NX Nastran Lumped mxNElp JE p Mass 342 1 414 7 Classical Consistent v j JE i p 173 JE i p Mass wm Ve or ox j 2 6 NX Nastran Basic Dynamic Analysis User s Guide Finite Element Input Data NX Nastran Coupled JE ip Eip 712 5 1 549 Mass mo N i Figure 2 1 Comparison of Mass Formulations for a ROD CBAR CBEAM Lumped Mass The CBAR element lumped mass matrix 1s identical to the CROD element lumped mass matrix The CBEAM element lumped mass matrix is identical to that of the CROD and CBAR mass matrices with the exception that torsional inertia 1s included CBAR CBEAM Coupled Mass The CBAR element coupled mass matrix is identical to the classical consistent mass formulation except for two terms 1 the mass in the axial dir
253. edom are given a very small mass or stiffness Inspect the listed degrees of freedom to ensure that masses or stiffnesses are not left out inadvertently UFM 4416 USER FATAL MESSAGE 4416 NO DYNAMIC LOAD TABLE AVAILABLE A frequency response or transient response analysis was requested but no dynamic load data is available Include dynamic load data DLOAD RLOADi TLOADDJ in model UFM 4417 USER FATAL MESSAGE 4417 NO TRANSIENT RESPONSE LIST AVAILABLE A transient response dynamic analysis was requested but no transient response list is available Include a TSTEP entry in the Bulk Data Section H 6 NX Nastran Basic Dynamic Analysis User s Guide UFM 4418 UWM 4420 UFM 4421 UFM 4501 UWM 4561 UFM 4562 UWM 4582 Diagnostic Messages for Dynamic Analysis USER FATAL MESSAGE 4418 NO EIGENVALUE EXTRACTION DATA IS AVAILABLE A dynamic analysis was requested but no eigenvalue extraction data was available Include eigenvalue extraction data EIGR or EIGRL in the Bulk Data Possible causes are e The METHOD command in the Case Control Section but no EIGR or EIGRL entry in the Bulk Data Section e Nocorrespondence between Set IDs on the METHOD command and the EIGR EIGRL entries USER WARNING MESSAGE 4420 THE FOLLOWING DEGREES OF FREEDOM ARE POTENTIALLY SINGULAR During decomposition the degrees of freedom listed had pivot ratios greater than MAXRATIO Verify that the degrees of freedom are not par
254. ee different ways to represent the two modes of a two DOF structure are shown in Figure 3 4 The graphical representation of the eigenvectors in the figure shows the modal displacements rotated by 90 degrees in order to view the deformation better 4 re L HI Be His H nm Mode 1 Mode 2 3 8 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis a t o fino Caspia fat oa am Las Figure 3 4 Representations of Mode Shapes for a Two DOF System A common misconception about mode shapes is that they define the structural response Again mode shapes are relative quantities They cannot be used alone to evaluate dynamic behavior As described earlier it is the relation between the structural loading and the natural frequencies that determines the absolute magnitude of dynamic response The relation of a specific loading to a set of natural frequencies provides explicit scale factors that are used to determine the extent to which each particular mode is excited by the loading After the individual modal responses to a particular loading are determined only then can the various engineering design decisions be made with the actual absolute values of stress and or displacement Methods that use the modal results to determine forced response are termed modal methods or modal superposition methods Modal frequency response analysis and modal transient response analysis are described in Fre
255. ent The response at resonance is inversely proportional to the amount of damping but the half power bandwidth is directly proportional to the amount of damping For lightly damped structures z lt 0 1 an approximate relationship between the half power bandwidth f5 f1 resonant frequency f and critical damping ratio Z is given by Equation10 1 This equation can be rewritten to define the appropriate value of Af f5 f1 m I Af Equation 10 4 m h F _ m L Af 8h 2f Equation 10 5 _ y m 1 Equation 10 6 Af where m 1s the number of frequency points within the half power bandwidth For example with 1 critical damping and six points used to define the half power bandwidth the maximum 10 10 NX Nastran Basic Dynamic Analysis User s Guide Guidelines for Effective Dynamic Analysis frequency increment is 0 0004 f The frequency increment is smaller for lighter damped structures Another good check is looking at the X Y plots If the response curves are not smooth there is a good chance that Af is too large Verification of the Applied Load The applied load can be verified by exciting your model at 0 0 Hz and comparing the results to a static solution with the same spatial load distribution The 0 0 Hz results should match the static results if direct frequency response analysis is used without structural damping If modal frequency response analysis is used without structural damping those re
256. ent Response of Submerged Fluid Coupled Double Walled Shell Structure to a Pressure Pulse J of the Acoustic Soc of America Vol 70 No 6 pp 1776 1782 December 1981 Pamidi P R On the Append and Continue Features in NASTRAN Seventh NASTRAN Users Colloq pp 405 418 October 1978 NASA CP 2062 Rose Ted A Method to Apply Initial Conditions in Modal Transient Solutions The MSC 1991 World Users Conf Proc Vol I Paper No 13 March 1991 Rose Ted McNamee Martin A DMAP Alter to Allow Amplitude Dependent Modal Damping in a Transient Solution MSC 1996 World Users Conf Proc Vol V Paper No 50 June 1996 Swan Jim A DMAP Alter for Interface Loads Across Superelements in Dynamic Analyses The MSC 1992 World Users Conf Proc Vol I Paper No 23 May 1992 Tang C C Space Station Freedom Solar Array Wing Nonlinear Transient Analysis of Plume Impingement Load MSC 1994 World Users Conf Proc Paper No 35 June 1994 Urban Michael R Dobyns Alan MSC NASTRAN Transient Analysis of Cannon Recoil Loads on Composite Helicopters The MSC 1991 World Users Conf Proc Vol I Paper No 28 March 1991 West Timothy S Approximate Dynamic Model Sensitivity Analysis For Large Complex Space Structures MSC 1996 World Users Conf Proc Vol I Paper No 6 June 1996 Wingate Robert T Jones Thomas C Stephens Maria V NASTRAN Postprocessor Program for Transient Response to Input Acceler
257. envalues must be calculated by taking the differences of coefficients that are dominated by the largest eigenvalue For this reason the ratio jis called a numerical conditioning number If this number is too large numerical truncation causes a loss of accuracy when computing the lowest eigenvalues of a system The assumptions that allow this simple analysis are often pessimistic in practice that is the bounds predicted by the error analysis are conservative However the effects it predicts do occur eventually so that models that produce acceptable results for one mesh size may produce unacceptable results with a finer mesh size due to the higher eigenvalues included in the larger sized matrices occurring from the finer mesh F5 Definiteness of Matrices A matrix whose eigenvalues are all greater than zero is said to be positive definite If some eigenvalues are zero but none are less than zero the matrix is positive semi definite A stiffness matrix assembled from elements is at least positive semi definite If all of the structure s NX Nastran Basic Dynamic Analysis User s Guide F 3 Appendix F Numerical Accuracy Considerations rigid body modes are constrained the stiffness matrix is positive definite Another category is the indefinite matrices category These matrices have zeroes or blocks of zeroes on the diagonal Although definiteness is most concisely defined in terms of eigenvalues it is not a practical test for large m
258. ep procedure for the four mass example 1 G 6 The GPWG module uses the global mass matrix which is the mass matrix before any constraints are applied In this example there are four grids each with six degrees of freedom resulting in a total of 24 degrees of freedom in the mass MJJ matrix The matrix is shown in Figure G 4 NX Nastran Basic Dynamic Analysis User s Guide Grid Point Weight Generator 200000000000 000000000000 1 o030000000000000000000000D0 8sb 0oO050000000 0000 0000000000 3 00Grid CO0000000 0000000000 a 000000000000 00000 0000000 5 0000000000000000000000001 amp 000000200000000000000000 7 o000o0o0oos3a3oooooooooooooo0o0o0 s 000000005000000000000000 9 0000000cGnd200000000000 070 10 o000000000o0o0ooooooooooooo n MJJ o00oo0o0oocooooooooooooooooo0o0o0 rg o000000000 00 20000 0000000 3B 000000000000 08000 0000000 14 o00000000000 005000000000 145 00000000 00 00 O0OCGridd 0000000 16 oO0000000 0000000000000 000 47 oO000000000 0000000 0000000 48 o000000000 00000 000200000 s 0000000000 0C 000000080000 20 000000000000 000000005 000 nun oO0000000 0000 0000000 CGrid olz COO CD UO OUR OOD B OOP Oa Deo ooo s o0000000 000000000 0000000 y 123 4 5 6 7 amp 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Figure G 4 Global Mass Matrix The MJJ matrix shows the mass contribution for each of the four grid points Note that the coordinate system associated with rows and columns 1 through 6 g
259. equal for a constant amplitude of sinusoidal motion NX Nastran Basic Dynamic Analysis User s Guide 2 9 Chapter 2 Finite Element Input Data Viscous LD amping P bu ibiumnu Structural Damping f f G Ku 5 Damping Force Forcing Frequency Figure 2 2 Structural Damping and Viscous Damping Forces for Constant Amplitude Sinusoidal Displacement If the frequency W is the circular natural frequency w Equation 2 8 becomes Gk b Guo m 4 H H Equation 2 9 Recall the definition of critical damping from Equation 1 11 b 2Jkm 2m CF Equation 2 10 Some equalities that are true at resonance w for constant amplitude sinusoidal displacement are HIQ Equation 2 11 and 1 1 Q 2t G Equation 2 12 where Q is the quality or dynamic magnification factor which is inversely proportional to the energy dissipated per cycle of vibration 2 10 NX Nastran Basic Dynamic Analysis User s Guide Finite Element Input Data The Effect of Damping Damping is the result of many complicated mechanisms The effect of damping on computed response depends on the type and loading duration of the dynamic analysis Damping can often be ignored for short duration loadings such as those resulting from a crash impulse or a shock blast because the structure reaches its peak response before significant energy has had time to dissipate Damping is important for long duration loadings such as earthquakes a
260. equal to zero Two or more identical natural frequencies Large amplitude vibrations that can grow without bound At resonance energy is added to the system This occurs for example when the harmonic excitation frequency is equal to one of the natural frequencies The response at resonance is controlled entirely by damping NX Nastran Basic Dynamic Analysis User s Guide A 1 Appendix A Glossary of Terms Transient displacements of an unconstrained model that grow continuously with time This is often caused by the a Body EH accumulation of small numerical errors when integrating the equations of motion Rigid Body Mode Stress free zero frequency motions of the entire structure SDOF Single degree of freedom Structural Damping Damping that 1s proportional to displacement Transient Response Analysis Computation of the response to general time varying excitation Viscous Damping Damping that 1s proportional to velocity A 2 NX Nastran Basic Dynamic Analysis User s Guide Appendix B Nomenclature for Dynamic Analysis The appendix provides nomenclature for terms commonly used in dynamic analysis B 1 General u i 0 II Mg p Multiplication i Approximately Matrix Uj Vector i il g Acceleration of Gravity At Time Step A T i Frequency Step i J K Subscripts Indices eo Infinity H Displacement Initial Displacement Velocity Initial Velocity Acceleration Mass Large Mass NX N
261. equired by you At first glance the FMS may be overwhelming due in part to its flexibility and the many options it has to offer However in its most commonly used form it can be quite simple Examples in the most commonly used format are presented throughout this appendix There are numerous FMS statements available in NX Nastran This section covers the commonly used FMS statements in dynamic analysis They are presented in their most commonly used format which in general 1s a simplified format E 2 NX Nastran Basic Dynamic Analysis User s Guide File Management Section If an FMS statement is longer than 72 characters it can be continued to the next line by using a comma as long as the comma is preceded by one or more blank spaces INIT Purpose Creates initializes permanent and or temporary DBsets The INIT statement has two basic formats one for all the DBsets and one specifically for the SCRATCH DBsets Format Simplified for All DBsets Except SCRATCH INIT DBset name LOGICAL log namel max sizel log name2 max size2 lognamei max sizei lognamen max sizen DBset name Logical name of the DBset being used e g DBALL i th logical name for the DBset name referenced in this INIT statement You log namei can have up to 10 logical names for each DBset 1 xi x 10 The i th physical file is assigned with the assignment statement Y ss Maximum allowable number of NX Nastran blocks which may be written to
262. er 1979 NASA CP 2131 Kalinowski A J Solution Sensitivity and Accuracy Study of NASTRAN for Large Dynamic Problems Involving Structural Damping Ninth NASTRAN Users Colloq pp 49 62 October 1980 NASA CP 2151 Kasai Manabu Real Eigenvalue Analysis by Modal Synthesis Method Taking Differential Stiffness into Account The First MSC NASTRAN User s Conf in Japan October 1983 in Japanese Kasai Manabu Recovery Method for Components by DMAP of Constrained Modal Type The Fifth MSC NASTRAN User s Conf in Japan October 1987 in Japanese NX Nastran Basic Dynamic Analysis User s Guide l 5 Appendix References and Bibliography Kasai Manabu DMAP Program for Modal Mass and Momentum The Sixth MSC NASTRAN User s Conf in Japan October 1988 in Japanese Kienholz Dave K Johnson Conor D Parekh Jatin C Design Methods for Viscoelastically Damped Sandwich Plates AIAA ASME ASCE AHS 24th Structures Structural Dynamics and Materials Conf Part 2 pp 334 343 May 1983 Lambert Nancy Tucchio Michael Ring Element Dynamic Stresses Ninth NASTRAN Users Colloq pp 63 78 October 1980 NASA CP 2151 Lee Jyh Chiang Investigation for the Large Stiffness Method The Fifth Annual MSC Taiwan Users Conf Proc November 1993 Lee Ting Yuan Lee Jyh Chiang Modal Analysis and Structural Modification for a Harpoon Launcher The Fifth Annual MSC Taiwan Users Conf Proc November 1993 LeMaste
263. er No 28 December 1994 Shieh Rong C A Superefficient MSC NASTRAN Interfaced Computer Code System for Dynamic Response Analysis of Nonproportionally Damped Elastic Systems The MSC 1993 World Users Conf Proc Paper No 14 May 1993 Soni Ravi et al Development of a Methodology to Predict the Road Noise Performance Characteristics The MSC 1993 World Users Conf Proc Paper No 9 May 1993 Tsutsui Keicchiro Nogami Ray Development of a Nonlinear Frequency Response Program for Simulating Vehicle Ride Comfort MSC 1995 World Users Conf Proc Paper No 37 May 1995 Visintainer Randal H Aslani Farhang Shake Test Simulation Using MSC NASTRAN MSC 1994 World Users Conf Proc Paper No 32 June 1994 Wamsler Manfred Krusemann Rolf Calculating and Interpreting Contact Forces Between Brake Disc and Linings in Frequency Response Analysis Proc of the 18th MSC Eur Users Conf Paper No 7 June 1991 Yen K Z Y Hsueh W C Hsui T C Chatter Suppression of a CNC Lathe in Inside Diameter Cutting The Sixth Annual MSC Taiwan Users Conf Proc Paper No 4 November 1994 DYNAMICS MODES FREQUENCIES AND VIBRATIONS Korean Structural Analysis of Solar Array Substate MSC 1994 Korea Users Conf Proc December 1994 in Korean Korean Optimal Design of Chip Mounter Considering Dynamic Characteristics MSC 1994 Korea Users Conf Proc December 1994 in Korean Korean A Study on
264. ers Conf Proc Vol I Paper No 12 March 1987 Corder P R Persh R Castigliano and Symbolic Programming in Finite Element Analysis Proceedings of the 16th Annual Energy Sources Technology Conference and Exhibition Houston 1993 Coyette J P Wijker J J The Combined Use of MSC NASTRAN and Sysnoise for Evaluating the Dynamic Behavior of Solar Array Panels Proc of the 20th MSC European Users Conf Paper No 16 September 1993 Curti G Chiandussi G Scarpa F Calculation of Eigenvalue Derivatives of Acousto Structural Systems with a Numerical Comparison MSC 23rd European Users Conf Proc Italian Session September 1996 Defosse H Sergent A Vibro Acoustic Modal Response Analysis of Aerospace Structures Proc of the MSC NASTRAN Eur Users Conf April 1985 Deloo Ph Dunne L Klein M Alter DMAPS for the Generation Assembly and Recovery of Craig Bampton Models in Dynamic Analyses Actes de la 2 me Conf rence Francaise Utilisateurs des Logiciels MSC Toulouse France September 1995 NX Nastran Basic Dynamic Analysis User s Guide l 3 Appendix References and Bibliography Denver Richard E Menichello Joseph M Alternate Approaches to Vibration and Shock Analysis Using NASTRAN Sixth NASTRAN Users Collog pp 199 212 October 1977 NASA CP 2018 Detroux P Geraets L H Instability at Restart or Change of Time Step with NASTRAN in the Presence of Nonlinear Loads Proc of t
265. ert MSC s Solvers Predict the Best Attachment of the Sunbeam Tiger Fiberglass Front End MSC 1996 World Users Conf Proc Vol II Paper No 16 June 1996 Marcus Melvyn 8 A Finite Element Method Applied to the Vibration of Submerged Plates J of Ship Research Vol 22 No 2 pp 94 99 June 1978 l 24 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Marcus Melvyn S Everstine Gordon C Hurwitz Myles M Experiences with the QUAD4 Element for Shell Vibrations Sixteenth NASTRAN Users Colloq pp 39 43 April 1988 NASA CP 2505 Mase M Saito H Application of FEM for Vibrational Analysis of Ground Turbine Blades MSC NASTRAN Users Conf March 1978 McMeekin Michael Kirchman Paul An Advanced Post Processing Methodology for Viewing MSC NASTRAN Generated Analyses Results MSC 1994 World Users Conf Proc Paper No 21 June 1994 Mei Chuh Rogers James L Jr NASTRAN Nonlinear Vibration Analyses of Beam and Frame Structures NASTRAN Users Exper pp 259 284 September 1975 NASA TM X 3278 Mei Chuh Rogers James L Jr Application of the TRPLT1 Element to Large Amplitude Free Vibrations of Plates Sixth NASTRAN Users Colloq pp 275 298 October 1977 NASA CP 2018 Meyer Karl A Normal Mode Analysis of the IUS TDRS Payload in a Payload Canister Transporter Environment Eighth NASTRAN Users Colloq pp 113 130 October 1979 NASA CP 2131 Michiue Shi
266. ey must be combined using NX Nastran Basic Dynamic Analysis User s Guide 5 19 Chapter 5 Frequency Response Analysis the DLOAD Bulk Data entry The total applied load is constructed from a linear combination of component load sets as follows iP SPS iP t i Equation 5 27 S overall scale factor S scale factor for the 1 th load set P i th load set P total applied load The DLOAD Bulk Data entry has the following format Field Contents SID Load Set ID S Overall scale factor Si Individual scale factors Li Load Set ID numbers for RLOAD1 and RLOAD2 entries As an example in the following DLOAD entry a dynamic Load Set ID of 33 is created by taking 0 5 times the loads in the Load Set ID of 14 adding to it 2 0 times the loads in the Load Set ID of 27 and multiplying that sum by an overall scale factor of 3 25 As with other frequency dependent loads a dynamic load combination defined by the DLOAD Bulk Data entry is selected by the DLOAD Case Control command 5 6 Solution Frequencies A major consideration when you conduct a frequency response analysis is selecting the frequency at which the solution is to be performed There are six Bulk Data entries that you can use to select the solution frequencies It is important to remember that each specified frequency results in an independent solution at the specified excitation frequency To select the loading frequencies use the FREQ FREQ1 FREQ2 FREQ3 FREQ
267. f Numerical Problems Static Analysis Models used in static analysis must be constrained to ground in at least a statically determinate manner even for unloaded directions For example a model intended for only gravity loading must be constrained in horizontal directions as well as vertical directions The evidence of unconstrained directions is that the entire model is a mechanism that is the large ratio occurs at the last grid point in the internal sequence Another source of high ratios arises from connecting soft elements to stiff elements Local stiffness is a function of element thickness moment per unit rotation through element thickness cubed force per unit deflection and is inversely proportional to mesh spacing again in linear through cubic ratios Some relief is possible by sequencing the soft degrees of freedom first in the internal sequence although this is difficult to control in the presence of automatic resequencing F 6 NX Nastran Basic Dynamic Analysis User s Guide Numerical Accuracy Considerations More reliable corrections are to replace the very stiff elements with rigid elements or to place the soft and stiff elements in different superelements A third source of high ratios is the elements omitted through oversight The corrective action here is to start with the grid points listed in the diagnostics and track back through the elements connected to them through the upstream grid points The missing elements may b
268. f no motion det denotes the determinant of a matrix 2 tn 1 2 Ifdet amp e M 0 then a non trivial solution Aoi 0 is obtained for K o M o 0 Equation 3 7 From a structural engineering point of view the general mathematical eigenvalue problem reduces to one of solving the equation of the form NX Nastran Basic Dynamic Analysis User s Guide 3 5 Chapter 3 Real Eigenvalue Analysis det K w M 0 Equation 3 8 or det K A M 0 Equation 3 9 where wW The determinant is zero only at a set of discrete eigenvalues or W There is an eigenvector 1 i which satisfies Equation 3 7 and corresponds to each eigenvalue Therefore Equation 3 7 can be rewritten as KK o M f 0 i 12 3 Equation 3 10 Each eigenvalue and eigenvector define a free vibration mode of the structure The i th eigenvalue is related to the i th natural frequency as follows E i AT Equation 3 11 where fi i th natural frequency w J The number of eigenvalues and eigenvectors is equal to the number of degrees of freedom that have mass or the number of dynamic degrees of freedom There are a number of characteristics of natural frequencies and mode shapes that make them useful in various dynamic analyses First when a linear elastic structure is vibrating in free or forced vibration its deflected shape at any given time is a linear combination of all of
269. ffness The Bulk Data is in free format modes The first six modes are requested ND is 6 with V1 and V2 blank The GRDSET Bulk NORMAL MODES TIME 240 SOL 03 CEND ECHO NONE ALL DISPLACEMENT PLOT 1 SPC 1 METHOD BEGIN BULK 5 SGRDSET GRDSET S CP SEIGRL BILGRE 5 NORM SHFSCL V1 V2 ND MSGLVL MAXSET er l SMATI MAT1 Gy NU RHO 1 00E7 0 334 E MID 3 j loapa basic model ENDDATA S Figure 3 27 Abridged Input File for Test Fixture Model 3 35 NX Nastran Basic Dynamic Analysis User s Guide Chapter 3 Real Eigenvalue Analysis Figure 3 28 shows the first four mode shapes The first mode is a bending mode the second and third modes are twist modes and the fourth mode is a bending mode Figure 3 28 Test Fixture Mode Shapes Quarter Plate Model This example is a quarter model of a simply supported flat plate shown in Figure 3 29 This example illustrates the use of multiple boundary conditions new in Version 68 for modeling symmetric structures In this case the plate is doubly symmetric 3 36 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis Lines of 5ymmetrv EB EI 55 Si 55 as amp 5 amp amp Full Model l v E 2 55 Quarter Model Figure 3 29 Derivation of Quarter Plate Model A portion of the input file is shown in Figure 3 30 Four subcases are used
270. for Heavy Truck Cabs Using Adams MSC NASTRAN and P FATIGUE MSC 1994 World Users Conf Proc Paper No 5 June 1994 Barber Pam Arden Kevin Dynamic Design Analysis Method DDAM Using MSC NASTRAN MSC 1994 World Users Conf Proc Paper No 31 June 1994 Barnett Alan R Ibrahim Omar M Sullivan Timothy L Goodnight Thomas W Transient Analysis Mode Participation for Modal Survey Target Mode Selection Using MSC NASTRAN DMAP MSC 1994 World Users Conf Proc Paper No 8 June 1994 Bellinger Dean Dynamic Analysis by the Fourier Transform Method with MSC NASTRAN MSC 1995 World Users Conf Proc Paper No 10 May 1995 Chargin M L Dunne L W Herting D N Nonlinear Dynamics of Brake Squeal MSC 1996 World Users Conf Proc Vol V Paper No 47 June 1996 NX Nastran Basic Dynamic Analysis User s Guide 1 31 Appendix References and Bibliography Cifuentes A O Herting D N Transient Response of a Beam to a Moving Mass Using a Finite Element Approach Innovative Numerical Methods in Engineering Proc of the Fourth Int Symp on Numerical Methods in Engineering Springer Verlag pp 533 539 March 1986 Cifuentes A O Lalapet S Transient Response of a Plate to an Orbiting Mass Proc of the Second Panamerican Cong of Applied Mechanics January 1991 Cifuentes A O Lalapet S A General Method to Determine the Dynamic Response of a Plate to an Orbiting Mass Computers and Structures V
271. formation of Large Finite Element Models Proc of the MSC NASTRAN Users Conf Paper No 12 March 1979 Vandepitte D Wijker J J Appel S Spiele H Normal Modes Analysis of Large Models and Applications to Ariane 5 Engine Frame Proc of the 18th MSC Eur Users Conf Paper No 6 June 1991 Vollan Arne Kaporin Igor Babikov Pavel Practical Experience with Different Iterative Solvers for Linear Static and Modal Analysis of Large Finite Element Models Proc of the 21st MSC European Users Conf Italian Session September 1994 NX Nastran Basic Dynamic Analysis User s Guide I 29 Appendix References and Bibliography Walker James W Evaluation of MSC NASTRAN Generalized Dynamic Reduction and Response Spectrum Analysis by Comparison with STARDYNE MSC NASTRAN Users Conf March 1978 DYNAMICS RESPONSE SPECTRUM Barber Pam Arden Kevin Dynamic Design Analysis Method DDAM Using MSC NASTRAN MSC 1994 World Users Conf Proc Paper No 31 June 1994 Cutting Fred Individual Modal Accelerations as the Result of a Shock Response Spectra Input to a Complex Structure The 1989 MSC World Users Conf Proc Vol I Paper No 11 March 1989 Gassert W Wolf M Floor Response Spectra of a Reactor Building Under Seismic Loading Calculated with a 3 D Building Model Proc of the MSC NASTRAN Eur Users Conf June 1983 Hirata M Ishikawa K Korosawa M Fukushima S Hoshina H Seismic Analy
272. frequencies for this example are 1 676 Hz and 10 066 Hz 3 42 NX Nastran Basic Dynamic Analysis User s Guide Chapter 4 Rigid Body Modes e Overview e SUPORT Entry e Examples NX Nastran Basic Dynamic Analysis User s Guide 4 1 Chapter 4 Rigid Body Modes 4 1 Overview A structure or a portion of a structure can displace without developing internal loads or stresses if it is not sufficiently tied to ground constrained These stress free displacements are categorized as rigid body modes or mechanism modes Rigid body Modes Rigid body modes occur in unconstrained structures such as satellites and aircraft in flight For a general unconstrained 3 D structure without mechanisms there are six rigid body modes often described as T1 T2 T3 R1 R2 and R3 or combinations thereof Rigid body modes can also be approximated for certain kinds of dynamic or modal tests in which the test specimen is supported by very flexible supports such as bungee cords or inflatable bags In this case the test specimen itself does not distort for the lowest mode s but instead displaces as a rigid body with all of the deformation occurring in the flexible support Rigid body modes can improperly occur if a structure that should be constrained is not fully constrained for example in a building model for which the boundary conditions SPCs were forgotten Mechanism Modes A mechanism mode occurs when a portion of the structure can displace as a rig
273. g forces contain little contribution from these higher modes In the mode acceleration method the inertia and damping forces are first computed from the modal solution These forces are then combined with the applied forces and are used to obtain more accurate displacements by performing a static analysis The mode acceleration method provides more accurate answers but with increased cost The mode acceleration method is selected by specifying PARAM DDRMM 1 and PARAM MODACCO O 11 7 Fluid Structure Interaction Four major methods are available in NX Nastran to model fluid effects These methods are described below Hydroelastic Analysis Small motions of compressible or incompressible fluids coupled to a structure may be analyzed with this option The fluid is modeled with axisymmetric hydroelastic elements CFLUIDi which may be connected to an arbitrary structure modeled with an axisymmetric wetted surface Each fluid point RINGFL on a cross section defines the scalar pressure which is expanded to a Fourier series around the circumference Complex modes and frequency response solutions are available for the coupled fluid structure problems Normal modes solutions are available for fluid only problems All solutions may include gravity effects 1 e sloshing on a free surface This capability was developed specifically to analyze liquid fueled booster rockets but may also be useful for problems involving other types of axisymmetric storage
274. ge Multiplier Method see the NX Nastran Advanced Dynamic Analysis User s Guide NX Nastran Basic Dynamic Analysis User s Guide 7 Chapter 1 Fundamentals of Dynamic Analysis e Overview e Equations of Motion e Dynamic Analysis Process e Dynamic Analysis Types NX Nastran Basic Dynamic Analysis User s Guide 1 1 Chapter 1 Fundamentals of Dynamic Analysis 1 1 Overview With static structural analysis it is possible to describe how to use NX Nastran without including a detailed discussion of the fundamental equations However because there are several types of dynamic analyses each with a different mathematical form you must have some knowledge of both the physics of dynamics and the manner in which the physics is represented to use NX Nastran efficiently for dynamic analysis This chapter e contains important information on notation and terminology used throughout the rest of the book e introduces the equations of motion for a single degree of freedom dynamic system see Equations of Motion e illustrates the dynamic analysis process see Dynamic Analysis Process e characterizes the types of dynamic analyses described in this guide see Dynamic Analysis Types Note See References and Bibliography for a list of references for structural dynamic analysis Dynamic Analysis Versus Static Analysis Two basic aspects of dynamic analysis differ from static analysis e Dynamic loads are applied
275. ger that 1s greater than or equal to the number of Bulk Data entries from your cold start run For conventional dynamic analysis i e non superelement restarts involving model changes e g changing the thickness of a plate are not very efficient Therefore the savings is probably minimal if any However in the case of additional output requests or a restart from a modes run to a response run the savings can be substantial This type of restart is covered extensively in Examples For superelement analysis even restarts involving model changes can be beneficial as long as these changes are localized 8 6 NX Nastran Basic Dynamic Analysis User s Guide Restarts in Dynamic Analysis 8 5 Determining the Version for a Restart Not all versions in the database are restartable For each run a message is printed near the top of the F04 file indicating the version number of the current job In general if a job completes without any fatal messages then that particular version is restartable It is a good idea to keep a brief log of all the restartable versions since this is probably the most reliable source of information regarding whether a version is restartable If a restart job failed e g due to Bulk Data error then this newly created version is not restartable which is indicated by the following error message at the bottom of the F06 file USER WARNING MESSAGE 784 XCLNUP VERSION yyy PROJECT zzz OP THIS DATA BASE IS NOT
276. gravity location which 1s relative to the reference point in the basic coordinate system For this example problem the center of gravity locations are determined to be Table G 3 Mass Center of Gravity Locations Mass Center of Gravity Location in Principal Mass Axes Component x x 1 x mas fos 0 02 0251 The center of gravity location given in Figure G 3 is the same as shown in Figure G 2 NX Nastran Basic Dynamic Analysis User s Guide G 13 Appendix G Grid Point Weight Generator 5 Following the center of gravity calculation is the calculation to determine the moments of 5 inertia for the center of gravity with respect to the principal mass axes as shown in Figure G 19 5 r hij Mu MZ MY n Mp MXY EE Mg MXZ IS M M X MZ Igy D3 Mp3 M Y Z S r 2 2 133 M33 M Y B M X Equation G 19 For the example the inertia matrix S is given by 4 3 7 877 662 H 5 877 5 623 342 662 342 3 432 Equation G 20 6 The final step is to compute the principal moments of inertia and the principal directions of the momental ellipsoid commonly referred to as the principal axes in text books An intermediate inertia matrix 7 is generated by reversing the sign on the off diagonal terms of S For the inertia matrix given in Equation G 20 7 is given by G 14 NX Nastran Basic Dynamic Analysis User s Guide Grid Point Weight Gene
277. he MSC NASTRAN Eur Users Conf June 1983 Deuermeyer D W Clifford G A Petesch D J Traditional Finite Element Analysis Opportunities for Parallelism Computing Systems in Engineering Vol 2 No 2 3 pp 157 165 1991 Dirschmid Dr W Nolte Dr F Dunne L W Application of an FRF Based Update Method to the Model Parameter Tuning of an Hydraulic Engine Mounting Proc of the 18th MSC Eur Users Conf Paper No 10 June 1991 Drago Raymond J Margasahayam Ravi N Resonant Response of Helicopter Gears Using 3 D Finite Element Analysis The MSC 1988 World Users Conf Proc Vol I Paper No 20 March 1988 Elchuri V Smith G C C Gallo A Michael An Alternative Method of Analysis for Base Accelerated Dynamic Response in NASTRAN Eleventh NASTRAN Users Colloq pp 89 112 May 1983 Everstine Gordon C Schroeder Erwin A The Dynamic Analysis of Submerged Structures NASTRAN Users Exper pp 419 430 September 1975 NASA TM X 3278 Everstine Gordon C Structural Analogies for Scalar Field Problems Int J for Numerical Methods in Engineering Vol 17 No 3 pp 471 476 March 1981 Everstine G C Dynamic Analysis of Fluid Filled Piping Systems Using Finite Element Techniques J of Pressure Vessel Technology Vol 108 pp 57 61 February 1986 Flanigan Christopher C Accurate and Efficient Mode Acceleration Data Recovery for Superelement Models The MSC 1988 World Users Conf Pro
278. he damped and undamped natural frequencies are nearly identical This result is significant because it avoids the computation of damped natural frequencies which can involve a considerable computational effort for most practical problems Therefore solutions for undamped natural frequencies are most commonly used to determine the dynamic characteristics of the system see Real Eigenvalue Analysis However this does not imply that damping is neglected in dynamic response analysis Damping can be included in other phases of the analysis as presented later for frequency and transient response see Frequency Response Analysis and Transient Response Analysis Forced Vibration Analysis Forced vibration analysis considers the effect of an applied load on the response of the system Forced vibrations analyses can be damped or undamped Since most structures exhibit damping damped forced vibration problems are the most common analysis types 1 8 NX Nastran Basic Dynamic Analysis User s Guide Fundamentals of Dynamic Analysis The type of dynamic loading determines the mathematical solution approach From a numerical viewpoint the simplest loading is simple harmonic sinusoidal loading In the undamped form the equation of motion becomes mi t ku t psinwt Equation 1 16 In this equation the circular frequency of the applied loading is denoted by w This loading frequency is entirely independent of the structural natural frequenc
279. he length of the bar the actual maximum deformation is printed at the top of the plot S PLOT COMMANDS FOR BAR MODAL FREQUENCY RESPONSE MAGNITUDE PHASE Executive Case Control OUTPUT REQUESTS MAGNITUDE PHASE ISPLACEMENT PHASE PLOT ALL STRUCTURE PLOTS OUTPUT PLOT DEFINE ELEMENTS IN PLOT SET SET 333 ALL PLOT AXES R Z S X T Y AXES MZ X Y VIEW 0 0 0 FIND SCALE ORIGIN 5 SET 333 S PLOT UNDEFORMED SHAPE PLOT SET 333 ORIGIN 5 PLOT DEFORMED SHAPE AT 2 05 HZ PLOT FREQUENCY DEFORMATION 0 RANGE 2 05 2 051 MAGNITUDE SET 333 5 BEGIN BULK 5 REQUIRED FOR FREQUENCY FROZEN STRUCTURE PLOTS PARAM DDRMM 1 PARAM CURVPLOT 1 nrnonnns gt rest of Bulk Data ENDDATA Figure 9 3 Frequency Response Structure Plot Commands for the Bar Model Magnitude Phase Undeformed Shape Max Def 0 394 ML Frequency 2 05 Figure 9 4 Frequency Response Structure Plots for the Bar Model Magnitude Phase The same plots are regenerated except that now the displacements are in real imaginary format the default Figure 9 5 shows the plot commands Note that the imaginary component is selected by PHASE LAG 90 Figure 9 6 shows the resulting plots The default is chosen such 9 4 NX Nastran Basic Dynamic Analysis User s Guide Plotted Output that the maximum plotted deformation is 5 of the length of the bar the actual maximum deformation is printed at the top of the plo
280. herwise required Figure 9 8 shows the resulting plots The plots show the displacements at the following times 0 25 0 50 and 0 75 seconds which are overlaid on the undeformed shape The default is chosen such that the maximum plotted deformation is 5 of the length of the bar the actual maximum deformation is printed at the top of the plot For this case it may be better to specify a maximum deformation so that the plots will show relative amplitudes S PLOT COMMANDS FOR BAR MODAL TRANSIENT RESPONSE Executive Case Control S OUTPUT REQUESTS DISPLACEMENT PLOT S STRUCTURE PLOTS OUTPUT PLOT S DEFINE ELEMENTS IN PLOT SET SET 333 ALL ALL PLOT AXES R Z S X T Y AXES MZ X Y VIEW O 0 0 FIND SCALE ORIGIN 5 SET 333 PLOT DEFORMED SHAPE AT TIMES 0 25 0 5 0 75 PLOT TRANSIENT DEFORMATION 0 RANGE 0 25 0 251 PLOT TRANSIENT DEFORMATION 0 RANGE 0 50 0 501 PLOT TRANSIENT DEFORMATION 0 RANGE 0 75 0 751 BEGIN BULK S S REQUIRED FOR TIME FROZEN STRUCTURE PLOTS PARAM DDRMM 1 gt rest of Bulk Data ENDDATA SET 333 OET 2323 SET 333 Figure 9 7 Transient Response Structure Plot Commands for the Bar Model 9 6 NX Nastran Basic Dynamic Analysis User s Guide Plotted Output Max Det 0 040 m C s Q Time 0 25 Max Def 0 069 y B NENNEN lime 0 50 Max Det 0 057 Time 0 75 Figure 9 8 Transient Response Structure Plots for the Bar Model Alth
281. ical approaches to solving for natural frequencies and modes shapes The reason for seven different numerical techniques is because no one method is the best for all problems While most of the methods can be applied to all problems the choice is often based on the efficiency of the solution process The methods of eigenvalue extraction belong to one or both of the following two groups e Transformation methods e Tracking methods In the transformation method the eigenvalue equation is first transformed into a special form from which eigenvalues may easily be extracted In the tracking method the eigenvalues are extracted one at a time using an iterative procedure The recommended real eigenvalue extraction method in NX Nastran is the Lanczos method The Lanczos method combines the best characteristics of both the tracking and transformation methods For most models the Lanczos method is the best method to use Two of the real eigenvalue extraction methods available in NX Nastran are transformation methods e Householder method e Modified Householder method 3 10 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis Tthe real eigenvalue extraction method available in NX Nastran is classified as tracking methods e Sturm modified inverse power method The remainder of this section briefly describes the various methods The theory and algorithms behind each method can be found in the NX Nastran Numerical Methods
282. id body which can occur when there is an internal hinge in the structure An example of a mechanism is a ball and socket joint or a rudder in an airplane A mechanism mode can also occur when two parts of a structure are improperly joined A common modeling error resulting in a mechanism is when a bar is cantilevered from a solid element the bar has rotational stiffness and the solid has no rotational stiffness resulting in a pinned connection when the two are joined The presence of rigid body and or mechanism modes is indicated by zero frequency eigenvalues Due to computer roundoff the zero frequency eigenvalues are numerical zeroes on the order of 1 0E 4 Hz or less for typical structures The same unconstrained model may give different values of the rigid body frequencies when run on different computer types Rigid body modes generated by NX Nastran are orthogonal with respect to each other and with respect to the flexible or elastic modes Each rigid body mode has the following property 6 1 IMH Oig gt 0 Orie KHO 0 Equation 4 1 7 where LP rig f denotes the rigid body mode shapes M denotes the mass matrix and K denotes the stiffness matrix The rigid body modes contain no strain energy Figure 4 1 depicts the rigid body modes for a two dimensional model of a straight beam Because the two dimensional model has three DOFs per grid point x translation y translation and z rotation there are three rigid body modes The
283. iderations involved in a static analysis are similarly applied in dynamic analysis However with a dynamic analysis you must also include additional input data to define the dynamic character of the structure In static analysis the stiffness properties are defined by element and material properties These same properties are also required for dynamic analysis along with the addition of mass and damping Mass Input describes mass input and Damping Input describes damping input Correct specification of units is very important for dynamic analysis Incorrect specification of units is probably more difficult to diagnose in dynamic analysis than in static analysis Because NX Nastran has no built in set of units you must ensure their consistency and accuracy Units in Dynamic Analysis describes the common variables and units for dynamic analysis Direct Matrix Input concludes this chapter with a discussion of direct matrix input 2 2 Mass Input Mass input is one of the major entries in a dynamic analysis Mass can be represented in a number of ways in NX Nastran The mass matrix is automatically computed when mass density or nonstructural mass is specified for any of the standard finite elements CBAR CQUAD4 etc in NX Nastran when concentrated mass elements are entered and or when full or partial mass matrices are entered Lumped and Coupled Mass Mass is formulated as either lumped mass or coupled mass Lumped m
284. ient Response Analysis mSi t k S t p t Equation 6 17 where m i th modal mass k i th modal stiffness Di i th modal force Note that there is no damping in the resulting equation The next subsection describes how to include damping in modal transient response Once the individual modal responses x are computed physical responses are recovered as the summation of the modal responses QUO 6 1t5C01 Equation 6 18 Since numerical integration is applied to the relatively small number of uncoupled equations there is not as large a computational penalty for changing A as there 1s in direct transient response analysis However a constant At is still recommended Another efficiency option in the modal transient solution is that the output time interval may be greater than the solution time interval In many cases it 1s not necessary to sample output response at each solution time For example if the solution is performed every 0 001 second the results can be output every fifth time step or every 0 005 second This efficiency reduces the amount of output Damping in Modal Transient Response Analysis If the damping matrix 5 exists the orthogonality property see Overview of Normal Modes Analysis of the modes does not in general diagonalize the generalized damping matrix 6 B 6 diagonal Equation 6 19 In the presence of a B matrix the modal transient approach solves the coupled prob
285. igan C An Alternate Method for Mode Acceleration Data Recovery in MSC NASTRAN Proc of the Conf on Finite Element Methods and Technology Paper No 7 March 1981 Flanigan Christopher C Efficient and Accurate Procedures for Calculating Data Recovery Matrices for Superelement Models The 1989 MSC World Users Conf Proc Vol II Paper No 44 March 1989 Flanigan Christopher C Implementation of the IRS Dynamic Reduction Method in MSC NASTRAN The MSC 1990 World Users Conf Proc Vol I Paper No 13 March 1990 Friberg Olof Karlsson Rune Akesson Bengt Linking of Modal and Finite Elements in Structural Vibration Analysis Proc of the 2nd Int Modal Analysis Conf and Exhibit Vol 1 pp 330 339 February 1984 Gallaher Bruce Determination of Structural Dynamic Response Sensitivity to Modal Truncation MSC NASTRAN Users Conf Proc Paper No 10 March 1986 Ghosh Tarun Nall Marsha Muniz Ben Cheng Joseph Space Station Solar Array Pointing System Control Structure Interaction Study Using CO ST IN for Modal Reduction The MSC 1993 World Users Conf Proc Paper No 68 May 1993 Gieseke R K Modal Analysis of the Mated Space Shuttle Configuration NASTRAN Users Exper pp 221 236 September 1971 NASA TM X 2378 Girard A Boullet A Dardel R Dynamic Analysis of a Satellite Using the Normal Modes of the Appendages Proc of the MSC NASTRAN Eur Users Conf April 1985 Grandle Robert E
286. ile for the DMIG Example In this example EXSTIF is chosen as the name of the input stiffness matrix Therefore in order to bring in this stiffness matrix and add it to the global stiffness matrix the Case Control command K2GG EXSTIF is required Note that these stiffness terms are additions to any existing terms in the global stiffness matrix at that location and not replacements of the stiffness terms at that location In the Bulk Data Section five DMIG entries are required one for the header entry and four for the data column entries since there are four non null columns in the above matrix For the header entry the same name EXSTIF must be used to match the name called out in the Case Control Section The third field is 0 which must be the value used for the header entry The fourth field IFO is set to 6 to denote a symmetric matrix input The fifth field TIN is set to 1 to denote that the matrix is real single precision The terms in the matrix are referenced in terms of their external grid IDs when using the DMIG entries Physically each term in a particular column of the stiffness matrix K represents the induced reactive load in the i th degree of freedom due to a unit displacement in the j th direction with all other displacement degrees of freedom held to zero Since the matrix is symmetric only the lower triangular portion of the matrix is input The first DMIG data column entry defines the first column of the abov
287. ility or database integrity problem UFM 6136 USER FATAL MESSAGE 6136 INSUFFICIENT CORE FOR SYMBOLIC NUMERIC PHASE OF SPARSE DECOMPOSITION USER ACTION INCREASE CORE BY WORDS USER INFORMATION NOW REVERTING BACK TO ACTIVE COLUMN DECOMPOSITION UPON USER REQUEST If this message is issued in the symbolic phase the memory estimate is not necessarily conservative and even more memory may be required although this estimate is fairly accurate for Version 68 Also the memory increase required is only for the symbolic phase It is not unusual for the decomposition phase to require more memory than the symbolic phase To increase the chances for a successful run increase the memory even more than the amount indicated in this message After the run is complete determine the amount of memory actually used and use this as a guideline for similar runs in the future The user information message is written if SYSTEM 166 1 that is if there is not enough memory for sparse decomposition and you should switch to regular decomposition UWM 6137 USER WARNING MESSAGE 6137 DFMSDD INPUT MATRIX IS RANK DEFICIENT RANK USER ACTION CHECK MODEL One of your matrices is singular See the NX Nastran Numerical Methods User s Guide for a discussion of singularity H 14 NX Nastran Basic Dynamic Analysis User s Guide UFM 6138 UIM 6214 UWM 6243 UIM 6361 UIM 6480 Diagnostic Messages for Dynamic A
288. in the Lanczos method There is possible ill conditioning check your model USER WARNING MESSAGE 5407 INERTIA STURM SEQUENCE COUNT DISAGREES WITH THE NUMBER OF MODES ACTUALLY COMPUTED IN AN SUB INTERVAL This message shows a serious problem Spurious modes were found in the Lanczos method Check the multiplicity of the roots given in the interval See the NX Nastran Numerical Methods User s Guide USER WARNING MESSAGE 5408 FACTORIZATION FAILED SHIFT CHANGED TO No user action to be taken This message occurs only for the Lanczos method USER WARNING MESSAGE 5411 NEGATIVE TERM ON DIAGONAL OF MASS MATRIX VIBRATION OR STIFFNESS BUCKLING ROW TEE VALUE KKK The message is given from the REIGL module which performs a necessary but not sufficient check on the positive semi definiteness of the indicated matrix Look for evidence of negative mass such as minus signs on input Negative terms on the factor of the indicated matrix must be removed for correct answers something has caused a negative term on the diagonal of the mass or stiffness matrix Look for explicitly defined negative mass and or stiffness terms Also check the continuation entries on the PBEAM entry An incorrect entry for the SO field may lead to improper mass definition For example if SO is set to NO at a particular X XB location the continuation entry for defining four stress locations on the cross section C D E F 1s not used If
289. ing the Set ID with SDAMPING Set ID Case Control command NX Nastran Basic Dynamic Analysis User s Guide 6 9 Chapter 6 Transient Response Analysis Field Contents TID Table identification number Type of damping units G default TYPE CRIT Q fi Frequency value cycles per unit time gi Damping value in the units specified At resonance the three types of damping are related by the following equations b G Ds 2 b 2m 1 1 9 3 Equation 6 23 The values of fi units cycles per unit time and gi define pairs of frequencies and dampings Note that gi can be entered as structural damping default critical damping or quality factor The entered damping is internally converted to structural damping using Equation 6 23 Straight line interpolation is used for modal frequencies between consecutive fi values Linear extrapolation is used at the ends of the table ENDT ends the table input For example if modal damping is entered using Table 6 1 and 1f modes exist at 1 0 2 5 3 6 and 5 5 Hz NX Nastran interpolates and extrapolates as shown in Figure 6 2 and the table Note that there is no table entry at 1 0 Hz NX Nastran uses the first two table entries at f 2 0 and f 3 0 to extrapolate the value for f 1 0 6 10 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis 0 20 0 10 entered value e computed value 0 0 en S 2 0 4 0 6 0 f Hz Figure 6 2 Ex
290. inimum of input Combining simple loadings to create complicated loading distributions that vary in position as well as frequency is also a straightforward task The remainder of this section describes the Bulk Data entries for frequency dependent excitation The description is given in terms of the coefficients that define the dynamic load See the NX Nastran Quick Reference Guide for more complete Bulk Data descriptions Frequency Dependent Loads RLOAD1 Entry The RLOAD1 entry is a general form in which to define a frequency dependent load It defines a dynamic loading of the form VOU ALC Pf Je i The values of the coefficients are defined in tabular format on a TABLEDi entry You need not explicitly define a force at every excitation frequency Only those values that describe the character of the loading are required NX Nastran will interpolate for intermediate values oa 2 4 5 o8 9 wo iTO 2xft1 08 7 DAREA DELAY DPHASE TYPE Field Contents SID Set ID defined by a DLOAD Case Control command or a DLOAD Bulk Data entry DAREA Identification number of the DAREA entry set that defines A Integer gt 0 DELAY Identification number of the DELAY entry set that defines t DPHASE Identification number of the DPHASE entry set that defines q TC TABLEDi entry that defines C f TD TABLEDi entry that defines D f TYPE Defines the type of the dynamic excitation Integer character or blank Default
291. iography l 1 Overview This appendix includes references of interest in the field of dynamic analysis Two categories are included The first category General References lists books that cover the general range of structural dynamic analysis The second category Bibliography is an excerpt from the dynamic analysis section of the NX Nastran Bibliography 1 2 General References 1 Paz M Structural Dynamics Theory and Computation Van Nostrand Reinhold New York N Y 1985 2 Bathe K J and Wilson E L Numerical Methods in Finite Element Analysis Prentice Hall Englewood Cliffs N J 1976 9 Harris C M and Crede C E Shock and Vibration Handbook McGraw Hill New York N Y 1976 4 Clough R W and Penzien J Dynamics of Structures McGraw Hill New York N Y 1975 5 Timoshenko S Young D H and Weaver Jr W Vibration Problems in Engineering John Wiley and Sons New York N Y 1974 6 Hurty W C and Rubinstein M F Dynamics of Structures Prentice Hall Englewood Cliffs N J 1964 I 3 Bibliography DYNAMICS GENERAL Abdallah Ayman A Barnett Alan R Widrick Timothy W Manella Richard T Miller Robert P Stiffness Generated Rigid Body Mode Shapes for Lanczos Eigensolution with Support DOF Via a MSC NASTRAN DMAP Alter MSC 1994 World Users Conf Proc Paper No 10 June 1994 Anderson William J Kim Ki Ook Zhi Bingchen Bernitsas Michael M Hoff Curtis Cho Kyu
292. ion Remark S FILE bd08barl dat S NORMAL MODES RUN 8 10 NX Nastran Basic Dynamic Analysis User s Guide Restarts in Dynamic Analysis ID CANT BEAM SOL 103 TIME 10 CEND TITLE CANTILEVER BEAM NORMAL MODES COLD START RUN SPC 1 METHOD 10 S BEGIN BULK S CBAR 1 CBAR CBAR CBAR CBAR CBAR CBAR CBAR CBAR CBAR EIGRL GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID GRID MAT1 Te DELO MCN 24 09T74 PARAM AUTOSPC YES PARAM WTMASS 102 PBAR 1 1 SPCL aL 123456 HBmPHBmpHmpBHBmpmpmp Co O QW Oc tO oo I 2 p pBHbpmpmpbmpmpbmpbpm HO XO CO 10Y O14 CO 2 IS S ES OOATD OB WN C9 NO ho NOI ERES CO CO CO CO O1 E 4 OO 10 O1 S CO PO S OO OO OG OO C2 C2 C CD FF CO 1 0 OB CO PO CO CO Co C5oCoCoCco Co Cocco C OO OCC 0000 OnBPROUNODWO gt mehe HO 158 4 3 8 Du QusB 2 414 K OY S ENDDATA Figure 8 2 Input File for Normal Modes Run FILE bd08bar2 dat S S NORMAL MODES RUN S REQUEST EIGENVECTOR PRINTOUTS FROM PREVIOUS RUN S RESTART VERSION 1 KEEP ASSIGN MASTER bd08barl MASTER S ID CANT BEAM SOL T03 TIME 10 CEND TITLE EIGENVECTORS DATA RECOVERY RESTART RUN SPC 1 METHOD 10 DISP ALL PRINT EIGENVECTORS BEGIN BULK ENDDATA Figure 8 3 Input File for Requesting Eigenvectors FILE bdO08bar3 dat S NORMAL MODES RUN MODIFY PBAR RESTART ASSIGN MASTER bd08barl MASTER ID CANT BEAM SOL 103 NX Na
293. ion is performed every time At changes thereby increasing the cost of the analysis if the time increment is changed Therefore the recommendation is to determine the smallest At required based on the loading and frequency range and then use that Atthroughout the entire transient response analysis Duration of the Computed Response The length of the time duration is important so that the lowest flexible e g non rigid body mode oscillates through at least one cycle For example if the lowest flexible mode has a frequency of 0 2 Hz then the time duration of the computed response should be at least 5 0second A better guideline is to make the duration the longer of the following twice the period of the lowest flexible mode or one period of the lowest flexible mode after the load has been removed or reached a constant value The time duration is set on the TSTEP entry by multiplying the integration time step by the number of time steps N Value of Damping The proper selection of the damping value is relatively unimportant for analyses that are of very short duration such as a crash impulse or a shock blast The specification of the damping value is most important for long duration loadings such as earthquakes and is critical for loadings such as sine dwells that continually add energy into the system Verification of the Applied Load The applied load can be verified by applying the load suddenly over one or two time increments a
294. ion sequences a different default causes a fatal error exit after printing the MECH matrix For both types of solution sequences the opposite action may be requested by setting the value of PARAM BAILOUT explicitly Also the criterion used for identifying large ratios may be changed using PARAM MAXRATIO For static analysis values between 10 and 109 are almost always acceptable Values between 107 and 108 are questionable When investigating structures after finding these values some types of structures may be found to be properly modeled It is still worthwhile to investigate the structures with questionable values The solutions with differential stiffness effects offer another method to obtain nonpositive definite stiffness matrices For example a column undergoing compressive gravity loading has a potential energy source in the gravity load A lateral load that 1s stabilizing 1n the absence of gravity 1 e a decreased load causes a decreased deflection is destabilizing when applied in a postbuckled state Eigensolutions Using the Inverse Iteration and Lanczos Methods The matrix K M is decomposed where is an eigenvalue shift and K and M are the stiffness and mass matrices respectively This condition allows the solution of models with rigid body modes since the singularities in K are suppressed if there are compensating terms in M The only conditions that should cause fatal messages due to singularity are 1 Th
295. ion program statements NX Nastran s DMAP capability enables you to modify these solution sequences and write your own solution sequences DMAP is a high level language with its own compiler and grammatical rules DMAP statements contain data blocks and parameters and operate on them in a specified manner For example the DMAP statement ADD U1 U2 U3 adds matrices U1 and U2 together and calls the output U3 The DMAP statement MATPRN U3 11 14 NX Nastran Basic Dynamic Analysis User s Guide Advanced Dynamic Analysis Capabilities prints the matrix U3 Numerous DMAP Alters for dynamic analysis are provided see the NX Nastran Release Guide for further information Many of these DMAP Alters are for dynamic analysis There are alters for model checkout modal initial conditions the addition of static results to transient response results frequency dependent impedance and modal test analysis correlation among others The NX Nastran Advanced Dynamic Analysis User s Guide describes a DMAP Alter for enforced motion using the Lagrange multiplier approach In summary DMAP is a powerful capability that allows you to modify NX Nastran to satisfy your needs NX Nastran Basic Dynamic Analysis User s Guide 11 15 Appendix A Glossary of Terms CMS Critical Damping Damping DOF Dynamic Amplification Factor Forced Vibration Analysis Free Vibration Analysis Frequency Response Analysis LMT Mechanism Mode Mode
296. ire structure for an enforced translational degree of freedom and 106 times the mass moment of inertia of the entire structure for a rotational DOF The factor 109 is a safe limit that should produce approximately six digits of numerical accuracy The large mass method is implemented in direct transient and frequency response analysis by placing large masses m on all enforced degrees of freedom and supplying applied dynamic loads specified by Equation 7 2 that is the function is input on entries normally used for the input of loads and the scale factor m can be input on DAREA or DLOAD Bulk Data entries whichever is more convenient CMASSi or CONMi entries should be used to input the large masses 7 2 is not directly helpful if enforced displacement or enforced velocity is specified rather than enforced acceleration However 7 2 can be made serviceable in frequency response analysis by noting that 7 2 NX Nastran Basic Dynamic Analysis User s Guide Enforced Motion M 2 H IWH H Equation 7 3 so that uH n u 2 p m iOm u O m u Equation 7 4 The added factor iw or W can be carried by the function tabulated on the TABLEDi entry used to specify the frequency dependence of the dynamic load In the case of transient analysis provision is made on the TLOAD1 and TLOAD2 entries for you to indicate whether an enforced displacement velocity or acceleration is supplied TYPE 1 2 or 3 NX Nastran then
297. is User s Guide References and Bibliography Cifuentes A O Herting D N Transient Response of a Beam to a Moving Mass Using a Finite Element Approach Innovative Numerical Methods in Engineering Proc of the Fourth Int Symp on Numerical Methods in Engineering Springer Verlag pp 533 539 March 1986 Cifuentes A O Non Linear Dynamic Problems Using a Combined Finite Element Finite Difference Technique Proc of the 6th Conf on the Mathematics of Finite Elements and Application April May 1987 Carney Kelly S Abdallah Ayma A Hucklebridge Arthur A Implementation of the Block Krylov Boundary Flexibility Method of Component Synthesis The MSC 1993 World Users Conf Proc Paper No 26 May 1993 Del Basso Steve Singh Sudeep Lindenmoyer Alan J Component Mode Synthesis of Space Station Freedom Using MSC NASTRAN Superelement Architecture The MSC 1990 World Users Conf Proc Vol II Paper No 48 March 1990 Duncan Alan E Application of Modal Modeling and Mount System Optimization to Light Duty Truck Ride Analysis 4th Int Conf on Veh Struct Mech pp 113 128 November 1981 SAE 811313 Flanigan Christopher C Abdallah Ayman Manella Richard Implementation of the Benfield Hruda Modal Synthesis Method in MSC NASTRAN The MSC 1992 World Users Conf Proc Vol I Paper No 11 May 1992 Garnek Michael Large Space Structure Analysis Using Substructure Modal Test Data AIAA ASME ASCE A
298. is filled and the job fails with the following error messages in the F06 file USER FATAL MESSAGE 1012 GALLOC DBSET DBALL IS FULL AND NEEDS TO BE EXPANDED NX Nastran Basic Dynamic Analysis User s Guide E 5 Appendix E File Management Section For small to medium size problems it is best to rerun the job from the beginning with a larger file allocation For large problems if rerunning the job is not practical then the database can be expanded with the following statements RESTART ASSIGN MASTER dynl MASTER ASSIGN DBADD morespace DB EXPAND DBALL LOGICAL DBADD 50000 These statements create an additional member with a logical name of DBADD to the existing DBset DBALL This member points to a new physical file called morespace DB which may contain up to a maximum of 50000 NX Nastran blocks In this case you are restarting from dynl1 MASTER RESTART Purpose Allows you to continue from the end of the previous run to the current run without resolving the problem from the beginning Format RESTART PROJECT proj ID VERSION version ID LAST KEEP NOKEEP Project identifier used in the original run which can have up to 40 characters This is optional and is normally not used The default proj ID is blank version ID The version number you are restarting from The default is the last version If this option is used then the version that you are restarting from 1s also saved KEEP
299. is skipped default Y The mass properties are computed relative to the origin of the basic coordinate system exist The mass properties are computed relative to grid point x If grid point x does not the properties are computed relative to the basic coordinate system For the four masses shown in Figure G 1 the resulting GPWG output is given in Figure G 2 OUTPUTFROMGRIDPOINTWEIGHTGENERATOR REFERENCE POINT O0 O 1 300000E 01 0 000000E 00 0 000000E 00 0 000000E 00 5 000000E 00 1 000000E 00 0 000000E 00 0 000000E 00 DIRECTION e ob oe ob ox Ig 0 000000E 00 0 000000E 00 0 000000E 00 5 000000E 00 3 000000E 00 1 300000E 01 0 000000E 00 5 000000E 00 0 000000E 00 7 000000E 00 0 000000E 00 1 300000E 01 3 000000E 00 7 000000E 00 0 000000E 00 5 000000E 00 3 000000E 00 8 000000E 00 1 500000E 00 2 500000E 00 0 000000E 00 7 000000E 00 1 500000E 00 1 000000E 01 0 000000E 00 3 000000E 00 7 000000E 00 0 000000E 00 2 500000ETDO 0 000000E 00 8 000000E 00 0 000000E 00 0 000000E 00 1 000000E 00 0 000000E 00 0 Q00000E 00 1 000000E 00 MASS AXIS SYSTEM S MASS X C G Y C G Z C G X 1 300000E 01 Y 1 300000E 01 Z 1 300000E 01 I S 5 384615E 00 0 000000E 00 2 307692E 01 3 846154E 01 5 384616E 01 0 000000E 00 3 846154E 01 5 384616E 01 2 307692E 01 0 000000E 00 1 153847E 01 1 923079E 01 1 153847E 01 4 307692E 00 1 153846E 00 x 1 923079E 01 1 153846E 00 3 538461E 00
300. isions For example in designing the supporting structure for a rotating fan the design requirements may require that the natural frequency of the supporting structure have a natural frequency either less than 85 or greater than 110 of the operating speed of the fan Specific knowledge of quantities such as displacements and stresses are not required to evaluate the design Forced response is the next step in the dynamic evaluation process The solution process reflects the nature of the applied dynamic loading A structure can be subjected to a number of different dynamic loads with each dictating a particular solution approach The results of a forced response analysis are evaluated in terms of the system design Necessary modifications are made to the system design These changes are then applied to the model and analysis parameters to perform another iteration on the design The process is repeated until an acceptable design is determined which completes the design process The primary steps in performing a dynamic analysis are summarized as follows 1 Define the dynamic environment loading 2 Formulate the proper finite element model NX Nastran Basic Dynamic Analysis User s Guide 1 13 Chapter 1 Fundamentals of Dynamic Analysis 3 Select and apply the appropriate analysis approach es to determine the behavior of the structure 4 Evaluate the results 1 4 Dynamic Analysis Types You can perform the following types of basic
301. isks in the general message text and indicates that 102 is the identification number of the undefined coordinate system The abbreviation UFM refers to User Fatal Message UWM refers to User Warning Message UIM refers to User Information Message and SFM refers to System Fatal Message UFM 2066 USER FATAL MESSAGE 2066 UNDEFINED GRID POINT ON DAREA CARD A dynamic loading entry references an undefined grid point UFM 2069 USER FATAL MESSAGE 2069 UNDEFINED GRID POINT IN TRANSIENT INITIAL CONDITION SET An attempt has been made to specify initial conditions for an undefined grid point All degrees of freedom with initial conditions must be in the analysis set NX Nastran Basic Dynamic Analysis User s Guide H 1 Appendix H UFM 2071 UFM 2074 UFM 2079 UFM 2088 UFM 2101A UFM 2107 UFM 2109 UFM 2133 UFM 2135 Diagnostic Messages for Dynamic Analysis USER FATAL MESSAGE 2071 DYNAMIC LOAD SET REFERENCES UNDEFINED TABLE A referenced dynamic load table was not present in the Bulk Data USER FATAL MESSAGE 2074 UNDEFINED TRANSFER FUNCTION A transfer function set was selected in the Case Control but was not present in the Bulk Data USER FATAL MESSAGE 2079 GRID OR SCALAR POINT HAS AN UNDEFINED COORDINATE REFERENCED ON A DAREA DELAY DPHASE CARD The C or component value for scalar type points must be zero or one USER FATAL MESSAGE 2088 DUPLIC
302. its e Mass e Damping e Boundary Conditions e Loads e Meshing e Eigenvalue Analysis e Frequency Response Analysis e Transient Response Analysis e Results Interpretation and Verification e Computer Resource Requirements NX Nastran Basic Dynamic Analysis User s Guide 10 1 Chapter 10 Guidelines for Effective Dynamic Analysis 10 1 Overview Dynamic analysis is more complicated than static analysis because of more input mass damping and time and frequency varying loads and more output time and frequency varying results Results from static analysis are usually easier to interpret and there are numerous textbook solutions for static analysis that make it relatively easy to verify certain static analyses Nevertheless the guidelines in this chapter help you to perform dynamic analysis in a manner that will give you the same level of confidence in the dynamic results that you would have with static results This chapter covers the following topics e Overall analysis strategy e Units e Mass e Damping e Boundary conditions e Loads e Meshing e Eigenvalue analysis e Frequency response analysis e Transient response analysis e Results interpretation e Computer resource estimation 10 2 Overall Analysis Strategy Part of any analysis strategy whether it be for dynamic analysis or static analysis is to gain confidence with the modeling procedures first The best way to accomplish this is to run small sim
303. its normal modes ug b5 Equation 3 12 where 3 6 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis u 19 5 Xi vector of physical displacements i th mode shape i th modal displacement Second if K and M are symmetric and real as is the case for all the common structural finite elements the following mathematical properties hold gt IMMO 0 ifi Equation 3 13 gt MHO Em j th generalized mass Equation 3 14 and oF KHO 0 ifi Equation 3 15 10 Y IK 6 k j th generalized stiffness om Equation 3 16 Also from Equation 3 14 and Equation 3 16 Rayleigh s equation is obtained OF KI O 6 1 IMHO Equation 3 17 Equation 3 13 and Equation 3 15 are known as the orthogonality property of normal modes which ensures that each normal mode is distinct from all others Physically orthogonality of modes means that each mode shape is unique and one mode shape cannot be obtained through a linear combination of any other mode shapes In addition a natural mode of the structure can be represented by using its generalized mass and generalized stiffness This 1s very useful in formulating equivalent dynamic models and in component mode synthesis see Advanced Dynamic Analysis Capabilities If a structure is not totally constrained in space it is possible for the structure to displace move as a rigid body or as a partial or comp
304. its base Modal frequency response is run from 0 to 100 Hz with a frequency step size of 0 2 Hz Eigenvalues to 1000 Hz are computed using the Lanczos method Modal damping is applied as 2 critical damping for all modes 5 36 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis Lo m Ps Figure 5 21 Bracket Model Figure 5 22 shows the abridged input file The LSEQ entry is used to apply the pressure loads PLOAD4 entries Note that the LSEQ and RLOAD1 entries reference a common DAREA ID 999 and that there 1s no explicit DAREA entry Table 5 10 shows the relationship between the Case Control commands and the Bulk Data entries FILE bd05bkt dat S BRACKET MODEL S CHAPTER 5 FREQUENCY RESPONSE SOL 111 S MODAL FREQUENCY RESPONSE TIME 100 CEND TITLE BRACKET MODEL SUBTITLE MODAL FREQUENCY RESPONSE ANALYSIS SPC 1 S METHOD 777 7 DLOAD 2 LOADSET 3 SDAMPING 4 FREQUENCY 5 OUTPUT REQUEST SET 123 999 DISPLACEMENT PHASE PLOT 123 S XYPLOTS S X Y plot commands BEGIN BULK S O s ae ee we 2 Sis dak Hau iae d Du d eae a D scu a wc a CN p Dr c ee DD rere s S NORMAL MODES TO 1000 HZ SEIGRL SID V1 V2 EIGRL ra 0 1 1000 S EXCITATION FREQUENCY DEFINITION 0 TO 100 HZ SFREQ1 SID F1 DE NDF PREOL 5 0 0 0 2 500 S MODAL DAMPING OF 2 CRITICAL FOR ALL MODES STABDMP1 TID TYPE TABD1 S TABD1 F1 G1 F2 G2 ETC TABDMP1 4 CRIT TAB
305. ixed for component mode analysis or dynamic reduction e Extra degrees of freedom introduced in dynamic analysis 1Strictly speaking sb and sg are not exclusive with respect to one another Degrees of freedom may exist in both sets simultaneously These sets are exclusive however from the other mutually exclusive sets NX Nastran Basic Dynamic Analysis User s Guide C 3 Appendix C The Set Notation System Used in Dynamic Analysis Table C 3 Sets in NX Nastran Combined Sets Indicates Union of Two Sets Set Name s shtes g All points eliminated by single point constraints The structural coordinates remaining after the reference coordinates are removed points left over The total set of physical boundary points for superelements aq Lt wq The set assembled in superelement analysis d ate The set used in dynamic analysis by the direct i method f dto Unconstrained free structural points fe f e Free structural points plus extra points a gt All structural points not constrained by n IS de multipoint constraints z All structural points not constrained by fie nte iae multipoint constraints plus extra points H4 H All structural grid points including scalar points g All physical points S p t sa Physical and constrained aerodynamic points a pst k Physical set for aerodynamics b Statically independent set minus the statically fr ofl atl paga
306. ixth Australasian MSC Users Conf Proc November 1992 Lee Jyh Chian Using Residual Vector in MSC NASTRAN Modal Frequency Response to Improve Accuracy The 4th MSC Taiwan Users Conf Paper No 8 November 1992 in Chinese Lee Sang H Effective Modal Mass for Characterization of Vibration Modes Proc of the Second MSC NASTRAN Users Conf in Korea Paper No 22 October 1991 Liepins Atis A Conaway John H Application of NASTRAN to Propeller Induced Ship Vibration NASTRAN Users Exper pp 361 376 September 1975 NASA TM X 3278 Lim Tae W Kashangaki Thomas A L Structural Damage Detection of Space Truss Structures Using Best Achievable Eigenvectors AIAA Journal v32 n 5 May 1994 Lipman Robert R Computer Animation of Modal and Transient Vibrations Fifteenth NASTRAN Users Colloq pp 111 117 August 1987 NASA CP 2481 Liu Dauh Churn Shieh Niahn Chung Vibration Suppression of High Precision Grinding Machine Using Finite Element Method MSC NASTRAN The Sixth Annual MSC Taiwan Users Conf Proc Paper No 7 November 1994 Lu Y P Killian J W Everstine G C Vibrations of Three Layered Damped Sandwich Plate Composites J of Sound and Vibration Vol 64 No 1 pp 63 71 1979 Lui C Y Mason D R Space Shuttle Redesigned Solid Rocket Motor Nozzle Natural Frequency Variations with Burn Time AIAA SAE ASME 27th Joint Propulsion Conf Paper No AIAA 91 2301 June 1991 Lundgren G
307. ized Input 0 0 05 lime sec Figure 7 10 Response for Enforced Displacement With the Rigid Body Mode NX Nastran Basic Dynamic Analysis User s Guide 7 17 Chapter 7 Enforced Motion Figure 7 11 Response for Enforced Displacement Without the Rigid Body Mode Now consider a change to the enforced displacement run In this case remove the rigid body mode s contribution either by not computing the rigid body mode by setting V1 to a small positive value such as 0 01 Hz or by neglecting the rigid body mode in the transient response by setting PARAM LFREQ to a small positive number such as 0 01 Hz Figure 7 12 shows the resulting displacement and acceleration responses at grid points 1 and 11 Note that the responses are relative to the structure and are not absolute The relative displacement of grid point 1 should be zero and it is very close to zero i e 10 10 as a result of the sufficiently large mass 7 18 NX Nastran Basic Dynamic Analysis User s Guide Enforced Motion Figure 7 12 Response for Enforced Displacement Without the Rigid Body Mode NX Nastran Basic Dynamic Analysis User s Guide 7 19 Chapter 8 Restarts in Dynamic Analysis e Overview e Automatic Restarts e Structure of the Input File e User Interface e Determining the Version for a Restart e Examples NX Nastran Basic Dynamic
308. l constraint terms The decomposition of this matrix with the sparse decomposition methods pivoting strategy 1s stable You may control the pivoting strategy with the THRESH DMAP parameter mentioned earlier The default value 6 1s adequate for most Lagrange multiplier solutions In fact higher ranging up to 2 values provide better accuracy while increasing the number of pivots may result in performance degradation NX Nastran Basic Dynamic Analysis User s Guide F 9 Appendix G Grid Point Weight Generator G 1 Overview The grid point weight generator GPWG calculates the masses centers of gravity and inertias of the mathematical model of the structure The data are extracted from the mass matrix by using a rigid body transformation calculation Computing the mass properties is somewhat complex because a finite element model may have directional mass properties that is the mass may differ in each of the three coordinate directions From a mathematical point of view the NX Nastran mass may have tensor properties similar to the inertia tensor This complexity is reflected in the GPWG output All of the transformations used in calculating the mass properties are shown for the general case Since most models have the same mass in each of the three coordinate directions the GPWG output provides more information than you generally need To avoid unnecessary confusion and at the same time provide the necessary information for the a
309. l Modes e Examples NX Nastran Basic Dynamic Analysis User s Guide 3 1 Chapter 3 Real Eigenvalue Analysis 3 1 Overview The usual first step in performing a dynamic analysis is determining the natural frequencies and mode shapes of the structure with damping neglected These results characterize the basic dynamic behavior of the structure and are an indication of how the structure will respond to dynamic loading Natural Frequencies The natural frequencies of a structure are the frequencies at which the structure naturally tends to vibrate if it is subjected to a disturbance For example the strings of a piano are each tuned to vibrate at a specific frequency Some alternate terms for the natural frequency are characteristic frequency fundamental frequency resonance frequency and normal frequency Mode Shapes The deformed shape of the structure at a specific natural frequency of vibration is termed its normal mode of vibration Some other terms used to describe the normal mode are mode shape characteristic shape and fundamental shape Each mode shape is associated with a specific natural frequency Natural frequencies and mode shapes are functions of the structural properties and boundary conditions A cantilever beam has a set of natural frequencies and associated mode shapes Figure 3 1 If the structural properties change the natural frequencies change but the mode shapes may not necessarily change For example if the ela
310. lding very little displacement response In this case the structure does not respond to the loading because the loading is changing too fast for the structure to respond In addition any measurable displacement response will be 180 degrees out of phase with the loading i e the displacement response will have the opposite sign from the force Finally if w w 1 resonance occurs In this case the magnification factor is 1 2Z and NX Nastran Basic Dynamic Analysis User s Guide 1 11 Chapter 1 Fundamentals of Dynamic Analysis the phase angle is 270 degrees The dynamic amplification factor and phase lead are shown in Figure 1 5 and are plotted as functions of forcing frequency Amplification Factor Forcing Freq Iency oD Figure 1 5 Harmonic Forced Response with Damping In contrast to harmonic loadings the more general forms of loading impulses and general transient loading require a numerical approach to solving the equations of motion This technique known as numerical integration is applied to dynamic solutions either with or without damping Numerical integration is described in Transient Response Analysis 1 3 Dynamic Analysis Process Before conducting a dynamic analysis you should first define the goal of the analysis prior to the formulation of the finite element model Consider the dynamic analysis process shown in Figure 1 6 You must evaluate the finite element model in terms of the type of dynamic loading to b
311. le point constraint for a set of grid points VELOCITY Grid point velocity time history for a set of grid points Table 6 6 Element Output from a Transient Analysis ELSTRESS or STRESS Element stress time history for a set of elements ELFORCE or FORCE Element force time history for a set of elements STRAIN Element strain time history for a set of elements Because the results may be output for many time steps the volume of output can be very large Prudent selection of the output quantities is recommended A number of Bulk Data entries are unique to transient response analysis They can be combined with other generic entries in the Bulk Data Bulk Data entries directly related to transient analysis are summarized in Table 6 7 Table 6 7 Bulk Data Entries for Transient Response Analysis Bulk Data Direct or et TSTEP Both Integration time step and Required solution control TLOADi Dynamic loading parameters NX Nastran Basic Dynamic Analysis User s Guide 6 25 Chapter 6 Transient Response Analysis Table 6 7 Bulk Data Entries for Transient Response Analysis LSEQ Both Dynamic loading from static Optional loads Time dependent tables for 1 TABLEDi TLOADi Optional TIC Direct Initial conditions on grid Optional scalar and extra points DAREA Both Load component and scale Required factor DELAY Time delay on dynamic load Dynamic load combination DLOAD Both required if TLOAD1 and Optional TLOAD2 are used
312. lem but should not be used for other purposes A possible cause of this error is when large offsets large relative to the element length are used for the BEAM element and coupled mass is selected USER FATAL MESSAGE 4671 LOAD COMBINATION REQUESTED BUT LSEQ CARDS DO NOT EXIST FOR SID Check the LSEQ entries H 8 NX Nastran Basic Dynamic Analysis User s Guide UFM 4683 UWM 4698 UIM 5010 UFM 5025 Diagnostic Messages for Dynamic Analysis USER FATAL MESSAGE 4683 MASS STIFFNESS MATRIX NEEDED FOR EIGENVALUE ANALYSIS The eigensolution module was given a purged that is nonexistent mass or stiffness matrix Common causes include the deletion of mass density input on MAT entries user restart errors in the superelement solution sequences It therefore sets the number of generalized coordinates to zero This condition can be detected from UIM 4181 Provide mass matrix generating data by any of several means including a mass density entry on material entries concentrated masses and g type DMIG entries Possibly no mass matrix is defined Check for the following e RHO entry on MATi e NSM entry on element properties 1 e PSHELL PBAR e CONMi or CMASSi NX Nastran needs at least one of the above to compute the mass matrix Incorrect cross sectional properties may also lead to this error but typically show up as another error USER WARNING MESSAGE 4698 STATISTICS FOR DECOMPOSITION OF MATRIX THE F
313. lem in terms of modal coordinates using the direct transient numerical integration approach described in Section 4 2 as follows A1 t5 13 A5 43 t5 1 A4115 11 Equation 6 20 where 6 8 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis T W grs Jed Ag o0 GITE P EP a ie o T wes 9 These equations are similar to the direct transient method except that they are in terms of modal coordinates Since the number of modes used in a solution is typically much less than the number of physical variables the direct integration of the modal equations is not as costly as with physical variables If damping is applied to each mode separately the decoupled equations of motion can be maintained When modal damping is used each mode has damping b The equations of motion remain uncoupled and have the following form for each mode mii bSi t k t pit Equation 6 21 or E t 20 wt t e Ef Spt S t 26 0 5 0 ej S pi I Equation 6 22 where Z 6 2m w modal damping ratio we k m J modal frequency eigenvalue The TABDMP1 Bulk Data entry defines the modal damping ratios A table is created by the frequency damping pairs specified on a TABDMP1 entry The solution refers to this table for the damping value to be applied at a particular frequency The TABDMP1 Bulk Data entry has a Set ID A particular TABDMP1 table is activated by select
314. leness Once you are satisfied apply the correct time variation to the load and compute the results Again use X Y plots to verify the accuracy of the results 6 Finally perform any other dynamic analyses such as response spectrum analysis random response nonlinear transient response or dynamic response optimization The confidence gained by using the previous steps first helps to ensure that you have an accurate model at this stage These and other guidelines are described further in the remainder of this chapter Verify Model Connectivity Properties Boundary Conditions Verify Static Analysis with gravity load with actual load Verify Normal Modes Analysis few modes many modes T Verify Frequency Response Analysis 0 0 Hz entire frequency range Verify Transient Response Analysis step load actual load Run Other Dynamic Response Analyses response spectrum random response etc Figure 10 1 Simplified Flow Chart of the Overall Analysis Strategy 10 4 NX Nastran Basic Dynamic Analysis User s Guide Guidelines for Effective Dynamic Analysis 10 3 Units Mistakes in units and boundary conditions Boundary Conditions are among the most common mistakes made when performing finite element analysis NX Nastran does not assume a particular set of units but it does assume that they are consistent It is up to you to ensure that the units that you use are both consistent and correct T
315. les per unit time P Phase angle degrees C Exponential coefficient B Growth coefficient Spatial Distribution of Loading DAREA Entry The DAREA entry defines the degrees of freedom where the dynamic load is to be applied and a scale factor to be applied to the loading The DAREA entry provides the basic spatial distribution of the dynamic loading Field Contents SID Set ID specified by TLOADi entries Pi Grid extra or scalar point ID Ci Component number Ai Scale factor A DAREA entry is selected by the TLOAD1 or TLOAD2 entry Any number of DAREA entries may be used all those with the same SID are combined Time Delay DELAY Entry The DELAY entry defines the time delay t in an applied load Field Contents SID Set ID specified by TLOADi entry Pi Grid extra or scalar point ID Ci Component number ty Time delay for Pi Ci A DAREA entry must be defined for the same point and component Any number of DELAY entries may be used all those with the same SID are combined 6 16 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis Dynamic Load Tabular Function TABLEDi Entries The TABLEDi entries i 1 through 4 each define a tabular function for use in generating frequency dependent dynamic loads The form of each TABLEDi entry varies slightly depending on the value of i as does the algorithm for y x The x values need not be evenly spaced The TABLED1 TABLED2 and TABLED8 ent
316. lete mechanism For each possible component of rigid body motion or mechanism there exists one natural frequency which is equal to zero NX Nastran Basic Dynamic Analysis User s Guide 3 7 Chapter 3 Real Eigenvalue Analysis The zero frequency modes are called rigid body modes Rigid body motion of all or part of a structure represents the motion of the structure in a stress free condition Stress free rigid body modes are useful in conducting dynamic analyses of unconstrained structures such as aircraft and satellites Also rigid body modes can be indicative of modeling errors or an inadequate constraint set For example the simple unconstrained structure in Figure 3 3 has a rigid body mode l H1 li FI 1 0 0 1015 Figure 3 3 Rigid Body Mode of a Simple Structure When both masses move the same amount as a rigid body there is no force induced in the connecting spring A detailed discussion of rigid body modes is presented in Rigid body Modes An important characteristic of normal modes is that the scaling or magnitude of the eigenvectors is arbitrary Mode shapes are fundamental characteristic shapes of the structure and are therefore relative quantities In the solution of the equation of motion the form of the solution is represented as a shape with a time varying amplitude Therefore the basic mode shape of the structure does not change while it is vibrating only its amplitude changes For example thr
317. licopter Structural Dynamics ALAA ASME ASCE AHS ASC 32nd Structures Structural Dynamics and Materials Conf Part 1 Paper No 91 0924 pp 227 237 April 1991 Stockwell Alan E Perez Sharon E Pappa Richard S Integrated Modeling and Analysis of a Space Truss Test Article The MSC 1990 World Users Conf Proc Vol I Paper No 16 March 1990 Struschka M Goldstein H Approximation of Frequency Dependant Nonlinearities in Linear FE Models Proc of the 15th MSC NASTRAN Eur Users Conf October 1988 Subrahmanyam K B Kaza K R V Brown G V Lawrence C Nonlinear Bending Torsional Vibration and Stability of Rotating Pre Twisted Preconed Blades Including Coriolis Effects National Aeronautics and Space Administration January 1986 NASA TM 87207 Tecco T C Analyzing Frequency Dependent Stiffness and Damping with MSC NASTRAN MSC NASTRAN Users Conf Proc Paper No 25 March 1985 Thornton E A Application of NASTRAN to a Space Shuttle Dynamics Model NASTRAN Users Exper pp 421 438 September 1971 NASA TM X 2378 Ting Tienko Test Analysis Correlation for Multiple Configurations The MSC 1993 World Users Conf Proc Paper No 74 May 1998 Tinti Francesco Carlo Scaffidi Costantino Structural Dynamics and Acoustic Design of Engine Component in View of Exterior Noise Reduction Using Numerical Techniques MSC 1995 European Users Conf Proc Italian Session September 1995 Tur
318. linear Transient Response Analysis The analysis techniques described thus far are applicable for linear elastic analysis for which the mass stiffness and damping matrices are constant over time and constant for all values of applied force However there are many cases for which the matrices are not constant and these cases must be solved with nonlinear analysis techniques Nonlinear analysis requires iterative solution methods thereby making it far more computationally intensive than a corresponding linear analysis Nonlinear transient response analysis is available in NX Nastran in SOL 129 Nonlinear problems are classified into three broad categories geometric nonlinearity material nonlinearity and contact 11 6 NX Nastran Basic Dynamic Analysis User s Guide Advanced Dynamic Analysis Capabilities Geometric Nonlinearity Geometrically nonlinear problems involve large displacements large means that the displacements invalidate the small displacement assumptions inherent in the equations of linear analysis For example consider a thin plate subject to an out of plane load If the deflection of the plate s midplane is approximately equal to the thickness of the plate then the displacement is considered large and a linear analysis is not applicable Another aspect of geometric nonlinear analysis involves follower forces Consider a clamped plate subject to a pressure load As shown in Figure 11 2 the load has followed the pla
319. lue calculated above by 1 182 NX Nastran Basic Dynamic Analysis User s Guide 10 15 Chapter 11 Advanced Dynamic Analysis Capabilities e Overview e Dynamic Reduction e Complex Eigenvalue Analysis e Response Spectrum Analysis e Random Vibration Analysis e Mode Acceleration Method e Fluid Structure Interaction e Nonlinear Transient Response Analysis e Superelement Analysis e Design Optimization and Sensitivity e Control System Analysis e Aeroelastic Analysis e DMAP NX Nastran Basic Dynamic Analysis User s Guide 11 1 Chapter 11 Advanced Dynamic Analysis Capabilities 11 1 Overview The previous chapters describe the most common types of dynamic analysis normal modes analysis frequency response analysis and transient response analysis However NX Nastran contains numerous additional types of dynamic analyses many of these types are documented in the NX Nastran Advanced Dynamic Analysis User s Guide The advanced dynamic analysis capabilities include e Dynamic reduction e Complex eigenanalysis e Response spectrum analysis e Random response analysis e Mode acceleration method e Fluid structure interaction e Nonlinear transient response analysis e Superelement analysis e Design sensitivity and optimization e Control systems e Aeroelastic analysis e DMAP These capabilities are described briefly in the remainder of this chapter 11 2 Dynamic Reduction Dynamic reduction is an optional nu
320. m Select the modal damping Select TIC entries for IC Direct initial conditions from Optional the Bulk Data Select the times for l lNot required when using initial conditions 6 24 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis The types of results available from a transient response analysis are similar to those for a static analysis except that the results vary with time Additional quantities are also available which is characteristic of dynamics problems The output quantities are summarized in Table 6 5 and Table 6 6 Table 6 5 Grid Point Output from a Transient Response Analysis Case Control Command ACCELERATION Grid point acceleration time history for a set of grid points a or Grid point displacement time history for a set of grid points GPSTRESS Grid point stress time history requires SURFACE VOLUME definition in the OUTPUT POST section of the Case Control OLOAD Requests applied load table to be output for a set of grid points SACCELERATION Requests solution set acceleration output d set in direct solutions and modal variables in modal solutions SDISPLACEMENT Requests solution set displacement output d set in direct solutions and modal variables in modal solutions SVECTOR Requests real eigenvector output for the a set in modal solutions SVELOCITY Requests solution set velocity output d set in direct solutions and modal variables in modal solutions SPCFORCES Requests forces of sing
321. m of uncoupled equations The modal method is particularly advantageous if the natural frequencies and mode shapes were computed during a previous stage of the analysis In that case you simply perform a restart see Restarts In Dynamic Analysis Using the modal approach to solve the uncoupled equations is very efficient even for very large numbers of excitation frequencies On the other hand the major portion of the effort in a modal frequency response analysis is the calculation of the modes For large systems with a large number of modes this operation can be as costly as a direct solution This result is especially true for high frequency excitation To capture high frequency response in a modal solution less accurate high frequency modes must be computed For small models with a few excitation frequencies the direct method may be the most efficient because it solves the equations without first computing the modes The direct method is more accurate than the modal method because the direct method is not concerned with mode truncation Table 5 2 provides an overview of which method to use Many additional factors may be involved in the choice of a method such as contractual obligations or local standards of practice 5 5 Frequency Dependent Excitation Definition An important aspect of a frequency response analysis 1s the definition of the loading function In a frequency response analysis the force must be defined as a function of f
322. make sure that LOADSET is spelled correctly USER FATAL MESSAGE 3047 NO MODES WITHIN RANGE AND LMODES 0 A MODAL FORMULATION CANNOT BE MADE The modes used for a modal formulation must be selected by a PARAM entry Set LFREQ HFREQ or LMODES to request modes USER FATAL MESSAGE 3051 INITIAL CONDITION SET WAS SELECTED FOR A MODAL TRANSIENT PROBLEM INITIAL CONDITIONS ARE NOT ALLOWED IN SUCH A PROBLEM The IC command is not allowed for modal transient response problems USER WARNING MESSAGE 3053 THE ACCURACY OF EIGENVALUE TS IN DOUBT HOU QR FAILED TO CONVERGE IN ITERATIONS Each eigenvalue is computed to the precision limits of each machine consistent with the maximum number of iterations allowed USER FATAL MESSAGE 3057 MATRIX I NOT POSITIVE DEFINITE A Cholesky decomposition was attempted on the above matrix but a diagonal term of the factor was imaginary or equal to zero such that the decomposition failed This message is from the regular as opposed to sparse decomposition method This message may be produced because of constraint problems Check the output for UWM 4698 for large factor diagonal ratios and constrain appropriately USER WARNING MESSAGE 4193 A GRID AND COMPONENT SPECIFICATION ON A DPHASE DELAY SID DOES NOT APPEAR ON A DAREA CARD The area specification is set to zero H 4 NX Nastran Basic Dynamic Analysis User s Guide SFM 4276 UWM 4312 UFM 434
323. matrices are generated internally based on the information that you provide in your NX Nastran model Once you provide the grid point locations element connectivities element properties and material properties NX Nastran generates the appropriate structural matrices External Matrices If structural matrices are available externally you can input the matrices directly into NX Nastran without providing all the modeling information Normally this is not a recommended procedure since it requires additional work on your part However there are occasions where the availability of this feature 1s very useful and in some cases crucial Some possible applications are listed below e Suppose you are a subcontractor on a classified project The substructure that you are analyzing 1s attached to the main structure built by the main contractor The stiffness and mass effects of this main structure are crucial to the response of your component but geometry of the main structure is classified The main contractor however can provide you with the stiffness and mass matrices of the classified structure By reading these stiffness and mass matrices and adding them to your NX Nastran model you can account for the effect of the attached structure without compromising security NX Nastran Basic Dynamic Analysis User s Guide 2 13 Chapter 2 Finite Element Input Data e Perhaps you are investigating a series of design options on a component attached to an ai
324. matrix and a MAXRATIO error This condition gives a high rigid body error ratio e The multipoint constraints are statically indeterminate This condition gives high strain energy and a high rigid body error ratio NX Nastran Basic Dynamic Analysis User s Guide 4 7 Chapter 4 Rigid Body Modes e There are too many single point constraints This condition gives high strain energy and a high rigid body error ratio e K is null This condition gives a unit value for the rigid body error but low strain energy see Advanced Dynamic Analysis Capabilities Modeling Considerations When using a SUPORT you must select a set of DOFs that is capable of constraining all the rigid body modes Another way to state this requirement is that the r set must be able to constrain the structure in a statically determinate manner There are usually many choices of DOFs that satisfy this requirement Two choices that work for simple three dimensional structures are e Six DOFs on one grid point when all its degrees of freedom have stiffness e Three translation DOFs normal to one plane two translation DOFs normal to an orthogonal plane and then one translational DOF normal to the last orthogonal plane Such a system can be used for instance on a model composed entirely of solid elements that have no inherent stiffness for grid point rotation See Figure 4 2 Plane 1 1 DM Plane 5 1 2 3 Normal to Plane 1 4 5 Normal to Plane
325. ments Table 3 1 Comparison of Eigenvalue Methods BEEN ur Householder Modified Householder Sturm Modified Inverse Power 3 12 NX Nastran Basic Dynamic Analysis User s Guide Real Eisenvalue Analysis Table 3 1 Comparison of Eigenvalue Methods Method Householder Modified Householder Sturm Modified Inverse Power Relative Cost Medium Low Medium Few Modes j High High Medium Many Modes Cannot analyze singular Expensive for many Limitations IM modes Expensive for many Difficulty with massless Expensive for problems Expensive for problems modes mechanisms l that do not fit in memor Small dense matrices Small dense matrices that fit in memory that fit in memory To determine a few modes Best Application Medium to large models Use with dynamic Backup method reduction Chapter 11 3 6 User Interface for Real Eigenvalue Analysis The EIGR and EIGRL Bulk Data entries define the method and select the parameters that control the eigenvalue extraction procedure The EIGRL entry is used for the Lanczos method and the EIGR entry is used for all of the other methods User Interface for the Lanczos Method The EIGRL entry has the following format Format C3 2 35 3 L5 I 5 1 l e option 1 value 1 option 2 value 2 etc Example Field Contents SID Set identification number Unique Integer 0 The V1 field defines the lower frequency bound the V2 field defines the upper Vi V9 frequency field For vibr
326. merical approach that can be used in NX Nastran to reduce a dynamic model to one with fewer degrees of freedom Typically the intent of dynamic reduction is to increase the efficiency of a dynamic solution by working with smaller matrices while maintaining the dynamic characteristics of the system Dynamic reduction is used for a number of reasons One possible reason may be that a particular model may be too large from a computer resource standpoint computer runtime and or disk space to be solved without using reduction A related issue is that the model may have more detail than required Many times dynamic analyses are performed on models that were initially created for detailed static stress analyses which typically require refined meshes to accurately predict stresses When these static models are used in a dynamic analysis the detailed meshes result in significantly more detail than is reasonably required to predict the natural frequencies and mode shapes accurately Static condensation also called Guyan reduction is the available method in NX Nastran for the dynamic reduction of the eigenequation prior to modal extraction Once the natural frequencies and mode shapes are calculated for the reduced model these modes can be used in the transient or frequency response solution process 11 2 NX Nastran Basic Dynamic Analysis User s Guide Advanced Dynamic Analysis Capabilities Static Condensation In the static condensation process
327. mes you may not know whether the mass matrix is singular To assist you in choosing the appropriate method automatic Householder is available Initially the automatic method uses the standard method In the first step of the method if the mass matrix is not well conditioned for decomposition the method shifts to the corresponding modified method The modified method is More expensive and may introduce numerical noise due to the shift but they resolve most of the numerical problems of the ill conditioned mass matrix The automatic method therefore uses the modified method when necessary for numerical stability but uses the standard method when the numerical stability is accurate Sturm Modified Inverse Power Method This method uses Sturm sequence logic to ensure that all modes are found The Sturm sequence check determines the number of eigenvalues below a trial eigenvalue then finds all of the eigenvalues below this trial eigenvalue until all modes in the designed range are computed This process helps to ensure that modes are not missed The Sturm modified inverse power method is useful for models in which only the lowest few modes are needed This method is also useful as a backup method to verify the accuracy of other methods 3 5 Comparison of Methods Since NX Nastran provides a variety of real eigensolution methods you must decide which is best for your application The best method for a particular model depends on four factors the
328. mic loads have Verify the results for reasonableness Do not go to dynamic analysis until you are satisfied with the results from your static analysis It is recommended at this stage that the model contain PARAM GRDPNT n where n is a reference grid point or 0 the origin of the basic coordinate system Verify the results from the grid point weight generator in order to ensure that the model s rigid body mass and inertia look reasonable This step in conjunction with the static analysis results helps to ensure that the proper mass units are specified Perform an eigenvalue analysis SOL 103 next Compute only a few modes first verify their frequencies and view their mode shapes for reasonableness If your graphical postprocessor can animate the mode shapes do so because that helps you to visualize them Things to check at this step are local mode shapes in which one or a few grid points are moving a very large amount relative to the rest of the model this can indicate poor stiffness modeling in that region and unwanted rigid body modes which can arise due to improper specification of the boundary conditions or a mechanism Once you are satisfied with these results perform the full eigenvalue analysis for as many modes as you need If you have frequency dependent loads perform frequency response analysis SOL 108 or SOL 111 using the dynamic load spatial distribution If your structure is constrained then apply the dynamic load
329. mmand is in the Case Control Section DLOAD 35 in addition to the following entries in the Bulk Data Section RLOAD1 m Bos DELAY DPHASE RLOAD1 DAREA POINT SCALE TABLED1 NNUS LINEAR The DLOAD Set ID 35 in Case Control selects the RLOAD1 entry in the Bulk Data having a Set ID 35 On the RLOAD1 entry is a reference to DAREA Set ID 29 DELAY Set ID 31 and TABLED1 Set ID 40 The DAREA entry with Set ID 29 positions the loading on grid point 30 in the 1 direction with a scale factor of 5 2 applied to the load The DELAY entry with Set ID 31 delays the loading on grid point 30 in the 1 direction by 0 2 units of time The TABLED1 entry with Set ID 40 defines the load in tabular form This table is shown graphically in Figure 5 5 NX Nastran Basic Dynamic Analysis User s Guide 5 17 Chapter 5 Frequency Response Analysis The result of these entries is a dynamic load applied to grid point 30 component T1 scaled by 5 2 and delayed by 0 2 units of time 10 Amplitude on 2 lABLEDI fet tt tt 0 2 4 6 Frequency Hz Figure 5 5 TABLEDI Amplitude Versus Frequency Static Load Sets LSEQ Entry NX Nastran does not have specific data entries for many types of dynamic loads Only concentrated forces and moments can be specified directly using DAREA entries To accommodate more complicated loadings conveniently the LSEQ entry is used to define static load entries that define the spatial distribution of dynamic loads o1
330. mmarized in Table 5 7 Table 5 7 Bulk Data Entries for Frequency Response Analysis FREQ FREQ TABLEDi Frequency dependent tables Load component and scale factor Time delay on dynamic load Phase angle on dynamic load Dynamic load combination required if RLOAD1 and RLOAD2 are used Modal damping table IRequired for RLOAD1 optional for RLOAD2 2The DAREA ID is required the DAREA Bulk Data entry is not required if an LSEQ entry is used 5 9 Examples This section provides several examples showing the input and output These examples are Mode Frequency Teen Bulk Data Output ntries bdO5two EIGRL FREQ1 TABDMP1 RLOAD1 X Y plots linear printed results ii DAREA TABLED1 SORT1 SORT2 EIGRL FREQ1 TABDMP1 DLOAD bd0Sbar RLOAD2 DAREA DPHASE TABLED1 Plots log EIGRL FREQ1 TABDMP1 RLOADI bd05bkt LSEQ TABLED1 PLOAD4 X plot log 5 26 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis These examples are described in the sections that follow Two DOF Model Consider the two DOF system shown in Figure 5 8 Modal frequency response SOL 111 is run with a 20 N load applied to the primary mass grid point 2 across a frequency range of 2 to 10 Hz with an excitation frequency increment of 0 05 Hz Uniform modal damping of 5 critical damping is used Part of the input file is shown below Auxiliary Structure Grid Point 1 V P 20 N sin wt
331. mmon damping case is the underdamped case where b lt b In this case the solution has the form bt A u t e CA sinc jf Bcosw f Equation 1 13 Again A and B are the constants of integration based on the initial conditions of the system The new term Ww represents the damped circular natural frequency of the system This term is related to the undamped circular natural frequency by the following expression NX Nastran Basic Dynamic Analysis User s Guide 1 7 Chapter 1 Fundamentals of Dynamic Analysis ho 2 wJ W l G Equation 1 14 The term Z is called the damping ratio and is defined by ARA CP Equation 1 15 The damping ratio is commonly used to specify the amount of damping as a percentage of the critical damping In the underdamped case the amplitude of the vibration reduces from one cycle to the next following an exponentially decaying envelope This behavior is shown in Figure 1 3 The amplitude change from one cycle to the next is a direct function of the damping Vibration is more quickly dissipated in systems with more damping Amplitude w t lime Figure 1 3 Damped Oscillation Free Vibration The damping discussion may indicate that all structures with damping require damped free vibration analysis In fact most structures have critical damping values in the 0 to 10 range with values of 1 to 5 as the typical range If you assume 10 critical damping Equation 1 4 indicates that t
332. mping These guidelines are only approximate but are nevertheless useful Running a normal modes analysis first helps to compute accurate frequency response results Number of Retained Modes Use enough modes to cover the range of excitation For example if the model is to be excited from 1 to 100 Hz you must use all of the modes with frequencies up to at least 100 Hz This is only a minimum requirement however A better guideline is to use enough modes to cover two to three times the range of excitation in order to provide accurate answers at the high end of the frequency range For example when excitation is applied to 100 Hz modes with frequencies up to 200 to 300 Hz should all be used Size of the Frequency Increment The size of the frequency increment Af must be small enough to ensure that the magnitude of the peak response is accurately computed To ensure this you need to choose a frequency increment small enough so that there are at least five to ten increments within the half power bandwidth frequencies illustrated in Figure 10 2 The frequency increment is defined by Af on the FREQ1 Bulk Data entry Note that FREQ and FREQ2 entries can be used in conjunction with FREQ1 to define more solutions in the areas of resonance the frequencies of these solutions should have been determined by a prior normal modes analysis A nonuniform Af imposes no cost increase relative to a uniform Af Relationship of Damping to the Frequency Increm
333. n F 6 where Z is the identity matrix Equation F 6 is the basis of all the transformation methods of NX Nastran HOU etc The iterative method SINV work directly from EquationF 5 The Lanczos method uses both If A is a symmetric matrix the eigenvectors are orthogonal and they can be normalized such that 6 Ifo WI Equation F 7 dt where o is a square matrix whose columns contain the eigenvectors With this normalization convention then 6 A1I6 A Equation F 8 and A 61 X1I 6 Equation F 9 where I is the eigenvalue diagonal matrix F 2 NX Nastran Basic Dynamic Analysis User s Guide Numerical Accuracy Considerations F 4 Matrix Conditioning Reordering the previous equations any matrix Z can be expressed as a sum of its eigenvalues multiplied by dyadic eigenvector products A AiO HOI A LO Oo tA 0 Ho Equation F 10 5 tale Defining Which 1s a full rank 1 matrix then A Y XB kc Equation F 11 where n is the dimension of A On the average an element of B has the same magnitude as the corresponding element of B Let Bmax be the magnitude of the largest coefficient of all B matrices Then la A tant A d D nax Equation F 12 This equation shows that the terms of A are dominated by the largest eigenvalues Unfortunately the smallest eigenvalues are those of greatest interest for structural models These small eig
334. n frequencies Character Default LINEAR Number of excitation frequencies within each subrange including the end points Integer gt 1 Default 10 A CLUSTER value greater than 1 provides closer spacing of excitation frequencies CLUSTER near the modal frequencies where greater resolution is needed Real gt 0 0 Default 1 0 TYPE NEF FREQ4 The example FREQA chooses 21 equally spaced frequencies across a frequency band of 0 7 fy to 1 3 fy for each natural frequency between 20 and 2000 EROR OR OR bho p ER k po wmm Bm m qw 1 1 1 5 22 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis Field Contents SID Set ID specified by a FREQUENCY Case Control command F1 Lower bound of modal frequency range in cycles per unit time Real 0 0 Upper bound of modal frequency range in cycles per unit time Real gt 0 0 F2 gt F1 Default F1 FSPD Frequency spread the fractional amount specified for each mode which occurs in the frequency range F1 to F2 1 0 gt Real gt 0 0 Default 0 10 NFM Number of evenly spaced frequencies per spread mode Integer gt 0 Default 3 If NFM is even NFM 1 will be used F2 FREQ5 The example FREQ5 will compute excitation frequencies which are 0 6 0 8 0 9 0 95 1 0 1 05 1 1 and 1 2 times the natural frequencies for all natural frequencies but use only the computed frequencies that fall within the
335. nalysis USER FATAL MESSAGE 6138 DFMSB INSUFFICIENT CORE FOR SPARSE FBS USER ACTION INCREASE CORE BY WORDS See UFM 6136 USER INFORMATION MESSAGE 6214 FEWER THAN REQUESTED VECTORS CALCULATED DUE TO INSUFFICIENT TIME This information message occurs in the READ module when there 1s insufficient time to compute eigenvectors Resubmit the job with an increased time limit TIME USER WARNING MESSAGE 6243 READ THE DEGREE OF FREEDOM D O F REQUESTED FOR POINT NORMALIZATION HAS NOT BEEN SPECIFIED ON THE EIGR OR EIGB ENTRY USER INFORMATION THE D O F PRECEDING THE REQUESTED D O F IN THE INTERNAL SEQUENCE LIST WILL BE USED The point requested was not in the a set so another point was chosen USER INFORMATION MESSAGE 6361 LANCZOS MODULE DIAGNOSTICS This message prints various levels of diagnostics for the Lanczos method The amount of print depends on the message level set on the EIGRL entry See the NX Nastran Numerical Methods User s Guide for more information USER INFORMATION MESSAGE 6480 REIGLA EXTERNAL IDENTIFICATION TABLE FOR DECOMPOSITION MESSAGES FOR MATRIX ROW NUMBER GRID ID COMPONENT This message is output from the REIGL module when using sparse decomposition to convert the internal row number oriented diagnostic messages to external grid and component form NX Nastran Basic Dynamic Analysis User s Guide H 15 Appendix I References and Bibl
336. nd Modal Frequency Response The steps described in the previous section must also be followed when a modal method of response analysis 1s used Also if the enforced degrees of freedom are not sufficient to suppress all rigid body motions which may be the case for an airplane in flight additional DOFs that describe the remaining rigid body motions can also be entered on the SUPORT entry Use of the SUPORT entry is discussed in Rigid body Modes Note that the use of the SUPORT entry is optional The rigid body mode s can be removed from consideration either by not computing them or by using PARAM LFREQ r where r is a small positive number 0 001 Hz for example If this is done the displacements velocities and accelerations obtained are relative to the overall motion of the structure and are not absolute response quantities Stresses and element forces are the same as when the rigid body modes are included because the rigid body modes do not contribute to them Rigid body modes can be discarded to remove rigid body drift Rigid body modes occur when the structure is unconstrained and large masses are applied at the DOFs which if constrained result in a statically determinate structure Redundant constrained DOFs which result in a statically indeterminate structure present a different situation when the constraints are removed and large masses are applied at those redundant DOFs In that case very low frequency modes occur but they are
337. nd comparing the results to a static solution with the same spatial load distribution The transient results should have a peak value of twice the static results If the transient results are not twice the static results check the LSEQ and DAREA entries Another way to verify the applied load is to inspect it visually via the X Y plots 10 12 Results Interpretation and Verification Because of the time and frequency varying nature of dynamic analysis results can be more difficult to interpret than for static analysis The key to proper results interpretation is plotting Structure plotting is necessary for a proper understanding of the deformed shapes of the modes and X Y plotting is necessary for a proper understanding of the frequency and transient response Comparing results to hand calculations to known results from similar models or to test data is also very useful Do not accept any analysis results without first performing some type of verification Consider the cantilever beam model shown in Figure 10 5 This is a planar model of the cantilever beam used in the examples in Chapter 3 through Chapter 7 Figure 10 5 shows the loads applied to the beam 10 12 NX Nastran Basic Dynamic Analysis User s Guide Guidelines for Effective Dynamic Analysis Ca aat watt ae att tata utut atat tuat utut DEEP wtatatat atat at tat a at at tuat utut Hus i P atata at atat tuat utut at aat atata at P atata at atat tuat utut
338. nd is critical for loadings such as rotating machinery that continually add energy to the structure The proper specification of the damping coefficients can be obtained from structural tests or from published literature that provides damping values for structures similar to yours As is discussed in detail in Frequency Response Analysis 5 and Transient Response Analysis certain solution methods allow specific forms of damping to be defined The type of damping used in the analysis is controlled by both the solution being performed and the NX Nastran data entries In transient response analysis for example structural damping must be converted to equivalent viscous damping Structural Damping Specification Structural damping is specified on the MATi and PARAM G Bulk Data entries The GE field on the MAT entry is used to specify overall structural damping for the elements that reference this material entry This definition is via the structural damping coefficient GE For example the MAT1 entry specifies a structural damping coefficient of 0 1 An alternate method for defining structural damping is through PARAM G r where r is the structural damping coefficient This parameter multiplies the stiffness matrix to obtain the structural damping matrix The default value for PARAM G is 0 0 The default value causes this source of structural damping to be ignored Two additional parameters are used in transient response analysis to co
339. nding mode shapes for a full model of the same structure Note that the quarter plate modes match the full plate modes 3 38 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis fF ae ae En E a AU i 1 x t ox x J i i i 1 t k r i ri E E E ue uw of Pew 5 j r we 1 rt d Jom ph yr i a F QM pg ia Tow h i agg Ba z Ji s a a FS e i Pa Y B Ti al x i en i F TOR Sa P gu r a 3 ii ie r s s Ae Figure 3 31 Mode Shapes for the Quarter Model Left and Full Model Right DMIG Example This example illustrates the use of a DMIG entry to input external mass and stiffness The cantilever beam model shown in Figure 3 32 1s used for this purpose The model consists of CBAR elements 1 through 4 Element 5 is a model from another subcontractor that 1s input via DMIG entries The model contains two DOFs R2 and T3 per grid point i se s Bs 2m 3 3 m 6 5 2 3 i y Grid Point ID L Element ID Figure 3 32 Planar Cantilever Beam The stiffness and mass matrices from the contractor for element 5 are as follows NX Nastran Basic Dynamic Analysis User s Guide 3 39 Chapter 3 Real Eigenvalue Analysis Jl 500038 8 Ov Ov Ul Ul QJ Ul QJ 250019 4 166679 6 500038 8 250019 4 5000388 250019 4 833398 250019 4 166679 6 Equation 3 19 53 5 5 63 6 5 5 3 3 5829 0 O0 O 5 25 0 6 3 0 6 9 0 0 0 3 5829 0 0 0 Equa
340. ner Patrick Ryan Integrating Finite Element Analysis with Quasi Static Loadings from a Large Displacement Dynamic Analysis The 1989 MSC World Users Conf Proc Vol II Paper No 37 March 1989 Tzong George T J Sikes Gregory D Dodd Alan J Large Order Modal Analysis Module in the Aeroelastic Design Optimization Program ADOP The MSC 1991 World Users Conf Proc Vol II Paper No 36 March 1991 Unger B Eichlseder Wilfried Schuch F Predicting the Lifetime of Dynamically Stressed Components Proc of the 20th MSC European Users Conf Paper No 36 September 1993 Vance Judy Bernard James E Approximating Eigenvectors and Eigenvalues Across a Wide Range of Design The MSC 1992 World Users Conf Proc Vol II Paper No 46 May 1992 NX Nastran Basic Dynamic Analysis User s Guide l 9 Appendix References and Bibliography Visintainer Randal H Aslani Farhang Shake Test Simulation Using MSC NASTRAN MSC 1994 World Users Conf Proc Paper No 32 June 1994 Vitiello P Quaranta V SEA Investigation Via a FEM Based Substructuring Technique MSC 1995 European Users Conf Proc Italian Session September 1995 Walton William B Blakely Ken Modeling of Nonlinear Elastic Structures Using MSC NASTRAN MSC NASTRAN Users Conf Proc Paper No 11 March 1983 Wamsler M Blanck N Kern G On the Enforced Relative Motion Inside a Structure Proc of the 20th MSC European Users Conf Sep
341. ning Polygon Assemblies Using MSC NASTRAN The MSC 1993 World Users Conf Proc Paper No 66 May 1993 Oei T H Broerse G Reduction of Forced Vibration Levels on Ro Ro Car Ferry Type Ships by Means of Minor Changes of the Inner Aft Body Construction Proc of the MSC NASTRAN Eur Users Conf April 1982 Ojalvo I U Extensions of MSC NASTRAN to Solve Flexible Rotor Problems MSC NASTRAN Users Conf Proc Paper No 18 March 1982 Palmieri F Nonlinear Dynamic Analysis of STS Main Engine Heat Exchanger Proc of the 15th MSC NASTRAN Eur Users Conf October 1988 Palmieri F W Analyzing Deployment of Spacecraft Appendages Using MSC NASTRAN The MSC 1990 World Users Conf Proc Vol I Paper No 6 March 1990 Pamidi P R Brown W K On Eigenvectors of Multiple Eigenvalues Obtained in NASTRAN NASTRAN Users Exper pp 285 300 September 1975 NASA TM X 3278 Paolozzi A Structural Dynamics Modification with MSC NASTRAN Proc of the 19th MSC European Users Conf Paper No 14 September 1992 Parthasarathy Alwar Force Sum Method for Dynamic Stresses in MSC NASTRAN Aeroelastic Analysis The MSC 1991 World Users Conf Proc Vol I Paper No 8 March 1991 NX Nastran Basic Dynamic Analysis User s Guide l 7 Appendix References and Bibliography Parthasarathy Alwar Elzeki Mohamed Abramovici Vivianne PSDTOOL A DMAP Enhancement to Harmonic Random Response Analysis in MSC NAS
342. no modes are noticeably excited This frequency is called the cutoff frequency The act of specifically not using all of the modes of a system in the solution is termed mode truncation Mode truncation assumes that an accurate solution can be obtained using a reduced set of modes The number of modes used in a solution is controlled in a modal transient response analysis through a number of methods The frequency range selected on the eigenvalue entry EIGRL or EIGR is one means to control the frequency range used in the transient response solution Also three parameters are available to limit the number of modes included in the solution PARAM LFREQ gives the lower limit on the frequency range of retained modes and PARAM HFREQ gives the upper limit on the frequency range of retained modes PARAM LMODES gives the number of the lowest modes to be retained These parameters can be used to include the desired set of modes Note that the default is for all computed modes to be retained It is very important to remember that truncating modes in a particular frequency range may truncate a significant portion of the behavior in that frequency range Typically high frequency modes are truncated because they are more costly to compute So truncating high frequency modes truncates high frequency response In most cases high frequency mode truncation is not of concern You should evaluate the truncation in terms of the loading frequency and the important char
343. not all rigid body modes some are modes that represent the motion of one large mass relative to the others These very low frequency nonrigid body modes do contribute to element forces and stresses and they must be retained in the solution In some cases their frequencies are not necessarily small they may be only an order or two in magnitude less than the frequency of the first flexible mode If PARAM LFREQ r is used to remove the true rigid body modes then r must be set below the frequency of the first relative motion mode Consider the two dimensional clamped bar in Figure 7 1 Assume that each end of the bar is subjected to the same enforced acceleration time history in the y direction One way to model the bar is to use two large masses one at each end which are unconstrained in the y direction This model provides two very low frequency modes one that is a rigid body mode and one that is not The second mode contributes to element forces and stresses and removing its contribution leads 7 4 NX Nastran Basic Dynamic Analysis User s Guide Enforced Motion to an error because with two such large masses one mass can drift over time relative to the other mass A better way to model the case of identical inputs at multiple locations is to use one large mass connected to the end points by an RBE2 element This model provides only one rigid body mode which can be safely discarded if only the answers relative to the structure are desired
344. ns in the database Run numbers 4 and 9 did not create any new versions Only Versions 3 and 7 are restartable This is an optional run This is a frequency response restart run Note that this can also be restarted from Version 3 since bd08bar8 dat 111 PC aba ae database Partial output is shown in Figure 8 13 A 2 critical damping value is applied to the structure p bdO8bar9 dat If the results for run number 1 are not going to be used for any future purposes then you may consider making run number 3 as a cold start run instead of a restart run Model changes do not save you much time if any in a non superelement analysis By making run 3 a cold start run you reduce the total amount of disk space required In this case run number 4 is not necessary since you are starting with a new database However if you want to keep both physical models in the database then run number 3 should be a restart run as shown in this example An application of this can be a parametric study of two different configurations This type of restart allows you to make efficient data recovery or response analysis from two different physical models However this type of restart is not used often in a non superelement analysis since in general it is not very efficient However in a superelement analysis see Advanced Dynamic Analysis Capabilities this type of restart can still be very efficient since the changes can be localized to a small reg
345. nse structural response 1s computed by solving a set of coupled equations using direct numerical integration Begin with the dynamic equation of motion in matrix form M tt 5 in o Aiea Plt Equation 6 1 The fundamental structural response displacement is solved at discrete times typically with a fixed integration time step At a 1 By using a central finite difference representation for the velocity LU and the acceleration Ui 1 i at discrete times 1 iat 5A na 1 H 1f i gt Il 5 iat lt 4174 tu if At Equation 6 2 and averaging the applied force over three adjacent time points the equation of motion can be rewritten as 6 2 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis M 5 eae DL 2u tua1 t aaas d f K 1 t HOT tu tu 1 3U n4 1 P Ide Equation 6 3 Collecting terms the equation of motion can be rewritten as Alita 45 Sol Azlin s l4ghi4 at Equation 6 4 where Stat LA Ap 2At 3 l Aol Es qn i ten thy it ieee Aa a g i a 3 5 5 A4 5 ape 2At 3 Matrix A4 is termed the dynamic matrix and A5 is the applied force averaged over three adjacent time points This approach is similar to the classical Newmark Beta direct integration method except that P is averaged over three time points and K is modified such that the dynamic equation of motion reduces to a static solution K lu j P if no
346. nse Solution Control Command Modal Required Optional Select the dynamic load set 5 24 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis Table 5 4 Case Control Commands for Frequency Response Solution Control Select FREQ entries from OFREQUENCY Both estou Gemak all The types of results available from a frequency response analysis are similar to those for a typical static analysis except that the results are a complex function of the applied loading frequency Additional quantities characteristic of dynamic problems are also available The output quantities are summarized in Table 5 5 and Table 5 6 Table 5 5 Grid Output from a Frequency Response Analysis Case Control Command ACCELERATION Grid point acceleration results for a set of grid points 2 T D or Grid point displacement results for a set of grid points OLOAD LT the applied load table to be output for a set of grid SACCELERATION Requests the solution set acceleration output d set in direct solutions and modal variables in modal solutions SDISPLACEMENT Requests the solution set displacement output d set in direct solutions and modal variables in modal solutions SVECTOR Requests the real eigenvector output for the a set in modal solutions SVELOCITY Requests the solution set velocity output d set in direct solutions and modal variables in modal solutions SPCFORCES Requests the forces of a single point constraint for
347. nsuke On the Accuracy in Vibration Analysis for Cylindrical Shell Comparison Between QUAD4 QUADS8 The First MSC NASTRAN User s Conf in Japan October 1983 in Japanese Miller R D Theoretical Analysis of HVAC Duct Hanger Systems Fifteenth NASTRAN Users Colloq pp 222 249 August 1987 NASA CP 2481 Nack Wayne V Joshi Arun M Friction Induced Vibration MSC 1995 World Users Conf Proc Paper No 36 May 1995 Nagayasu Katsuyosi Method for Prediction of Noise Oriented Vibration on Pipe Lines to Refrigerators The Third MSC NASTRAN User s Conf in Japan October 1985 in Japanese Nagendra Gopal K Herting David N Design Sensitivity for Modal Analysis The 1989 MSC World Users Conf Proc Vol I Paper No 22 March 1989 Nagy Lajos I Cheng James Hu Yu Kan A New Method Development to Predict Brake Squeal Occurence MSC 1994 World Users Conf Proc Paper No 14 June 1994 Neads M A Eustace K I The Solution of Complex Structural Systems by NASTRAN within the Building Block Approach NASTRAN User s Conf May 1979 Newman Malcolm Pipano Aaron Fast Modal Extraction in NASTRAN via the FEER Computer Program NASTRAN Users Exper pp 485 506 September 1973 NASA TM X 2893 Nishiwaki Nobukiyo Coupled Vibration of Rotating Disc and Blades The Second MSC NASTRAN User s Conf in Japan October 1984 in Japanese Overbye Vern D MSC NASTRAN Dynamic Analysis Modal or Direct
348. number of eigenvectors is Desired number of roots If this field is determined from F1 and F2 If all three blank and METHOD SINV then al 2re blank then ND is automatically ts bet F1 and F2 hed Set to one more than the number of n Po dp is do ae B degrees of freedom listed on SUPORT entries Integer 2 0 Default 0 The rules for METHOD HOU MHOU and AHOU are identical If any of these methods are selected NX Nastran finds all of the eigenvalues but only computes the eigenvectors specified by F1 and F2 or those specified by ND the desired number F1 and F2 specify the lower and upper bounds of the frequency range in which eigenvectors are computed and ND specifies the number of eigenvectors beginning with the lowest or the first rigid body mode if present If F1 F2 and ND entries are present ND takes precedence If METHOD SINV the values of F1 F2 and ND determine the number of eigenvalues and eigenvectors that are computed These entries also provide hints to help NX Nastran find the eigenvalues F1 and F2 specify the frequency range of interest within which NX Nastran searches for modes NX Nastran attempts to find all of the modes in the range between F1 and F2 or the number specified by ND whichever is less If searching stops because ND modes are found there is no guarantee that they are the lowest eigenvalues If ND modes are not found in the range of interest SINV usually finds one mode or possibly
349. nvalue selection entry EIGR or EIGRL The EIGR entry is used to select the modal extraction parameters for the inverse power Sturm modified inverse power Householder modified Householder and automatic Householder methods The EIGRL entry is used to select the modal extraction parameters for the Lanczos method 3 8 Examples This section provides several normal modes analysis examples showing the input and output These examples are as follows 3 18 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis Nu eror Element Types Output Requests DISPLACEMENT CELAS2 bd03two SPCFORCE AHOU Metric CONM2 ELFORCE bd03barl 11 CBAR DISPLACEMENT SINV Metric bd03bar2 bdO3bkt DISPLACEMENT STRESS Lanczos English ESE MODES DISPLACEMENT bd03car CTRIA3 Lanczos English CELAS2 CHEXA bdO8fix 8157 DISPLACEMENT Lanes Bosish CPENTA CBAR bd03dmi None Lace Maie DMIG These examples are described in the sections that follow Two DOF Model This example is a restrained two DOF model with two springs and two masses as illustrated in Figure 3 5 NX Nastran Basic Dynamic Analysis User s Guide 3 19 Chapter 3 Real Eigenvalue Analysis Grid Point 1 Ha 0 1 kg 100 N m Grid Point 2 My 10 kg 1 0F4 N m Ce ee ee ee an a at atan a at at a an at ata a at a a gt an ut un uut utu uum aM MMM aaa aat a a GM GM MG a a at C atat at at at atat atat at tat atat at at at at a atat atat at tat atat tat at at
350. nvert structural damping to equivalent viscous damping PARAM W3 and PARAM W4 PARAM G and GE can both be specified in the same analysis Viscous Damping Specification Viscous damping is defined by the following elements Scalar damper between two degrees of freedom DOFs with reference CDEN Cees to a PDAMP property entry CDAMP2 entry Scalar damper between two DOFs without reference to a property entry Scalar damper between two scalar points SPOINTs with reference to CDAMPS entry a PDAMP property entry CDAMP4 entr Scalar damper between two scalar points SPOINTs without reference y to a property entry CVISC entr Element damper between two grid points with reference to a PVISC y property entry NX Nastran Basic Dynamic Analysis User s Guide 2 11 Chapter 2 Finite Element Input Data A generalized spring and damper structural element that may be CBUSH entry nonlinear or frequency dependent It references a PBUSH entry Viscous damping for modal transient response and modal frequency response is specified with the TABDMP1 entry Note that GE and G by themselves are dimensionless they are multipliers of the stiffness The CDAMPi and CVISC entries however have damping units Damping is further described in Frequency Response Analysis and Transient Response Analysis as it pertains to frequency and transient response analyses 2 4 Units in Dynamic Analysis Because NX Nastran doesn t assume a particular set
351. o James Chi Dian Structural Dynamic and Thermal Stress Analysis of Nuclear Reactor Vessel Support System NASTRAN Users Exper pp 465 476 September 1972 NASA TM X 2637 l 4 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Grasso A Tomaselli L Whirling Speed Analysis of Multispool Systems Proc of the MSC NASTRAN Eur Users Conf May 1984 Grimes Roger G Lewis John G Simon Horst D Komzsik Louis Scott David S Shifted Block Lanczos Algorithm in MSC NASTRAN MSC NASTRAN Users Conf Proc Paper No 12 March 1985 Harn Wen Ren Lin Shyang Kuang Chen Jeng Tzong Localization of Dynamic Model Modification Based on Constrained Minimization Method The 2nd Annual MSC Tarwan Users Conf Paper No 14 October 1990 Herting David N Bella David F Kimbrough Patty A Finite Element Simulation of Coupled Automobile Engine Dynamics The MSC 1987 World Users Conf Proc Vol I Paper No 10 March 1987 High Gerald D An Iterative Method for Eigenvector Derivatives The MSC 1990 World Users Conf Proc Vol I Paper No 17 March 1990 Hill R G Transient Analysis of an IVHM Grapple Impact Test NASTRAN Users Exper pp 161 178 September 1972 NASA TM X 2637 Howells R W Sciarra J J Finite Element Analysis Using NASTRAN Applied to Helicopter Transmission Vibration Noise Reduction NASTRAN Users Exper pp 321 340 September 1975 NASA TM X 3278
352. o basic types of sets e combined sets e mutually exclusive sets Combined sets are formed through the union i e combination of two or more sets Mutually exclusive sets are important in the solution process because if a DOF is a member of a mutually exclusive set it cannot be a member of any of the other mutually exclusive sets The importance of this property is demonstrated as the sets are described below When NX Nastran starts to assemble the structural equations it allocates six equations for each grid point GRID and 1 equation for each scalar point SPOINT These equations are associated with a displacement set defined as the g set Fundamentally the g set represents an unconstrained set of structural equations The next step in the solution process is to partition the g set into two subsets the m set and the n set The dependent DOFs of all multipoint constraint relations MPCs RBEs etc that define the m set are condensed into a set of independent DOFs the n set The n set represents all of the independent DOFs that remain after the dependent DOFs were removed from the active set of equations NX Nastran Basic Dynamic Analysis User s Guide C 1 Appendix C The Set Notation System Used in Dynamic Analysis Using the n set SPCs are applied to the independent equations to further partition the equations The degrees of freedom defined on SPC entries define the DOFs in the s set When you reduce the n set by applying the s
353. o be ignored in transient analysis Units for PARAM W3 and PARAM W4 are radians per unit time The choice of W3 or W4 is typically the dominant frequency at which the damping is active Often the first natural frequency is chosen but isolated individual element damping can occur at different frequencies and can be handled by the appropriate data entries Damping Structural Damping f iGku Force Equivalent b Gk qw or wy Viscous Damping 04 or Wy un i bu ibmu Figure 6 1 Structural Damping Versus Viscous Damping Constant Oscillatory Displacement Initial Conditions in Direct Transient Response You may impose initial displacements and or velocities in direct transient response The TIC Bulk Data entry is used to define initial conditions on the components of grid points The IC Case Control command is used to select TIC entries from the Bulk Data NX Nastran Basic Dynamic Analysis User s Guide 6 5 Chapter 6 Transient Response Analysis If initial conditions are used initial conditions should be specified for all DOFs having nonzero values Initial conditions for any unspecified DOFs are set to zero T fi H o 01 and 01 are used to determine the values of i i Po and iH Initial conditions UP jJ used in Equation 6 4 to calculate Uf gt lg At Equation 6 10 P K fu 41 B g Equation 6 11 In the presence of initial conditions the applied load specified at
354. oc of the MSC NASTRAN Eur Users Conf June 1983 Shalev D Unger A Nonlinear Analysis Using a Modal Based Reduction Technique Composite Structures v31 n 4 1995 Shalev Doron Unger A Nonlinear Analysis Using a Modal Based Reduction Technique The MSC 1993 World Users Conf Proc Paper No 51 May 1993 Shippen J M Normal Modes Analysis of Spin Stabilised Spacecraft Possessing Cable Booms Proc of the 18th MSC Eur Users Conf Paper No 29 June 1991 Shirai Yujiro Arakawa Haruhiko Toda Nobuo Taneda Yuji Sakura Kiyoshi Active Vibration Control for Aircraft Wing JSME International Journal v 36 n 3 Spe 1993 Shy Tyson Hsiu T C Yen K Z Y Optimization of Structure Design of a Machining Center The Sixth Annual MSC Taiwan Users Conf Proc Paper No 6 November 1994 I 26 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Somayajula Gopichand Stout Joseph Tucker John Eigenvalue Reanalysis Using Subspace Iteration Techniques The 1989 MSC World Users Conf Proc Vol I Paper No 26 March 1989 Stack Charles P Cunningham Timothy J Design and Analysis of Coriolis Mass Flowmeters Using MSC NASTRAN The MSC 1993 World Users Conf Proc Paper No 54 May 1993 Starnes James H Jr Vibration Studies of a Flat Plate and a Built Up Wing NASTRAN Users Exper pp 637 646 September 1971 NASA TM X 2378 Su Hong Structural Analysis of Ka BAND
355. ode is accessible from within MATLAB then typing help taucs must cite the Copyright and type taucs must also cite this License and the Availability note Permission to modify the code and to distribute modified code is granted provided the Copyright this License and the Availability note are retained and a notice that the code was modified is included This software is provided to you free of charge Availability As of version 2 1 we distribute the code in 4 formats zip and tarred gzipped tgz with or without binaries for external libraries The bundled external libraries should allow you to build the test programs on Linux Windows and MacOS X without installing additional software We recommend that you download the full distributions and then perhaps replace the bundled libraries by higher performance ones e g with a BLAS library that is specifically optimized for your machine If you want to conserve bandwidth and you want to install the required libraries yourself download the lean distributions The zip and tgz files are identical except that on Linux Unix and MacOS unpacking the tgz file ensures that the configure script is marked as executable unpack with tar zxvpf otherwise you will have to change its permissions manually 2 NX Nastran Basic Dynamic Analysis User s Guide Contents Veet ae ell DOOR ee ee 4 Fundamentals of Dynamic Analysis ccce tmt 1 1 Goa on See ee eee RSTERERIACSIESSEAXUAXEGS
356. odel Right then Run the Analysis Machine Design October 24 1991 Blakely Ken Rose Ted Cross Orthogonality Calculations for Pre Test Planning and Model Verification The MSC 1993 World Users Conf Proc Paper No 72 May 19938 Blakely Ken Bush Richard Using MSC NASTRAN to Match Dynamic Test Data Proc of the Int Conf on Structural Dynamics Modelling July 1993 Blakely Ken Rose Ted Cross Orthogonality Calculations for Pre Test Planning and Model Verification Proc of the 20th MSC European Users Conf September 1993 Blakely Ken Matching Frequency Response Test Data with MSC NASTRAN MSC 1994 World Users Conf Proc Paper No 17 June 1994 Blakely Ken Matching Frequency Response Test Data with MSC NASTRAN Proc of the 21st MSC European User s Conf Italian Session September 1994 Brillhart Ralph Hunt David L Kammer Daniel C Jensen Brent M Mason Donald R Modal Survey and Test Analysis Correlation of the Space Shuttle SRM Proc of the 6th Int Modal Analysis Conf pp 863 870 February 1988 Brughmans Marc Leuridan Jan Blauwkamp Kevin The Application of FEM EMA Correlation and Validation Techniques on a Body in White The MSC 1993 World Users Conf Proc Paper No 6 May 1993 Brughmans M Lembregts PhD F Furini PhD F Storrer O Modal Test on the Pininfarina Concept Car Body ETHOS 1 Actes de la 2eme Conf rence Francaise Utilisateurs des Logiciels MSC Toulouse
357. ol 42 No 1 pp 31 36 1992 Dai Chung C Yang Jackson C 8 Direct Transient Analysis of a Fuse Assembly by Axisymmetric Solid Elements Thirteenth NASTRAN Users Colloq pp 431 452 May 1985 NASA CP 2373 Deloo Ph Klein M In Orbit Disturbance Sensitivity Analysis of the Hubble Space Telescope New Solar Arrays Proc of the 19th MSC European Users Conf Paper No 11 September 1992 Everstine Gordon C A NASTRAN Implementation of the Doubly Asymptotic Approximation for Underwater Shock Response NASTRAN Users Exper pp 207 228 October 1976 NASA TM X 3428 Flanigan Christopher C Accurate Enforced Motion Analysis Using MSC NASTRAN Superelements MSC 1994 World Users Conf Proc Paper No 25 June 1994 Frye John W Transient Analysis of Bodies with Moving Boundaries Using NASTRAN NASTRAN Users Exper pp 377 388 September 1975 NASA TM X 3278 Hirata M Ishikawa K Korosawa M Fukushima S Hoshina H Seismic Analysis of Plutonium Glovebox by MSC NASTRAN January 1993 Katnik Richard B Deutschel Brian Cherukuri Ravi Transient Response of a Vehicle Over Road Bumps Using the Fourier Transform in a Modal Subspace The MSC 1992 World Users Conf Proc Vol I Paper No 6 May 1992 Kim Hyoung M Bartkowicz Theodoore J Van Horn David A Data Recovery and Model Reduction Methods for Large Structures The MSC 1993 World Users Conf Proc Paper No 23 May 1993
358. om vibration include earthquake ground motion ocean wave heights and frequencies wind pressure fluctuations on aircraft and tall buildings and acoustic excitation due to rocket and jet engine noise These random excitations are usually described in terms of a power spectral density PSD function NX Nastran performs random response analysis as a postprocessing step after frequency response analysis The frequency response analysis is used to generate the transfer function which is the ratio of the output to the input The input PSD multiplies the transfer function to form a response PSD The input PSD can be in the form of auto or cross spectral densities Random response output consists of the response PSD autocorrelation functions number of zero crossings with positive slope per unit time and RMS root mean square values of response 11 6 Mode Acceleration Method The mode acceleration method is an alternate form of data recovery for modal frequency response and modal transient response The mode acceleration method accounts for the higher truncated modes to give more accurate answers than either the mode displacement or matrix methods see Modal Frequency Response Analysis and Modal Transient Response Analysis particularly if the number of retained modes is small compared to the number of physical degrees of freedom The higher modes respond in a quasi static manner to lower frequency excitation Therefore the inertia and dampin
359. on of time is the objective of a dynamic analysis The primary task for the dynamic analyst 1s to determine the type of analysis to be performed The nature of the dynamic analysis in many cases governs the choice of the appropriate mathematical approach The extent of the information required from a dynamic analysis also dictates the necessary solution approach and steps Dynamic analysis can be divided into two basic classifications free vibrations and forced vibrations Free vibration analysis 1s used to determine the basic dynamic characteristics of the system with the right hand side of Equation 1 2 set to zero i e no applied load If damping is neglected the solution 1s known as undamped free vibration analysis 1 4 NX Nastran Basic Dynamic Analysis User s Guide Fundamentals of Dynamic Analysis Free Vibration Analysis In undamped free vibration analysis the SDOF equation of motion reduces to m t ku t O Equation 1 3 Equation1 3 has a solution of the form u t Asinw t B coso f Equation 1 4 The quantity u t is the solution for the displacement as a function of time As shown in Equation 1 4 the response is cyclic in nature Circular Natural Frequency One property of the system is termed the circular natural frequency of the structure w The subscript n indicates the natural for the SDOF system In systems having more than one mass degree of freedom and more than one natural frequency the sub
360. on sequences numbers greater than 100 The automatic restart logic is available only for these solution sequences Restart is no longer available for the rigid format solution sequences Use these new Structured Solution Sequences rather than the old ones since all the new features are automatically implemented in these new solution sequences Improvements made to the automatic restart logic for Version 67 and later have made it even more efficient and robust In this chapter we will address the restart logic for the Structured Solution Sequences Note that you are not required to use superelements in order to use the superelement solution sequences If you are familiar with the rigid format solutions converting to the new Structured Solution Sequences only requires that you replace the solution command For example a normal modes run only requires replacing the SOL 3 command with the SOL 103 command in the Executive Control Section 8 2 NX Nastran Basic Dynamic Analysis User s Guide Restarts in Dynamic Analysis 8 3 Structure of the Input File Before presenting details on how restarts work the following simple flow diagram of the NX Nastran input file structure may be beneficial Table 8 1 Structure of the NX Nastran Input File NASTRAN Statement Optional File Management Statements Optional Executive Control Statements Required Section CEND Required Delimiter Case Control Commands Required Section BEGIN BULK Required Delimiter Bulk
361. on vectors for the example are as follows 0 1 D D ity 407 i rs 40 5 i fa 4lgp i f4 40 0 0 L Equation G 3 Using the location vectors the grid point transformation matrix Tr is computed for each grid point by expanding the location vectors to a 3x3 matrix as shown in Equation G 4 0 ry Ta d rg 0 r ry Ty Equation G 4 For the example problem the grid point transformation matrices are 000 000 0 0 1 0 10 fr looo l o o 1 Erl lo o s Hrlh 7 3 0 5 000 0 10 1 50 0 50 Equation G 5 G 8 NX Nastran Basic Dynamic Analysis User s Guide Grid Point Weight Generator The coordinate system transformation matrices from the global coordinate system to the basic system coordinates are given by the direction cosine matrices as follows cos 45 sin 45 0 1 0 sin 45 cos 45 0 Hil 01 0 0 1 0 0 Ti mM C2 cos 60 sin 60 0 1 0 Ti z sin 60 cos 60 0 Ti 01 0 0 1 0 0 T m Co Equation G 6 The grid point transformation 77r and the coordinate system transformation Ti are combined to form the individual grid point transformation matrix d for each grid point using Equation G 7 Ti Ti T d 0 Tr Equation G 7 The rows of each d form the columns of the global transformation matrix D as shown in Equation G 8 I pv T d T D E d i Equation G 8 Using Equation G 9 the global transformation matrix for the ex
362. or the steady state component of response The response occurs at the same frequency as the loading and in phase with the load 1 e the peak displacement occurs at the time of peak loading As the applied loading frequency becomes approximately equal to the structural natural frequency the ratio WW approaches unity and the denominator goes to zero Numerically this condition results in an infinite or undefined dynamic amplification factor Physically as this condition is reached the dynamic response is strongly amplified relative to the static response This condition is known as resonance The resonant buildup of response is shown in Figure 1 4 LLL aO BT ECL TT Amplitude n t EU UL Figure 1 4 Harmonic Forced Response with No Damping It is important to remember that resonant response is a function of the natural frequency and the loading frequency Resonant response can damage and even destroy structures The dynamic analyst 1s typically assigned the responsibility to ensure that a resonance condition is controlled or does not occur Solving the same basic harmonically loaded system with damping makes the numerical solution more complicated but limits resonant behavior With damping the equation of motion becomes m t bu t ku t psinwt Equation 1 18 1 10 NX Nastran Basic Dynamic Analysis User s Guide Fundamentals of Dynamic Analysis In this case the effect of the initial conditions decays ra
363. orrect answers One such improper specification of boundary conditions is forgetting to fully constrain the structure Unlike static analysis for which an under constrained model does not run an under constrained model does run in dynamic analysis You should perform an eigenvalue analysis first and verify that there are no unwanted rigid body modes The large mass used for enforced motion simulates a constrained condition as well as adds a rigid body mode The value of the large mass is important for obtaining accurate answers The large mass value must be large enough to properly simulate the constrained condition but it must not be so large as to create numerical difficulties when solving the equations A range of 10 to 106 times the overall structural mass is adequate to meet both conditions One way to verify that a proper value is chosen is to run a normal modes analysis with the enforced DOF constrained via SPCs Then run a normal modes analysis with your choice of the large mass es and compare the frequencies of the flexible modes If the frequencies compare favorably 1 e to within four or five significant digits then the large mass value is accurate If the frequencies do not compare then increase the value of the large mass es A common mistake is to use too low a value or omit it entirely for the rotational components Using the grid point weight generator is very important to obtain the overall structural mass and inertias so that
364. os NoSUPORT FO These examples are described in the sections that follow Unconstrained Beam Model The constraints SPCs on the example cantilever beam model from Cantilever Beam Model are removed to create an unconstrained structure as shown in Figure 4 3 A GRDSET entry is added with the z translation x rotation and y rotation directions constrained to make the problem two dimensional Therefore there are three DOFs per grid point x translation y translation and z rotation and three rigid body modes NX Nastran Basic Dynamic Analysis User s Guide 4 9 Chapter 4 Rigid Body Modes Y Figure 4 3 Unconstrained Beam Model Modes are computed using two methods Lanczos and SINV with and without a SUPORT entry The SUPORT entry is used in three ways e Statically determinate grid point 1 components 1 2 and 6 e Underdetermined grid point 1 components 1 and 2 e Overdetermined grid point 1 components 1 2 and 6 plus grid point 11 component1 Figure 4 4 shows a portion of the input file for the statically determinate SUPORT and the Lanczos method FILE bd ZbarZ dat CANTILEVER BEAM MODEL CHAPTER 4 RIGID BODY MODES SOL 103 TIME 10 CEND TITLE CANTILEVER BEAM SUBTITLE NORMAL MODES LABEL USE SUPORT STATICALLY DETERMINATE OUTPUT REQUEST DISPLACEMENT ALL SELECT EIGRL ENTRY METHOD 10 5 BEGIN BULK STATICALLY DETERMINATE SUPORT SSUPORT G C SUPOR
365. ough structure plotting is best performed in an interactive environment outside of NX Nastran the batch structure plotting capability in NX Nastran is nevertheless a useful tool for model verification and results processing The batch plotting capability can save time and effort when many plots are required for a model that is run repeatedly 9 3 X Y Plotting X Y plots are used to display frequency and transient response results where the x axis is frequency or time and the y axis is any output quantity Unlike structure plotting which is often performed in an interactive environment X Y plotting is ideal for the NX Nastran batch environment due to the large volume of data X Y plot commands are contained in the OUTPUT XYPLOT section that immediately precedes the Bulk Data Section You define the titles XTITLE and YTITLE and plots XYPLOT You can specify the plots to be generated in log format XLOG and YLOG and you can specify different line styles You can also specify that the plots are to be made in pairs with a top and a bottom plot which is particularly useful for frequency response results when you want to display magnitude phase or real imaginary pairs Details about X Y plotting and its commands are located in the NX Nastran User s Guide Element force and stress component numbers are also described in the manual The X Y plot commands use numbers to identify a single component of grid point and element data Note that frequency
366. outside of the table boundaries There are N 1 entries to this table Constant acceleration is the easiest to apply since the force is proportional to the mass for all frequencies The power series for this case becomes x Xl AQ 4 AI M X2 Equation 7 13 where AO 1 0 X1 0 0 X2 1 0 Therefore these terms define a constant 1 0 in this case Constant velocity involves a scale factor that is directly proportional to circular frequency 2m The power series for this case becomes x Xl AQ 4 AI etn X2 Equation 7 14 where AO 0 0 Al 2rn 6 283185 X1 0 0 X2 1 0 Note that a phase change of 90 degrees is also required this change is input using the TD field field 7 of the RLOAD1 entry Constant displacement involves a scale factor that is proportional to the circular frequency squared 2nf 2 with a sign change The power series for this case becomes NX Nastran Basic Dynamic Analysis User s Guide 7 13 Chapter 7 Enforced Motion AO a1 Ax DAD Equation 7 15 where AO 0 0 Al 0 0 A2 2n 39 4784 X1 0 0 X2 1 0 Table 7 2 summarizes the coefficients for the power series Table 7 2 Coefficients for the Power Series Type of Excitation A0 a A Enforeedu 00 foo J Qm 2n Enforced u oo fe fe 1 0 Enforced B wo fee Cantilever Beam Model Consider the cantilever beam first introduced in Frequency Response Analy
367. pectral transformation of um X Equation F 14 where is an eigenvalue shift This transformation is shown in Figure F 1 F 4 NX Nastran Basic Dynamic Analysis User s Guide Numerical Accuracy Considerations Figure F 1 Spectral Transformation The spectral transformation ensures uniform accuracy throughout the frequency by shifting to the area of interest Another effect of this transformation is the welcomed p space separation of closely spaced eigenvalues When is close to an eigenvalue the decomposition of the shifted matrix K A M L ED LE Equation F 15 may produce high MAXRATIO messages Automatic logic to perturb the value in this case is implemented in NX Nastran F7 Sources of Mechanisms In all of the decomposition methods a null row or column in A causes a fatal error message All other causes of singularity are not distinguishable from near singularity because of the effects of numerical truncation Only warning messages are usually provided for these cases In standard decomposition A L D L Equation F 16 the process starts to compute the first term of D with the first internal degree of freedom and then processes each additional degree of freedom and its associated terms It can be shown that when processing the k th row the k th row and all rows above it are in effect free and all rows below it are constrained to ground The term of D at the k th row
368. per second natural frequency f cycles per second generalized mass see Equation 3 14 and generalized stiffness see Equation 3 16 for each mode The eigenvectors SPC forces and spring forces are shown for each mode REAL MODE EXTRACTION EIGENVALUE RADIANS NO ORDER 1 1 9 048751E 02 3 008114E 01 2 2 1 105125E 03 3 324342E 01 EIGENVALUE 9 048751E 02 CYCLES 4 787562E 00 REAL EIGENVIE POINT ID TYPE EL T2 T3 1 G 0 0 1 000000E 00 0 0 2 G 0 0 9 512492E 02 0 0 EIGENVALUE 1 105125E 03 CYCLES 5 290854E 00 REAL E IGENVE POINT ID TYPE TL T2 T3 1 G 0 0 1 000000E 00 0 0 2 G 0 0 1 051249E 01 0 0 EIGENVALUE 9 048751E 02 FORCES O F SINGLE POINT ID TYPE T1 T2 T3 3 G 0 0 9 512491E 02 0 0 EIGENVALUE 1 105125E 03 FORCES O F SINGLE POINT ID TYPE T1 T2 T3 3 G 0 0 1 051249E 03 0 0 EIGENVALUE 9 048751E 02 FORCES I N SCALAR ELEMENT FORCE ELEMENT FORCE ID ID 11 9 048751E 01 12 9 512491E 02 EIGENVALUE 1 105125E 03 FORCES I N SCALAR ELEMENT FORCE ELEMENT FORCE ID ID 11 1 105125E 02 12 1 051249E 03 EIGENVALUES CYCLES 4 787562E 00 290854E 00 R N Bl exe exe O R NO R1 O O O O N T CONST R1 N T CONST R1 SPRINGS ELEMENT TD o E RIN GS ELEMENT ID Figure 3 7 Output from the Two DOF System Cantilever Beam Model GENERALIZED GENERALIz MASS STIFFNESS 1 904875E 01 1 7236745 2 105125E 01 2 3264265 1 R2 R3 0 0 0 0 0 0 0 0 2 R2 R3 0 0 0 0 0 0 0 0 RAINT R2 R3 0 0 0
369. phy Charron Francois Donato Louis Fontaine Mark Exact Calculation of Minimum Margin of Safety for Frequency Response Analysis Stress Results Using Yielding or Failure Theories The MSC 1993 World Users Conf Proc Paper No 5 May 1993 de la Fuente E San Millan J Calculation within MSC NASTRAN of the Forces Transmitted by Multipoint Constraints MPC and the Forces Generated in Support Constraints MSC 1996 World Users Conf Proc Vol IL Paper No 20 June 1996 Herbert S Janavicius P MSC NASTRAN Frequency Response Analysis of the Raven Army Communication Shelter The Third Australasian MSC Users Conf Proc Paper No 14 November 1989 Herting D N Parameter Estimation Using Frequency Response Tests MSC 1994 World Users Conf Proc Paper No 18 June 1994 Kajiwara Itsurou Nagamatsu Akio Seto Kazuto New Theory for Elimination of Resonance Peak and Optimum Design of Optical Servosystem 1994 MSC Japan Users Conf Proc Paper No 1 Liew K M Jiang L Lim M K Low 8 C Numerical Evaluation of Frequency Responses for Delaminated Honeycomb Structures Computers and Structures v 55 n 2 Apr 17 1995 Parker G R Brown J J Evaluating Modal Contributors in a NASTRAN Frequency Response Analysis MSC NASTRAN Users Conf Proc Paper No 14 March 1983 Rose Ted Using Optimization in MSC NASTRAN to Minimize Response to a Rotating Imbalance 1994 MSC Japan Users Conf Proc Pap
370. pidly and may be ignored in the solution The solution for the steady state response is sin ot 0 2 J w a 260 a Equation 1 19 u t p k The numerator of the above solution contains a term that represents the phasing of the displacement response with respect to the applied loading In the presence of damping the peak loading and peak response do not occur at the same time Instead the loading and response are separated by an interval of time measured in terms of a phase angle q as shown below 1 2 0 Q9 o tan 3 5 1 w Equation 1 20 The phase angle qis called the phase lead which describes the amount that the response leads the applied force Note Some texts define q as the phase lag or the amount that the response lags the applied force To convert from phase lag to phase lead change the sign of qin Equation 1 19 and Equation1 20 Dynamic Amplification Factor with Damping The dynamic amplification factor for the damped case is 1 2 0 o 7 o 2607 c Equation 1 21 The interrelationship among the natural frequency the applied load frequency and the phase angle can be used to identify important dynamic characteristics If Ww is much less than 1 the dynamic amplification factor approaches 1 and a static solution 1s represented with the displacement response in phase with the loading If Ww is much greater than 1 the dynamic amplification factor approaches zero yie
371. ple models preferably models that have textbook solutions The references see References and Bibliography provide numerous textbook solutions Start with a simple model first and then gradually add complexity verifying the results at each stage Follow the steps outlined below and in Figure 10 1 Once you have confidence in a small model and are ready to analyze your actual model again do the analysis in steps The following is a suggested order for performing dynamic analysis on any structure 1 Create the initial model only do not apply any loads Verify the model s connectivity element and material properties and boundary conditions Make sure that mass is specified for this model 2 Perform a static analysis SOL 101 first in order to verify proper load paths and overall model integrity Note that you have to constrain the structure for static analysis even if you were not planning to do so for dynamic analysis For a three dimensional model you 10 2 NX Nastran Basic Dynamic Analysis User s Guide Guidelines for Effective Dynamic Analysis should run three load cases each with a 1g gravity load applied in a different direction Compute displacements and SPC forces and verify the results Check for unusually large grid point displacements and unreasonable SPC forces Using a graphical postprocessor can aid you at this step Next apply static loads that have the same spatial distribution that your subsequent dyna
372. pled to ground be included in the SPC Force calculations for the linear dynamic solutions SOLs 103 107 112 115 118 145 146 and 200 OLD neglects these effects and gives the same SPC Force results prior to the new algorithm Default 1 E 8 Specifies the minimum value that indicates a singularity See AUTOSPC Default 0 0 G specifies the uniform structural damping coefficient in the formulation of dynamics problems To obtain the value for the parameter G multiply the critical damping ratio C Co by 2 0 PARAM G is not recommended for use in hydroelastic or heat transfer problems If PARAM G is used in transient analysis PARAM W3 must be greater than zero or PARAM G will be ignored Default 1 30 D 6 NX Nastran Basic Dynamic Analysis User s Guide KDAMP LFREQ LMODES MAXRATIO MODACC NONCUP Common Commands for Dynamic Analysis The parameters LFREQ and HFREQ specify the frequency range LFREQ is the lower limit and HFREQ is the upper limit of the modes to be used in the modal formulations Note that the default for HFREQ will usually include all vectors computed A related parameter is LMODES Default 1 If KDAMP is set to 1 viscous modal damping is entered into the complex stiffness matrix as structural damping Default 0 0 See HFREQ Default 0 LMODES is the number of lowest modes to use in a modal formulation If LMODES 0 the retained modes are determined by the parameters LFREQ and H
373. plied Loads 3 Force 6 N Time v 1 sec pp L 0 1 0 5 6 E Force 11 N f Time i sec 0 0 5 Figure 6 10 Applied Loads for the Beam Model S FILE bd06bar dat S S CANTILEVER BEAM MODEL S CHAPTER 6 TRANSIENT RESPONSE SOL 112 S MODAL TRANSIENT RESPONSE TIME 10 CEND TITLE CANTILEVER BEAM SUBTITLE MODAL TRANSIENT RESPONSE S SPC 21 DLOAD 22 TSTEP 27 SDAMPING 25 S METHOD 10 S PHYSICAL OUTPUT REQUEST SET 11 6 11 DISPLACEMENT PLOT ACCELERATION PLOT 11 11 S MODAL SOLUTION SET OUTPUT SET 12 1 2 SDISP PLOT 12 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis S ELEMENT FORCE OUTPUT SET 13 6 ELFORCE PLOT 13 APPLIED LOAD OUTPUT SET 15 6 11 OLOAD PLOT 15 XYPLOTS X Y plot commands BEGIN BULK Pe eee caeca eae Zass A i EEE OESE TP Oi eae EN Sus ic As ash L4 533 S SEIGRL SID V1 V2 MSGLVL aan 10 esL au 3000 0 TSTEP SID N1 Ln NO1 TSTEP 27 2000 0 001 1 S MODAL DAMPING OF 5 IN ALL MODES STABDMP1 TID TYPE TABD S TABD F1 G1 F2 G2 ETC TABDMP1 25 CRIT TABD TABD 0 0 05 1000 0 05 ENDT DYNAMIC LOADING SDLOAD SID S S1 L1 S2 L2 DLOAD 22 1 0 1 0 231 1 0 232 STLOAD2 SID DAREA DELAY TYPE T1 T2 F P TL1 TL1 C B TLOAD2 231 241 0 0 0 0 5 2 0 90 TLOAD2 232 242 262 0 0 0 05 4 0 90 SDAREA SID P1 eal Al DAREA 241 11 2 6 0 DAREA 242 6 2 3 0 SDELAY SID P1 DI T1
374. power method is requested for the first six modes found in the range specified 0 1 to 100 Hz The POINT normalization method 1s requested with each eigenvector scaled such that grid point 32 in the T3 direction has a magnitude of 1 0 Note that this degree of freedom must be in the a set 3 Solution Control for Normal Modes Analysis This section describes input required for the selection and control of normal modes analysis Executive Control Section You can run a normal modes analysis as an independent solution in SOL 103 of the Structured Solution Sequences The Executive Control Section can also contain diagnostic DIAG16 which prints the iteration information used in the SINV method You may also run a normal modes analysis as part of the other solution sequences such as modal transient response modal frequency response design optimization and aeroelasticity NX Nastran Basic Dynamic Analysis User s Guide 3 17 Chapter 3 Real Eigenvalue Analysis Case Control Section The most important eigenanalysis command in the Case Control is the METHOD command This command is required The set identification number specified by the METHOD Case Control command refers to the set identification number of an EIGR or EIGRL entry in the Bulk Data When you perform a modal analysis the NX Nastran output file contains various diagnostic messages and an eigenvalue analysis summary Optional grid and element output are available using standard C
375. quency Response Analysis and Transient Response Analysis respectively Mode Shape Normalization Although the scaling of normal modes is arbitrary for practical considerations mode shapes should be scaled i e normalized by a chosen convention In NX Nastran there are three normalization choices MASS MAX and POINT normalization MASS normalization is the default method of eigenvector normalization This method scales each eigenvector to result in a unit value of generalized mass gt IMHO LO Equation 3 18 Numerically this method results in a modal mass matrix that is an identity matrix This normalization approach is appropriate for modal dynamic response calculations because it simplifies both computational and data storage requirements When mass normalization is used with a model of a heavy massive structure the magnitude of each of the terms of the eigenvectors is very small In MAX normalization each eigenvector is normalized with respect to the largest a set component Advanced Dynamic Analysis Capabilities and The Set Notation System Used in Dynamic Analysis provide discussions of the a set This normalization results in the largest a set displacement value being set to a unit 1 0 value This normalization approach can be very useful in the determination of the relative participation of an individual mode A small generalized mass obtained using MAX normalization may indicate such things as local modes o
376. r v otedtr The set free to vibrate in dynamic reduction and component mode synthesis determinate supports O 4 NX Nastran Basic Dynamic Analysis User s Guide The Set Notation System Used in Dynamic Analysis Physical Set h X p x lt a rigid body zero frequency modal coordinates finite frequency modal coordinates Xo X the set of all modal coordinates X Uo the set used in dynamic analysis by the modal method Figure C 2 Set Notation for Physical and Modal Sets NX Nastran Basic Dynamic Analysis User s Guide C 5 Appendix D Common Commands for Dynamic Analysis D 1 Solution Sequences for Dynamic Analysis This section lists the solution sequences SOLs for the dynamic analysis types described in this guide The SOLs are listed for the preferred structured solution sequences rigid formats and unstructured superelement solution sequences The NX Nastran Quick Reference Guide lists all of the solution sequences for all of the NX Nastran analysis types Structured Solution Sequences for Basic Dynamic Analysis SOL Number SOL Name 108 SEMODES Normal Modes 108 SEDFREQ Direct Frequency Response 109 SEDTRAN Direct Transient Response 111 SEMFREQ Modal Frequency Response 112 SEMTRAN Modal Transient Response D 2 Case Control Commands for Dynamic Analysis This section lists the Case Control commands that are often u
377. r R A Runyan R B Dynamic Certification of a Thrust Measuring System for Large Solid Rocket Motors Eleventh NASTRAN Users Colloq pp 207 225 May 1983 Lewis J Komzsik L Symmetric Generalized Eigenproblems in Structural Engineering SIAM Conf on Applied Numerical Analysis 1985 Lin Chih Kai Harn Wen Ren Lin Shyang Kuang The Dynamic Response of Bridge Due to Passing of Vehicle The 2nd Annual MSC Taiwan Users Conf Paper No 6 October 1990 Lin S L Yang T W Chen J T MSC NASTRAN Application in Inertia Relief The 1st MSC Taiwan Users Conf Paper No 13 October 1989 in Chinese Lin Shan Time Dependent Restrained Boundary Condition Simulation The MSC 1988 World Users Conf Proc Vol I Paper No 9 March 1988 Lu Ming Ying Yang Joe Ming Analysis of Static and Dynamic Responses on Ship Structures Under Wave Loadings The Sixth Annual MSC Taiwan Users Conf Proc Paper No 14 November 1994 Magari P J Shultz L A Murthy V R Dynamics of Helicopter Rotor Blades Computers and Structures Vol 29 No 5 pp 763 776 1988 Malcolm D J Dynamic Response of a Darrieus Rotor Wind Turbine Subject to Turbulent Flow Engineering Structures Vol 10 No 2 pp 125 134 April 1988 Maritan M Micelli D Dynamic Behaviour of a High Speed Crankshaft MSC 23rd European Users Conf Proc Italian Session September 1996 Masters Steven G Plant Troubleshooting with MSC NASTRAN
378. r The number failed is the number of pairs above the criteria You can improve the numerical conditioning of the problem by reducing the range of mass ratios stiffness ratios and eigenvalue range NX Nastran Basic Dynamic Analysis User s Guide H 3 Appendix H UIM 3035 UWM 3045 UFM 3046 UFM 38047 UFM 3051 UWM 3053 UFM 3057 UWM 4193 Diagnostic Messages for Dynamic Analysis USER INFORMATION MESSAGE 3035 FOR DATA BLOCKS SUPORT PT NO EPSILON STRAIN ENERGY EPSILONS LARGER THAN 001 ARE FLAGGED WITH ASTERISKS One line of output is printed for each component on a SUPORT entry Large values of either EPSILON or STRAIN ENERGY indicate errors in the constraints MPCs or offsets USER WARNING MESSAGE 3045 INSUFFICIENT TIME TO COMPLETE THE REMAINING SOLUTION S IN MODULE The estimated time for completion of the module is less than the time remaining as specified on the Executive Control TIME statement The module computes one solution for example one excitation frequency in frequency response analysis and then processes all output requests The remaining frequencies can be obtained on restart by adding or changing a FREQ command USER FATAL MESSAGE 3046 YOUR SELECTED LOADING CONDITION INITIAL CONDITION AND NONLINEAR FORCES ARE NULL A ZERO SOLUTION WILL RESULT Transient solutions must have one of the above nonzero loading condition initial condition or nonlinear forces Also
379. r isolated mechanisms POINT normalization of eigenvectors allows you to chose a specific displacement component at which the modal displacement is set to 1 or 1 This method is not recommended because for complex structures the chosen component in the non normalized eigenvector may have a very small value of displacement especially in higher modes This small value can cause larger numbers to be normalized by a small number resulting in possible numerical roundoff errors in mode shapes Although mode shapes are relative quantities a number of modal quantities can be helpful in predicting qualitative responses or in 1solating troublesome modal frequencies Since relative NX Nastran Basic Dynamic Analysis User s Guide 3 9 Chapter 3 Real Eigenvalue Analysis strains internal loads and stresses develop when a structure deforms in a mode shape you may recover these quantities during a normal modes analyses Basically any quantity that you can recover for static analysis is also available for normal modes analysis It is important to remember that these output quantities are based on the relative displacements of a mode shape The output quantities can be compared for a given mode but not necessarily from one mode to another However they can still be effectively used in the analysis design process Modal quantities can be used to identify problem areas by indicating the more highly stressed elements Elements that are consistently highl
380. r 6 Transient Response Analysis is not concerned with mode truncation For systems with initial conditions direct transient response is the only choice Table 6 2 provides a starting place for evaluating which method to use Many additional factors may be involved in the choice of a method such as contractual obligations or local standards of practice 6 5 Transient Excitation Definition An important aspect of a transient response analysis is the definition of the loading function In a transient response analysis the force must be defined as a function of time Forces are defined in the same manner whether the direct or modal method is used You can use the following Bulk Data entries to define transient loads TLOAD1 Tabular input TLOAD2 Analytical function DAREA Spatial distribution of dynamic load TABLEDI Tabular values versus time LSEQ Generates the spatial distribution of dynamic loads from static load entries DLOAD Combines dynamic load sets DELAY Time delay The particular entry chosen for defining the dynamic loading is largely a function of user convenience for concentrated loads Pressure and distributed loads however require a more complicated format There are two important aspects of dynamic load definition First the location of the loading on the structure must be defined Since this characteristic locates the loading in space it is called the spatial distribution of the dynamic loading Secondly the time vari
381. r and Type of Roots Found 1 v1 v2 ND Lowest ND in range or all in range whichever is smaller V2 JAlinrage S ND Lowest ND in range V1 e Lowest root in range V1 e S _ ND Lowest ND roots in l e o 0000000000000 6 lowestrot S 7 V2 ND Lowest ND or all in range e V2 whichever is smaller 8 V2 QJ fAlblowV2 4e Q QU 5 0 The MSGLVL field of the EIGRL entry is used to control the amount of diagnostic output The value of 0 produces no diagnostic output The values 1 2 or 3 provide more output with the higher values providing increasingly more output In some cases higher diagnostic levels may help to resolve difficulties with special modeling problems The MAXSET field is used to control the block size The default value of 7 1s recommended for most applications There may be special cases where a larger value may result in quicker convergence of many multiple roots or a lower value may result in more efficiency when the structure is lightly coupled However the default value has been chosen after reviewing the results from a wide range of problems on several different computer types with the goal of minimizing the computer time A common occurrence is for the block size to be reset by NX Nastran during the run because there is insufficient memory for a block size of 7 Computational efficiency tends to degrade as the block size decreases Therefore you sho
382. r can readily occur The response is comprised of two frequencies as given below fl f2 Thigher 08 Viger E 9 Equation 6 32 where fl lower of the closely spaced mode frequencies f2 higher of the closely spaced mode frequencies In this example fhigher 18 5 04 Hz and flower 1s 0 25 Hz The lower frequency is called the beat frequency and is the frequency at which energy transfer occurs 6 28 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis Co R TO ah Figure 6 8 Displacements of Grid Points 1 and 2 Cantilever Beam Model Consider the cantilever beam shown below This beam model is the same as in Examples in Chapter 5 Modal transient response SOL 112 is run with loads applied to grid points 6 and 11 as shown in Figure 6 10 The analysis is run for a duration of 2 seconds with a At of 0 001 second Modal damping of 5 critical damping is used for all modes Modes up to 3000 Hz are computed using the Lanczos method Figure 6 11 shows part of the input file NX Nastran Basic Dynamic Analysis User s Guide 6 29 Chapter 6 Transient Response Analysis 6 30 i 3 E DER aat ee eat at atat utut atat tuat utut tat aa atata atta a at tata utut tat mataa at ata utut tata utut teat ee at tata a at tata utut at aata atat tuat utut atat atat utut DEEP watatatat at at ata a at at ata utut me pC pU Figure 6 9 Cantilever Beam Model with Ap
383. r hand if your SUPORT entry defines four DOFs then only the first three are treated as rigid body modes and the fourth is not replaced Furthermore the use of a SUPORT entry forces an extra decomposition which increases the computer run time Because the SUPORT entry is not used to compute the rigid body eigenvectors there is probably little to be gained by using the SUPORT entry with the Lanczos method unless response spectrum analysis is being performed Theoretical Considerations Degrees of freedom defined on the SUPORT entry are placed in the r set When an r set is present static rigid body vectors are calculated in NX Nastran by first partitioning the a set into the r and sets 4 4 NX Nastran Basic Dynamic Analysis User s Guide Rigid Body Modes eg E A E Equation 4 2 Introducing this partitioning in the stiffness matrix results in Ky Ky t _ 0 P K Ky y i Equation 4 3 for the rigid body modes defined in the r set There is no load on set DOFs The load P on the r set is not needed in subsequent equations Then solve for u in terms of u uj D l u Equation 4 4 where D K K The matrix D is used to construct a set of rigid body vectors y rig D r Equation 4 5 where yrig represents the motion of the a set for a unit motion of each SUPORT DOF with all other SUPORT DOFs constrained and Z is an r r identity matrix The rigid body vectors can be used to crea
384. r linear independence is a slightly curved bar modeled using coordinate systems that follow the curve of the bar such that the x axis is always tangent to the bar The x DOFs at each end of the bar describe linearly independent DOFs in a mathematical sense However numerical truncation produces poor conditioning if the angle between the ends is less than a few degrees This condition is detected by the automatic diagnostics discussed earlier This problem can be corrected or better yet avoided by making a careful sketch of all r set DOFs including their locations in space and the orientation of their global coordinates Then apply the three plane test described earlier Using a physical analogy a good r set can be chosen by finding one grid point that sustains all possible loadings well if 1t 1s tied to ground in an actual hardware test If there 1s no such grid point the ties to ground should be spread over enough grid points to sustain the loads without damaging the structure An RBE3 element used for this purpose can provide good rigid body modes without affecting the flexible modes 4 3 Examples This section provides several rigid body modes examples showing input and output These examples are as follows Table 4 1 Unconstrained SUPORT No Redundancy of Analysis Method SUPORT SUPORT d04barl o SUPORT a d04bar2 dOAbar3 d04bar4 d04bar5 SINV NoSUPORT fF gt d04bar6 d04bar7 Underdetermined d04bar8 dO4bkt Lancz
385. r method fail if the mass matrix is not positive definite To minimize this problem degrees of freedom with null columns are removed by the automatic application of static condensation see Advanced Dynamic Analysis Capabilities called auto omit Applying the auto omit process is a precaution and may not remove all possible causes of mass matrix singularity such as a point mass offset from a grid point but it greatly improves the reliability and convenience of the Householder method The Householder method uses different transformation schemes to obtain the eigenvalues The Householder method can take advantage of parallel processing computers Modified Householder Methods The modified Householder method issimilar to the standard method with the exception that the mass matrix can be singular Although the mass matrix is not required to be nonsingular in the modified method a singular mass matrix can produce one or more infinite eigenvalues Due to roundoff error these infinite eigenvalues appear in the output as very large positive or negative eigenvalues To reduce the incidence of such meaningless results degrees of freedom with null masses are eliminated by automatic static condensation as in the case of the unmodified method The modified methods requires more computer time than the standard method NX Nastran Basic Dynamic Analysis User s Guide 3 11 Chapter 3 Real Eigenvalue Analysis Automatic Householder Methods Many ti
386. raction The F2 field specifies the highest frequency of interest in the eigenvalue extraction The units are cycles per unit time The value for F1 must be greater than or equal to 0 0 NX Nastran Basic Dynamic Analysis User s Guide 3 15 Chapter 3 Real Eigenvalue Analysis The ND field is used to specify the desired number of roots for tracking methods or eigenvectors for transformation methods beginning with F1 The NORM field on the continuation entry is used to specify the method of eigenvector normalization The choices are MASS Mass normalization default if used the continuation entry is not required MAX Normalization to a unit value of the largest component in the analysis set POINT Normalization to a unit value at a user specified a set grid point G and component There is an interrelationship among the F1 F2 and ND fields on the EIGR entry as defined in Table 3 3 Table 3 3 Relationship Between the METHOD Field and Other Fields METHOD Field HOU MHOU or AHOU Frequency range of interest If ND is Frequency range of interest F1 must not blank F1 and F2 are ignored If ND be input If METHOD SINV and NDjis blank eigenvectors are found whose is blank then F2 must be input natural frequencies lie in the range between F1 and F2 Real 2 0 0 Real 2 0 0 F1 F2 Estimate of number of roots 1n range Not used by SINV method Integer 0 Desired number of eigenvectors If ND is zero the
387. raft to time or frequency varying excitations Atmospheric turbulence is the primary example of this type of excitation but wind shear and control surface motion can also have an aeroelastic component Methods of generalized harmonic Fourier analysis are applied to the linear system to obtain the response to the excitation in the time domain The gust response analysis may be regarded either as a stationary random loading or as a discrete gust The gust analysis capability computes the response to random atmospheric turbulence discrete one dimensional gust fields and control surface motion and other dynamic loading The random response parameters calculated are the power spectral density root mean square response and mean frequency of zero crossings The response to the discrete gust and control surface motion is calculated by direct and inverse Fourier transform methods since the oscillatory aerodynamics are known only in the frequency domain The time histories of response quantities are the output in the discrete case see Figure 11 9 3 0E8 T TIT Root Bending Moment in Ibs ee l1 LL LL LLL l lime sec 8 i i I m Figure 11 9 Transient Response Resulting from a Gust 11 13 DMAP NX Nastran provides a series of solution sequences SOL 103 for normal modes analysis for example written in their own language tailored to matrix manipulation These solution sequences consist of a series of DMAP direct matrix abstract
388. range 20 and 2000 Field Contents SID Set ID specified by a FREQUENCY Case Control command F1 Lower bound of modal frequency range in cycles per unit time Real 0 0 F9 Upper bound of modal frequency range in cycles per unit time Real 0 0 F2 2 F1 Default F1 FRi Fractions of the natural frequencies in the range F1 to F2 Real 0 0 5 Frequency Response Considerations Exciting an undamped or modal or viscous damped system at 0 0 Hz using direct frequency response analysis gives the same results as a static analysis and also gives almost the same results when using modal frequency response depending on the number of retained modes Therefore if the maximum excitation frequency is much less than the lowest resonant frequency of the system a static analysis 1s probably sufficient Undamped or very lightly damped structures exhibit large dynamic responses for excitation frequencies near resonant frequencies A small change in the model or running it on another computer may result in large changes in such responses Use a fine enough frequency step size Af to adequately predict peak response Use at least five points across the half power bandwidth which is approximately 2xf for an SDOF system as shown in Figure 5 7 NX Nastran Basic Dynamic Analysis User s Guide 5 23 Chapter 5 Frequency Response Analysis Peak Response Peak p Hal Power Point Response J2 Frequency Half
389. rata M Ishikawa K Korosawa M Fukushima S Hoshina H Seismic Analysis of Plutonium Glovebox by MSC NASTRAN January 1993 Liepins Atis A Nazemi Hamid Virtual Mass of Fluid in Egg Shaped Digesters The MSC 1993 World Users Conf Proc Paper No 77 May 1998 Nomura Yoshio Seismic Response Analysis by MSC NASTRAN for Coupled Structure Ground and Pile The Fifth MSC NASTRAN User s Conf in Japan October 1987 in Japanese Pamidi M R Pamidi P R Modal Seismic Analysis of a Nuclear Power Plant Control Panel and Comparison with SAP IV NASTRAN Users Exper pp 515 530 October 1976 NASA TM X 3428 Tsaur D H Chyuan S W Chen J T On the Accuracy of MSC NASTRAN on Response of Two Span Beams to Spatially Varying Seismic Excitation The 4th MSC Taiwan Users Conf Paper No 9 November 1992 Yiak K C Pezeshk S Seismic Study of a Cable Stayed Bridge Proceedings of the Structures Congrees 794 Atlanta 1994 Zhou Hongye Chen Youping The Influence of Phase Difference Effects on Earthquake Response of Cable Stayed Bridges MSC 1994 World Users Conf Proc Paper No 37 June 1994 DYNAMICS TRANSIENT ANALYSIS Korean Vibration Analysis for Outercase in Drum Washer and Floor MSC 1994 Korea Users Conf Proc December 1994 in Korean Aslani Chang Yatheendar Manicka Visintainer Randal H Rohweder David S Lopez de Alda Juan Simulation of Proving Ground Events
390. rator 4 377 877 662 7 877 5 623 342 662 342 3 432 Equation G 21 An eigensolution is performed on the 7 matrix to determine the principal directions The resulting eigenvalues are the principal moments of inertia which are assumed to be the diagonal terms of the principal inertia matrix nQ The eigenvectors form the columns of the matrix Q which is the transformation relating the intermediate inertia matrix 7 to the principal inertia matrix 0 as shown in Equation G 22 U Q Q1 7O Equation G 22 For the example Q and Z Q are given by 4 463 0 0 0 6 076 0 0 0 2893 Q 720 459 521 O 372 889 269 386 0 810 Equation G 23 The matrices S and Q matrices are the coordinate rotation matrices which when taken together relate the principal directions of the momental ellipsoid to the basic coordinate system The matrices given in Equation G 23 are in agreement with those given in Equation G 2 The example for the four mass model is now complete NX Nastran Basic Dynamic Analysis User s Guide G 15 Appendix H Diagnostic Messages for Dynamic Analysis This appendix lists common diagnostic messages for dynamic analysis The text for each message is given in uppercase letters and is followed by additional explanatory material including suggestions for remedial action The messages in this section have the following format ee SYSTEM USER FATAL WAR
391. rcraft bulkhead Your component consists of 500 DOFs and the aircraft model consists of 100 000 DOFs The flexibility of the backup structure is somewhat important You can certainly analyze your component by including the full aircraft model 100 500 DOFs However as an approximation you can reduce the matrices for the entire aircraft down to a manageable size using dynamic reduction see Advanced Dynamic Analysis Capabilities These reduced mass and stiffness matrices can then be read and added to your various component models In this case you may be analyzing a 2000 DOF system instead of a 100 500 DOF system e The same concept can be extended to a component attached to a test fixture If the finite element model of the fixture is available then the reduced mass and stiffness matrices of the fixture can be input Furthermore there are times whereby the flexibility of the test fixture at the attachment points can be measured experimentally The experimental stiffness matrix is the inverse of the measured flexibility matrix In this instance this experimental stiffness matrix can be input to your model One way of reading these external matrices is through the use of the direct matrix input feature in NX Nastran Direct Matrix Input The direct matrix input feature can be used to input stiffness mass viscous damping structural damping and load matrices attached to the grid and or scalar points in dynamic analysis These matrice
392. requency Forces are defined in the same manner regardless of whether the direct or modal method is used The following Bulk Data entries are used for the frequency dependent load definition RLOADI Tabular input real and imaginary RLOAD2 Tabular input magnitude and phase DAREA Spatial distribution of dynamic load LSEQ Generates the spatial distribution of dynamic loads from static load entries DLOAD Combines dynamic load sets TABLEDi1 Tabular values versus frequency DELAY Time delay DPHASE Phase lead The particular entry chosen for defining the dynamic loading is largely a function of user convenience for concentrated loads Pressure and distributed loads however require a more complicated format NX Nastran Basic Dynamic Analysis User s Guide 5 11 Chapter 5 Frequency Response Analysis There are two important aspects of dynamic load definition First the location of the loading on the structure must be defined Since this characteristic locates the loading in space it is called the spatial distribution of the dynamic loading Secondly the frequency variation in the loading is the characteristic that differentiates a dynamic load from a static load This frequency variation is called the temporal distribution of the load A complete dynamic loading is a product of spatial and temporal distributions Using Table IDs and Set IDs in NX Nastran makes it possible to apply many complicated and temporally similar loadings with a m
393. rid scalar or extra point USER FATAL MESSAGE 2133 INITIAL CONDITION IN SET SPECIFIED FOR POINT NOT IN ANALYSIS SET Initial conditions can only be specified for analysis set points Therefore the point component mentioned on TIC entries must belong to the analysis set USER FATAL MESSAGE 2135 DLOAD CARD HAS A DUPLICATE SET ID FOR SET ID The Li Set IDs on a DLOAD entry are not unique See the DLOAD Bulk Data description H 2 NX Nastran Basic Dynamic Analysis User s Guide UFM 2136 UIM 2141 UFM 2200 UFM 3031 UWM 3034 Diagnostic Messages for Dynamic Analysis USER FATAL MESSAGE 2136 DUPLICATE DLOAD RLOAD OR TLOAD SET ID NUMBER HAS BEEN ENCOUNTERED FOR DLOAD SET Dynamic loads may not be defined by giving multiple data entries with the same ID Use unique IDs USER INFORMATION MESSAGE 2141 TIME ESTIMATE IS SECONDS PROBLEM SIZE IS SPILL WILL OCCUR FOR THIS CORE AT A PROBLEM SIZE OF The time estimate includes the time of the tridiagonalization and eigenvalue calculation when the HOU method is used If ND is given on the EIGR entry it also includes the time of the eigenvector generation If F1 and F2 are used instead the eigenvector times are not estimated This condition can underestimate the time when the range includes many eigenvectors USER FATAL MESSAGE 2200 INCONSISTENT RIGID BODY SYSTEM This message occurs if a SUPORT is used and the
394. rid point 1 is coordinate system 1 the coordinate system associated with rows and columns 13 through 18 grid point 3 is coordinate system 3 The remaining rows and columns are in the basic coordinate system 2 To generate the 6x6 rigid body mass matrix MO for the structure it is necessary to compute the mass matrix in the basic coordinate system relative to the reference point This computation requires the transformation matrix D that relates the rigid body displacements in the global system u to the six unit displacements in the basic coordinate system located at the reference grid point u as shown in Equation G 1 LN D iu rt Equation G 1 Reference Point NX Nastran Basic Dynamic Analysis User s Guide G 7 Appendix G Grid Point Weight Generator The transformation matrix D is assembled from the individual transformation matrices d computed for each grid point Each individual transformation matrix d consists of two transformations 7r which relates the location of the grid point to the reference grid point in the basic coordinate system and T7 which relates the global coordinate system at the grid point to the basic coordinate system The Tr transformation matrices are first computed by constructing the location vectors in the basic coordinate system r for each grid point in the model relative to the reference point as shown in Equation G 2 irh RH Rig i e Equation G 2 The locati
395. ries linearly interpolate between the end points and linearly extrapolate outside of the endpoints as shown in Figure 6 3 The TABLED1 entry gives you the option to perform logarithmic interpolation between points also The TABLED4 entry uses the endpoint values for values beyond the endpoints Linear Interpolation Between Endpoints Ll E Linear Extrapolation of Segment x x Linear Extrapolation ot segment X5 X4 X X4 Ms Ya X4 Me X X5 Figure 6 3 Interpolation and Extrapolation for TABLED1 TABLED2 and TABLEDS3 Entries The TABLED1 entry has the following format Field Contents TID Table identification number XAXIS Specifies a linear or logarithmic interpolation for the x axis Character LINEAR or LOG Default LINEAR YAXIS Specifies a linear or logarithmic interpolation for the y axis Character LINEAR or LOG Default LINEAR Xl yl Tabular values Values of x are frequency in cycles per unit time ENDT Ends the table input The TABLED1 entry uses the algorithm y yra Equation 6 27 The algorithms used for interpolation and extrapolation are as follows NX Nastran Basic Dynamic Analysis User s Guide 6 17 Chapter 6 Transient Response Analysis YAXIS In xj x In x xi ms S In xj Zxi In Gj 7 xi xj Xx x xi LINEAR LOG ln x xi LOG LOG 7 7 8 7 REED In xj xi Ing xi The TABLED2 entry has the following format
396. rigid body mass matrix is not positive definite Possible causes are unconstrained mechanisms or input of negative mass terms A diagnostic method is to remove all SUPORT entries and inspect the resulting eigenvectors for implausible behavior USER FATAL MESSAGE 3031 UNABLE TO FIND SELECTED SET IN TABLE IN SUBROUTINE A particular set used in the problem was not included in the data Good examples are loads initial conditions or frequency sets Include the required data or change the Case Control commands to select data already in the problem Set zero 0 has a special meaning A set selection was required but none was made For example no METHOD was selected for an eigenvalue extraction problem or no FREQ was selected for frequency response This message can also indicate that a LOAD entry references another LOAD entry which 1s not permitted This message can also occur if a DLOAD entry references a nonexisting LOAD entry e g RLOADI USER WARNING MESSAGE 3034 ORTHOGONALITY TEST FAILED LARGEST TERM NUMBER FAILED PAIR e eem EPSILON This indicates that eigenvector accuracy is in doubt This message is printed only when the off diagonal terms of the modal mass matrix are larger than 1 0E 10 The eigenvectors are not orthogonal to this extent This nonorthogonality is especially important if a modal formulation is used The pair of eigenvectors listed exhibit the worst behavio
397. s It controls the physical record size for data storage transfer that is contained in many NX Nastran logical units The default and maximum allowable buffsize is machine dependent The default value is recommended except for large problems It can be modified by using the following NASTRAN statement NASTRAN BUFFSIZE XXXXX where xxxxx 1s the desired buffsize This is often referred to as a NX Nastran GINO block Each GINO block contains one NX Nastran buffer A brace indicates that the quantity within this bracket is mandatory The underlined item within is the default value A square bracket indicates that the quantity within this bracket is optional NX Nastran Basic Dynamic Analysis User s Guide E 1 Appendix E File Management Section E 3 NX Nastran Database When submitting a NX Nastran job a series of standard output files is created e g F06 file Conventions for the filenames are machine dependent Furthermore four permanent MASTER DBALL USRSOU USROBJ and one scratch SCRATCH DBsets are created during the run This is the directory DBset that contains a list of all the DBsets used in the job all the physical file names assigned and an index pointing to all the data blocks created and where they are stored In addition it also contains the NX MASTER Nastran Data Definition Language NDDL used NDDL is the internal NX Nastran language that describes the database You do not need to understand NDDL to use
398. s Equation 6 6 The structural damping force is a displacement dependent damping The structural damping force is a function of a damping coefficient G and a complex component of the structural stiffness matrix M lt L c iG K tu t y iP Equation 6 7 Assuming constant amplitude oscillatory response for an SDOF system the two damping forces are identical if 6 4 NX Nastran Basic Dynamic Analysis User s Guide Transient Response Analysis Gk bw Equation 6 8 or bez 1 Equation 6 9 Therefore if structural damping G is to be modeled using equivalent viscous damping 5 then the equality Equation 6 9 holds at only one frequency see Figure 6 1 Two parameters are used to convert structural damping to equivalent viscous damping An overall structural damping coefficient can be applied to the entire system stiffness matrix using PARAM WS r where r is the circular frequency at which damping is to be made equivalent This parameter is used in conjunction with PARAM G The default value for W3 is 0 0 which causes the damping related to this source to be ignored in transient analysis PARAM W4 is an alternate parameter used to convert element structural damping to equivalent viscous damping PARAM W4 r is used where r is the circular frequency at which damping is to be made equivalent PARAM WA is used in conjunction with the GE field on the MAT entry The default value for W4 is 0 0 which causes the related damping terms t
399. s R A Schmid R Adrick H C Rotor Dynamic Analysis with MSC NASTRAN via the Important Modes Method The 1989 MSC World Users Conf Proc Vol I Paper 13 March 1989 Barnett Alan R Abdallah Ayma A Ibrahim Omar M Manella Richard T Solving Modal Equations of Motion with Initial Conditions Using MSC NASTRAN DMAP Part 1 Implementing Exact Mode Superposition The MSC 1993 World Users Conf Proc Paper No 12 May 1993 Barnett Alan R Abdallah Ayma A Ibrahim Omar M Sullivan Timothy L Solving Modal Equations of Motion with Initial Conditions Using MSC NASTRAN DMAP Part 2 Coupled vs Uncoupled Integration The MSC 1993 World Users Conf Proc Paper No 13 May 1993 Bella David F Steinhard E Critical Frequency Determination of a Flexible Rotating Structure Attached to a Flexible Support Proc of the 18th MSC Eur Users Conf Paper No 28 June 1991 Bella David Hartmueller Hans Muehlenfeld Karsten Tokar Gabriel Identification of Critical Speeds of Rotors Attached to Flexible Supports The MSC 1993 World Users Conf Proc Paper No 34 May 1993 Blakely Ken Rose Ted Cross Orthogonality Calculations for Pre Test Planning and Model Verification The MSC 1993 World Users Conf Proc Paper No 72 May 1993 Blakely Ken Rose Ted Cross Orthogonality Calculations for Pre Test Planning and Model Verification Proc of the 20th MSC European Users Conf September 1993 Brughmans M
400. s Structural Dynamics and Materials Conf Part 2 pp 334 343 May 1983 Li Tsung hsiun Bernard James Optimization of Damped Structures in the Frequency Domain The MSC 1993 World Users Conf Proc Paper No 28 May 1993 Lu Y P Everstine G C More on Finite Element Modeling of Damped Composite Systems J of Sound and Vibration Vol 69 No 2 pp 199 205 1980 Mace M Damping of Beam Vibrations by Means of a Thin Constrained Viscoelastic Layer Evaluation of a New Theory Journal of Sound and Vibration v 172 n 5 May 19 1994 Merchant D H Gates R M Ice M W Van Derlinden J W The Effects of Localized Damping on Structural Response NASTRAN Users Exper pp 301 320 September 1975 NASA TM X 3278 Parekh Jatin C Harris Steve G The Application of the Ritz Procedure to Damping Prediction Using a Modal Strain Energy Approach Damping 89 Paper No CCB November 1989 Rose Ted DMAP Alters to Apply Modal Damping and Obtain Dynamic Loading Output for Superelements The MSC 1993 World Users Conf Proc Paper No 24 May 1993 Rose Ted McNamee Martin A DMAP Alter to Allow Amplitude Dependent Modal Damping in a Transient Solution MSC 1996 World Users Conf Proc Vol V Paper No 50 June 1996 Shieh Rong C A Superefficient MSC NASTRAN Interfaced Computer Code System for Dynamic Response Analysis of Nonproportionally Damped Elastic Systems The MSC 1993 World Users Conf Proc
401. s 0 iwe oa Note that f is the frequency in cycles per unit time and that E cot wt t isin wt Frequency Dependent Loads RLOAD2 Entry The RLOAD2 entry is a variation of the RLOAD1 entry used for defining a frequency dependent load Whereas the RLOAD1 entry defines the real and imaginary parts of the complex load the RLOADJ2 entry defines the magnitude and phase The RLOADJ2 entry defines dynamic excitation in the form 5 12 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis IP AB fye tO 97 Any Equation 5 21 The RLOAD2 definition may be related to the RLOAD1 definition by C iD Boe RLOADI RLOAD Definition Definition Equation 5 22 Field Contents SID Set ID defined by a DLOAD Case Control command DAREA Identification number of the DAREA entry set that defines A Integer gt 0 DELAY Identification number of the DELAY entry set that defines t Integer gt 0 Identification number of the DPHASE entry set that defines qin degrees Integer DPHASE 0 TB TABLEDi entry defining amplitude versus frequency pairs for B Integer gt 0 TP TABLEDi entry defining phase angle versus frequency pairs for f f in degrees Integer 0 TYPE Defines the type of the dynamic excitation Integer character or blank Defaults 0 Note that f is the frequency in cycles per unit time Spatial Distribution of Loading DAREA Entry The DAREA entry defines the degrees of freedom
402. s a column of nonzero terms for the matrix Header Entry Format oa 2 8 4 s e6 7 s o w Column Entry Format Duc sme o e e qo yg o qo o DMIG STIF poop fb gom LL a o je b he qo 5 Field Contents NAME Name of the matrix IFO Form of matrix input 1 Square 9 or 2 Rectangular 6 Symmetric input only the upper or lower half TIN Type of matrix being input 1 Real single precision one field is used per element 2 Real double precision one field per element 3 Complex single precision two fields are used per element 4 Complex double precision two fields per element TOUT Type of matrix to be created 0 Set by precision system cell default 1 Real single precision 2 Real double precision 3 Complex single precision 4 Complex double precision POLAR Input format of Ai Bi Integer blank or 0 indicates real imaginary format integer gt 0 indicates amplitude phase format NCOL Number of columns in a rectangular matrix Used only for IFO 9 Grid scalar or extra point identification number for the column index or GJ column number for IFO 9 CJ Component number for GJ for a grid point Gi Grid scalar or extra point identification number for the row index NX Nastran Basic Dynamic Analysis User s Guide 2 15 Chapter 2 Finite Element Input Data Field Contents Ci Component number for Gi for a grid point Ai Bi Real and imaginary or
403. s and Test Results Proc of the 20th MSC European Users Conf September 1993 NX Nastran Basic Dynamic Analysis User s Guide l 21 Appendix References and Bibliography Deutschel Brian William A Systematic Approach Using Finite Elements for Improving Vehicle Ride CAD CAM Robotics and Factories of the Future Integration of Design Analysis and Manufacturing Proc Springer Verlag Berlin Heidelberg Vol I pp 150 154 1989 Deutschel Brian W Katnik Richard B Bijlani Mohan Cherukuri Ravi Improving Vehicle Response to Engine and Road Excitation Using Interactive Graphics and Modal Reanalysis Methods SAE Trans Paper No 900817 September 1991 Egashira Yuji Large Scale Vibration Analysis of Car Body Using Superelement Method The Second MSC NASTRAN User s Conf in Japan October 1984 in Japanese El Bayoumy Lotfi Identification and Correction of Damaging Resonances in Gear Drives Gear Technology Vol 1 No 2 pp 14 19 August September 1984 Ferg D Foote L Korkosz G Straub F Toossi M Weisenburger R Plan Execute and Discuss Vibration Measurements and Correlations to Evaluate a NASTRAN Finite Element Model of the AH 64 Helicopter Airframe National Aeronautics and Space Administration January 1990 NASA CR 181973 Flanigan Chris Methods for Calculating and Using Modal Initial Conditions in MSC NASTRAN Proc of the Conf on Finite Element Methods and Technology March 1980 Flan
404. s are referenced in terms of their external grid IDs and are input via DMIG Bulk Data entries As shown in Table 2 3 there are seven standard kinds of DMIG matrices available in dynamic analysis Table 2 3 Types of DMIG Matrices in Dynamics Matrix G Type P Type tiffness K2GG K2PP Mass Structural Damping K42GG 00 0000000000000 Load PO The symbols for g type matrices in mathematical format are K M7 B K47 and peg The four matrices K2GG M2GG B2GG and K42GG must be resi and symmetric These matrices are implemented at the g set level see Ihe Set Notation System Used in Dynamic Analysis for a description of the set notation for dynamic analysis In other words these terms are added to the corresponding structural matrices at the specified DOFs prior to the application of constraints MPCs SPCs etc The symbols for p type matrices in standard mathematical format are K M2 pl and B The p set is a union of the g set and extra points These matrices need not be real or symmetric The p type matrices are used in applications such as control systems Only the g type DMIG input matrices are covered in this guide 2 14 NX Nastran Basic Dynamic Analysis User s Guide Finite Element Input Data DMIG Bulk Data User Interface In the Bulk Data Section the DMIG matrix is defined by a single DMIG header entry followed by a series of DMIG data entries Each of these DMIG data entries contain
405. s here indicates that poor eigenvectors were computed The row number where the negative term occurs is printed in the diagnostic This row number does not refer to a physical degree of freedom but refers instead to an eigenvector number The usual cause is computing eigenvectors for computational infinite roots in the modified transformation methods This problem can be avoided after the fact by setting ND on the EIGR entry to a value less than the row number that appears in the diagnostics or before the fact by setting F2 on the EIGR entry to a realistic value instead F 8 NX Nastran Basic Dynamic Analysis User s Guide Numerical Accuracy Considerations Frequency Response Analysis Negative terms on the factor and high factor to matrix diagonal ratios can be expected when using coupled methods and may often be safely ignored These messages are merely an indication that the excitation frequency is above one or some of the natural frequencies of the system negative terms or is near a natural frequency high ratio Transient Response Analysis A well conditioned model should have neither negative terms nor high ratios on its factor terms The causes of such messages include all of the effects described above Negative mass terms can be detected by rapidly diverging oscillations in the transient solution The Large Mass Method One of the methods for enforcing motion is the large mass method It may be used with direct methods as well as
406. s input is to apply gravity in several directions and print the SPC forces This verification ensures that the mass 1s correctly applied and that the units are correct 10 5 Damping Proper specification of damping is probably the most difficult modeling input to verify because its verification can only be done via dynamic response analysis In addition its units are not necessarily familiar because damping is normally not a modeling input that you use frequently unless dynamic response analysis is all you run Also there are several ways to specify damping in NX Nastran which increase the chances of making a mistake Finally even though the damping units are correct and the damping is input correctly in NX Nastran it is difficult to know that the damping specification itself is correct from a physical standpoint While there are relatively easy checks for correctness in mass and stiffness input including comparison to static and modal test data there are no such easy checks for damping input The easiest way to specify damping is to use modal damping which is often specified as the percentage of critical damping The TABDMP1 Bulk Data entry is used to specify modal damping The following are several potential mistakes associated with using modal damping e Forgetting to select the TABDMP1 entry using the SDAMPING Case Control command e Forgetting to specify the damping TYPE field 3 The default damping type is structural damping which i
407. s of 0 0 for W3 and W4 cause the K7 and K terms to be ignored in the damping matrix regardless of the presence of the PARAM G or K K7 5 is the stiffness K4 7 is the structural damping and is created when GE is specified on the MAT entries D 8 NX Nastran Basic Dynamic Analysis User s Guide Appendix E File Management Section E 1 Overview This appendix provides an overview of how NX Nastran s database structure and File Management Section FMS work so that you can allocate your computer resources efficiently especially for large models For many problems due to the default values the use or knowledge of the FMS is either transparent or not required by you E 2 Definitions Before presenting the details of the database description it is helpful to define some of the basic terms that are used throughout this appendix DBset Database Data block Logical name Word Buffsize Database set This consists of an NX Nastran logical name such as MASTER DBALL etc which refers to an entity within the NX Nastran database It consists of a collection of physical files Collection of all DBsets assigned to a run Matrix or table e g KAA LAMA that is stored in the database Local internal name log name used by NX Nastran for a file or DBset For 32 and 64 bit machines each word is equivalent to four and eight bytes respectively Length of an NX Nastran buffer in terms of words 32 or 64 bit word
408. s the satellite Each contractor can reduce his model to its boundary degrees of freedom which is suitable for superelement analysis The systems integrator then combines these reduced models into one model for a liftoff analysis Superelement analysis has the advantage that matrices can be passed from one organization to another without revealing proprietary modeling details or concern about whether the same superelement interior grid point and element numbers are used by every participant Figure 11 5 Superelements Used to Model a Car Door Component Mode Synthesis Component mode synthesis CMS is a form of superelement dynamic reduction wherein matrices are defined in terms of modal coordinates corresponding to the superelement modes and physical coordinates corresponding to the grid points on the superelement boundaries CMS is advantageous because there are fewer modal coordinates than physical coordinates perhaps only one percent as many In addition CMS can utilize modal test data thereby increasing the accuracy of the overall analysis 11 10 Design Optimization and Sensitivity Design optimization is used to produce a design that possesses some optimal characteristics such as minimum weight maximum first natural frequency or minimum noise levels Design optimization is available 1n NX Nastran in SOL 200 in which a structure can be optimized considering simultaneous static normal modes buckling transient response frequen
409. s twice the critical damping percentage NX Nastran Basic Dynamic Analysis User s Guide 10 5 Chapter 10 Guidelines for Effective Dynamic Analysis e Not making the table cover an adequate range of frequencies Like almost all of the NX Nastran tables the TABDMP1 entry extrapolates beyond the endpoints of the table by using the first two or the last two entered values As a rule you should try to provide enough input points so that the table lookup point is always an interpolated value Modal damping can be used only in modal frequency response and modal transient response Other forms of damping have to be used for the direct methods of response For frequency response analysis GE field 9 of the MAT1 entry and PARAM G define structural damping These variables are also used to specify structural damping for transient response analysis but are not activated unless PARAM W3 and PARAM W4 are set to nonzero values A common mistake is to forget to set these values Note that damping is additive that is the damping matrix is comprised of all of the input damping sources For example damping due to CDAMPi elements adds to damping due to PARAM G and GE Mixing of damping types can increase the chances for error and you are cautioned against the mixing of damping types unless it is necessary In many cases damping is not an important consideration For example a structure s peak response due to an impulsive load is relatively unaffected by d
410. script may indicate a frequency number For an SDOF system the circular natural frequency is given by K Equation 1 5 The circular natural frequency is specified in units of radians per unit time Natural Frequency The natural frequency f is defined by d f Equation 1 6 The natural frequency is often specified in terms of cycles per unit time commonly cycles per second cps which is more commonly known as Hertz Hz This characteristic indicates the number of sine or cosine response waves that occur in a given time period typically one second The reciprocal of the natural frequency is termed the period of response T given by NX Nastran Basic Dynamic Analysis User s Guide 1 5 Chapter 1 Fundamentals of Dynamic Analysis Equation 1 7 The period of the response defines the length of time needed to complete one full cycle of response In the solution of Equation 1 4 A and B are the integration constants These constants are determined by considering the initial conditions in the system Since the initial displacement of the system u t 0 and the initial velocity of the system a t U are known A and B are evaluated by substituting their values into the solution of the equation for displacement and its first derivative velocity resulting in u t m B u t 0 and A Equation 1 8 These initial value constants are substituted into the solution resulting in u 0 u t lina t u
411. se Analysis ccce tmt 5 1 CIO uu eee HORE eee ESR See EEE ee eee RE 8 ee 5 2 Direct Frequency Response Analysis ee ee ee eee 5 3 Modal Frequency Response Analysis oonu anaana 5 5 Modal Versus Direct Frequency Response leen 5 10 Frequency Dependent Excitation Definition cen 5 11 Solution ODER uu 2x99 4 93 s Xx oe See CES FSEBETRTEXETRITX 5 20 Frequency Response Considerations 0 0 ce ee ee rs 5 23 Solution Control for Frequency Response Analysis 0 0 eee eee eee eee 5 24 eee PERTE ee a ee ee ee ee a a TE ET EE ee 5 26 Transient Response Analysis ccc ccc c cece cccerecesesescsescscees 6 1 A IL 3445446644445 44th a oe eee EES ee E EE EE 6 2 NX Nastran Basic Dynamic Analysis User s Guide 3 Contents Direct Transient Response Analysis ceres 6 2 Modal Transient Response Analysis nuana aaa 6 6 Modal Versus Direct Transient Response 0 cee ee ee ene 6 13 Transient Excitation Definition eee rs 6 14 Integration Time Step cud dq koe m3 EON OE Ke AUE edo ER EROR RR CREAR ee 6 23 Transient Excitation Considerations ees 6 23 Solution Control for Transient Response Analysis eee 6 24 PODES 15asws9 49 44 A ARTARSRRREGREKRERLERERRERARERSSESZASRSAGSSSRL fx 6 26 TO Bt 56S dioe REOR d EORR E E e cda 9E OEE e DEO De E C de e T 7 1 Bui o 5 ee OE EGER OSE ER EER SE EEEE TETELE
412. se Lanczos method Testing has shown that this model provides a very good guideline for most industry models Memory requirements increase with problem size Empirical formulas were developed for these benchmark problems to estimate the memory requirement given the number of degrees of freedom DOF contained in the model For the equation Log mem 7934 Log DOF 2 3671 Equation 10 7 mem The memory required in megabytes DOF The number of degrees of freedom contained in the model Note that these memory requirements are for no spill conditions The symmetric solver can run with less memory but because of spill conditions the performance is degraded in both computer runtime and disk space usage Empirical formulas were developed for these benchmark problems to estimate the disk space requirement given the number of degrees of freedom DOF contained in the model For the equation Log space 1 0815 Log DOF 2 5411 Equation 10 8 space The disk space usage in megabytes DOF Represents the number of degrees of freedom contained in the model These values were obtained from a 32 bit computer and therefore should be doubled for a 64 bit computer If you wish to calculate more than ten modes then multiply the space calculated 10 14 NX Nastran Basic Dynamic Analysis User s Guide Guidelines for Effective Dynamic Analysis above by 1 18 modes 10 1 For example for 30 modes you would multiply the space va
413. se in generating frequency dependent dynamic loads The form of each TABLEDi entry varies slightly depending on the value of i as does the algorithm for y x The x values need not be evenly spaced The TABLED1 TABLED2 and TABLED S entries linearly interpolate between the end points and linearly extrapolate outside of the endpoints as shown in Figure 5 4 The TABLED1 entry also performs logarithmic interpolation between points The TABLED4 entry assigns the endpoint values to any value beyond the endpoints 5 14 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis Linear Interpolation Between Endpoints Linear Extrapolation of Segment x x5 r Linear Extrapolation of Segment x Y lt Figure 5 4 Interpolation and Extrapolation for TABLED1 TABLED2 and TABLED3 Entries The TABLED entry has the following format Field Contents TID Table identification number XAXIS Specifies a linear or logarithmic interpolation for the x axis Character LINEAR or LOG default LINEAR YAXIS Specifies a linear or logarithmic interpolation for the y axis Character LINEAR or LOG default LINEAR Xl yl Tabular values Values of x are frequency in cycles per unit time ENDT Ends the table input The TABLED1 entry uses the algorithm y yrl Equation 5 23 The ae used for interpolation and extrapolation are as follows Y
414. sed for dynamic analysis Commands that apply to statics such as FORCE and STRESS are not listed The dynamic analysis Case Control commands are listed alphabetically The description of each command is similar to that found in the NX NASTRAN Quick Reference Guide The descriptions in this guide have been edited to apply specifically to the dynamic analysis capabilities described herein The NX NASTRAN Quick Reference Guide describes all of the Case Control commands The Case Control commands described in this appendix are summarized as follows Input Specification B2GG Direct Input Viscous Damping Matrix Selection K2GG Direct Input Stiffness Matrix Selection K42GG Direct Input Structural Damping Matrix Selection M2GG Direct Input Mass Matrix Selection NX Nastran Basic Dynamic Analysis User s Guide D 1 Appendix D Common Commands for Dynamic Analysis Analysis Specification BC DLOAD FREQUENCY IC METHOD SDAMPING SUPORT1 TSTEP Output Specification ACCELERATION DISPLACEMENT MODES OFREQUENCY OLOAD OTIME SACCELERATION SDISPLACEMENT SVECTOR SVELOCITY VELOCITY Boundary Condition Identification Dynamic Load Set Selection Frequency Set Selection Transient Initial Condition Set Selection Real Eigenvalue Extraction Method Selection Structural Damping Selection Fictitious Support Set Selection Transient Time Step Set Selection for Linear Analysis Acceleration Output Request Displacement Output Request Subcase
415. sequent partition Table C 1 Basic Partitioning Operations g set m set n set n set s set f set f set o set a set a set r set set In the above table the m s o and r sets form the mutually exclusive sets Physically the mutually exclusive set partitioning ensures that operations cannot be performed on DOFs that are no longer active For example if you apply an SPC to a DOF which is a dependent degree of freedom on an RBAR a FATAL error is issued Using an SPC entry moves a DOF to the s set but this cannot occur if the same DOF is already a member of the m set Both the m set and s set are mutually exclusive Table C 1 is a representation of all sets set partitions and set combinations used in NX Nastran A number of additional mutually independent sets of physical displacements namely q set c set b set and e set are used in dynamic analysis to supplement the sets used in static analysis The q c and b sets facilitate component mode synthesis The e set is used to represent control systems and other nonstructural physical variables The p set is created by combining the g set with the e set variables In addition to the combined sets described above the v set is a combined set created by combining the c r and o sets The DOFs in these sets are the DOFs free to vibrate during component mode synthesis Some additional sets sa k ps and pa sets represented in Figure C 1 are defined
416. ser Hans Jurgen Meyer Jurgen Finite Element Analysis of the Dynamic Behaviour of an Engine Block and Comparison with Experimental Modal Test Results The MSC 1990 World Users Conf Proc Vol I Paper No 14 March 1990 Paolozzi A Structural Dynamics Modification with MSC NASTRAN Proc of the 19th MSC European Users Conf Paper No 14 September 1992 Park H B Suh J K Cho H G Jung G S A Study on Idle Vibration Analysis Technique Using Total Vehicle Model MSC 1995 World Users Conf Proc Paper No 6 May 1995 Parker Grant R Rose Ted L Brown John J Kinetic Energy Calculation as an Aid to Instrumentation Location in Modal Testing The MSC 1990 World Users Conf Proc Vol II Paper No 47 March 1990 Preve A Meneguzzo M Merlo A Zimmer H Simulation of Vehicles Structural Noise Numerical Experimental Correlation in the Acoustic Simulation of the Internal Noise Proc of the 21st MSC European Users Conf Italian Session September 1994 NX Nastran Basic Dynamic Analysis User s Guide I 13 Appendix References and Bibliography Rabani Hadi Static and Dynamic FEM Test Correlation of an Automobile Body The 1989 MSC World Users Conf Proc Vol II Paper No 49 March 1989 Rainer I G MSC NASTRAN as a Key Tool to Satisfy Increasing Demand for Numerical Simulation Techniques Proc of the 20th MSC European Users Conf September 1993 Ray William F The Use of MSC NA
417. sis and shown in Figure 7 6 In this case the planar model is analyzed for bending therefore only three DOFs per grid point are considered T1 x translation T2 y translation and R3 z rotation An acceleration ramp function in the y direction is enforced at the base grid point 1 by applying a large mass and a force T1 and R3 are constrained at grid point 1 since the enforced motion is in only the T2 direction Modal transient response analysis SOL 112 is run with 5 critical damping used for all modes Modes up to 3000 Hz are computed with the Lanczos method Figure 7 7 shows the idealized ramp function and the NX Nastran implementation The excitation is not cut off abruptly instead it is cut off over two time steps A time step of 0 001 second is used and the analysis is run for 1 0 second Figure 7 8 shows the abridged input file Large Mass LOE9 kg Grid Point 1 Figure 7 6 Beam Model with Large Mass 7 14 NX Nastran Basic Dynamic Analysis User s Guide Enforced Motion 0 15 Idealized Input P e Y msec 0 Time sec 0 15 NX Nastran Input Y m sec Time sec 0 05 0 052 Figure 7 7 Idealized Ramp Function Versus NX Nastran Ramp Function FILE bd 7barl dat CANTILEVER BEAM MODEL CHAPTER 7 ENFORCED MOTION SOL 112 TIME 10 CEND TITLE CANTILEVER BEAM SUBTITLE MODAL TRANSIENT RESPONSE LABEL ENFORCED ACCELERATION 2 SPC 21 DLOAD 22 TSTEP 27
418. sis can be used to determine stability when control systems include damping and unsymmetrical matrices 11 12 Aeroelastic Analysis NX Nastran provides efficient solutions of the problems of aeroelasticity which is a branch of applied mechanics that deals with the interaction of aerodynamic inertial and structural forces It is important in the design of airplanes helicopters missiles suspension bridges tall chimneys and power lines Aeroservoelasticity is a variation in which the interaction of automatic controls requires additional consideration The primary concerns of aeroelasticity include flying qualities that is stability and control flutter and structural loads arising from maneuvers and atmospheric turbulence Methods of aeroelastic analysis differ according to the time dependence of the inertial and aerodynamic forces that are involved For the analysis of flying qualities and maneuvering loads wherein the 11 12 NX Nastran Basic Dynamic Analysis User s Guide Advanced Dynamic Analysis Capabilities aerodynamic loads vary relatively slowly quasi static methods are applicable The remaining problems are dynamic and the methods of analysis differ depending on whether the time dependence is arbitrary that is transient or random or simply oscillatory in the steady state NX Nastran considers two classes of problems in dynamic aeroelasticity aerodynamic flutter and dynamic aeroelastic response Aerodynamic Flutter Fl
419. sis of Plutonium Glovebox by MSC NASTRAN January 1993 Kubota Minoru Response Spectrum Analysis of Underground Tank Dome Roof Using Image Superelement Method The Fifth MSC NASTRAN User s Conf in Japan October 1987 in Japanese Moharir M M Shock Wave Propagation and NASTRAN Linear Algorithms MSC NASTRAN Users Conf Proc Paper No 7 March 1986 Overbye Vern D MSC NASTRAN Dynamic Analysis Modal or Direct MSC NASTRAN Users Conf Proc Paper No 6 March 1986 Parris R A Aspects of Seismic Analysis Using MSC NASTRAN Proc of the MSC NASTRAN Eur Users Conf Paper No 7 June 1983 Parthasarathy A CONSPEC A DMAP System for Conventional Response Spectrum Analysis in MSC NASTRAN MSC NASTRAN Users Conf Proc Paper No 8 March 1986 Petteno L Rossetto P Tecnomare Experiences in DMAP Processing Proc of the MSC NASTRAN Eur Users Conf May 1984 Rose Ted L Using Superelements for Response Spectrum and Other Handy Alters The 1989 MSC World Users Conf Proc Vol II Paper No 45 March 1989 Walker James W Evaluation of MSC NASTRAN Generalized Dynamic Reduction and Response Spectrum Analysis by Comparison with STARDYNE MSC NASTRAN Users Conf March 1978 DYNAMICS SEISMIC Bonaldi P Peano A Ruggeri G Venturuzzo M Seismic and Impact Analyses of Nuclear Island Buildings of Italian Unified Nuclear Design Proc of the 15th MSC NASTRAN Eur Users Conf October 1
420. size of the model the total number of degrees of freedom as well as the number of dynamic degrees of freedom the number of eigenvalues desired the available real memory of your computer and the conditioning of the mass matrix whether there are massless degrees of freedom In general the Lanczos method is the most reliable and efficient and is the recommended choice For small dense models whose matrices fit into memory we recommend using the automatic method automatic Householder The automatic Householder runs modified methods if the mass matrix is singular however it runs the unmodified methods which isfaster if the mass matrix is not singular The automatic Householder method runs faster on computers with vector processing and also supports parallel processing computers Note that most real world problems are not small and dense unless you use reductive methods such as superelements The Sturm modified inverse power method can be the best choice when the model is too large to fit into memory only a few modes are needed and a reasonable eigenvalue search range is specified This method is also a backup method for the other methods and is used when a check of the other methods results is needed For medium to large models the Lanczos method is the recommended method In addition to its reliability and efficiency the Lanczos method supports sparse matrix methods that substantially increase its speed and reduce disk space require
421. slational masses diagonal translational mass matrix Also the NX Nastran principal mass axes are not the axes of the inertia ellipsoid The S matrix is the transformation from the principal mass direction to the basic coordinate system This additional step may sound confusing but it is necessary In real structures the mass of structure is generally the same in all directions so there is no coupling between the translational mass terms Since text books are written to solve real structural problems there is no need to discuss the principal mass axes as they are called in NX Nastran However with NX Nastran you are not restricted to the same mass in each coordinate direction a situation that may not be physically realizable but still is quite useful for certain modeling situations Therefore the additional step of computing principal mass axes is necessary If your model has the same mass in all coordinate directions then the S matrix is the identity matrix indicating that the principal mass axes is the basic coordinate system Always check the S matrix If it is not the identity matrix verify that the mass distribution is correct Do not use the directional mass and center of gravity location blindly Remember these quantities are in the principal mass axes To fully understand how the GPWG module works it is useful to trace the steps NX Nastran follows to generate the output shown in Figure G 2 The following shows the step by st
422. ssure loads PLOAD4 entries Note that the LSEQ and TLOAD1 entries reference a common DAREA ID 999 and that there is no explicit DAREA entry Table 6 10 shows the relationship between the Case Control commands and the Bulk Data entries FILE bd06bkt dat S BRACKET MODEL CHAPTER 6 IRANSIENT RESPONSE SOL 112 MODAL TRANSIENT RESPONSE TIME 100 CEND TITLE BRACKET MODEL SUBTITLE MODAL TRANSIENT RESPONSE ANALYSIS SPC 1 S METHOD 777 DLOAD 2 LOADSET 3 SDAMPING 4 TSTEP 5 S OUTPUT REQUEST SET 123 999 DISPLACEMENT PLOT 123 NX Nastran Basic Dynamic Analysis User s Guide 6 37 Chapter 6 Transient Response Analysis S XYPLOTS Y plot commands lt a BEGIN BULK En rie idee Ge AC Pee Ud SN E wA io EP c E su dogs ee x a CRM S NORMAL MODES TO 3000 HZ SEIGRL SID V1 V2 EIGRL 777 0 1 3000 S 4 SECONDS OF RESPONSE STSTEP SID N1 DT1 NO1 TSTEP 5 800 0 005 1 S MODAL DAMPING OF 2 CRITICAL STABDMP1 TID TYPE S TABD1 F1 G1 F2 G2 ETC TABDMP1 4 CRIT TABD1 0 0 0 02 3000 0 0 02 ENDT S LOAD DEFINITION S STLOADI SID DAREA DELAY TYPE TID TLOAD1 2 999 22 SLSEQ SID DAREA LID TID LSEQ 3 999 1 S TIME HISTORY STABLED1 TID S TABL1 X1 Y1 X2 Y2 ETC TABLED1 22 TABL1 0 0 0 0 0 1 0 0 0 15 1 0 5 0 TABL2 ENDT S PRESSURE LOAD OF 3 PSI PER ELEMENT SPLOADA SID PLOAD4 1 PLOAD4 1 PLOAD4 1 etc EID P 171 O 172 x 160 3 basic model END
423. stic modulus of the cantilever beam is changed the natural frequencies change but the mode shapes remain the same If the boundary conditions change then the natural frequencies and mode shapes both change For example if the cantilever beam is changed so that it is pinned at both ends the natural frequencies and mode shapes change see Figure 3 2 Figure 3 1 The First Four Mode Shapes of a Cantilever Beam 3 2 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis fm x Figure 3 2 The First Four Mode Shapes of a Simply Supported Beam Computation of the natural frequencies and mode shapes is performed by solving an eigenvalue problem as described in Rigid Body Mode of a Simple Structure Next we solve for the eigenvalues natural frequencies and eigenvectors mode shapes Because damping is neglected in the analysis the eigenvalues are real numbers The inclusion of damping makes the eigenvalues complex numbers see Advanced Dynamic Analysis Capabilities The solution for undamped natural frequencies and mode shapes is called real eigenvalue analysis or normal modes analysis The remainder of this chapter describes the various eigensolution methods for computing natural frequencies and mode shapes and it concludes with several examples 3 2 Reasons to Compute Normal Modes There are many reasons to compute the natural frequencies and mode shapes of a structure One reason is to assess the dynami
424. stran Basic Dynamic Analysis User s Guide 8 11 Chapter 8 Restarts in Dynamic Analysis 8 12 TIME 10 CEND TITLE CANTILEVER BEAM NORMAL MODES RESTART RUN SPC 1 METHOD 10 DISP ALL BEGIN BULK S S DELETE OLD PBAR ENTRY LINE 26 OF SORTED BULK DATA COUNT 7 20 ADD NEW PBAR ENTRY UY Ur Uo dX BEBAR 1 15 0 19904 2 9 9 94 199 709 2414 ENDDATA Figure 8 4 Input File for Modifying a Bar Element S FILE bd08bar4 dat assign master bd08barl MASTER dbclean version 1 endjob Figure 8 5 Input File for Cleaning a Database Se FILE bd08bar5 dat THIS IS A TRANSIENT RESTART RUN FROM THE MODES S CALCULATED BY THE RUN bd08bar3 dat RESTART VERSION 3 KEEP ASSIGN MASTER bd08barl MASTER ID CANT BEAM SOL 112 TIME 10 CEND TITLE TRANSIENT RESTART UNIT STEP FUNCTION INPUT SUBTITLE REQUEST DISPLACEMENT TIME HISTORY AT GRID POINT 11 SPC 1 METHOD 10 SET 1 11 DISP 1 SUBCASE 1 SDAMP 100 TSTEP 100 DLOAD 100 S BEGIN BULK S ADDITIONAL ENTRIES FOR DYNAMIC LOADS FOR UNIT STEP FUNCTION SID DAREA DELAY TYPE TID TLOAD1 100 101 102 DAREA 101 11 3 1 0 TABLEDI lUZ apria uri EBD PTBIIS0 040505001 120510 0514 0 ENDT S TRANSIENT TIME STEPS SID N 1 DT 1 NO 1 TSTEP 100 600 001 5 S MODAL DAMPING TABLE TABDMP1 100 CRIT TDAMP TDAMP 0 01 200 01 ENDT S ENDDATA Figure 8 6 Input File for Transient Response NX Nastran Basic D
425. stresses Costly operations are proportional to the number of modes Since the number of modes is usually much less that the number of excitation frequencies the matrix method is usually more efficient and 1s the default The mode displacement method can be selected by using PARAM DDRMM 1 in the Bulk Data The mode displacement method is required when frequency frozen structural plots are requested see Plotted Output The mode acceleration method Advanced Dynamic Analysis Capabilities is another data recovery method for modal frequency response analysis This method can provide better accuracy since detailed local stresses and forces are subject to mode truncation and may not be as accurate as the results computed with the direct method 5 4 Modal Versus Direct Frequency Response Some general guidelines can be used when selecting modal frequency response analysis versus direct frequency response analysis These guidelines are summarized in Table 5 2 5 10 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis Table 5 2 Modal Versus Direct Frequency Response mall Model Large Model F Mom Diet LX O X eee Few Excitation Frequencies OX Many Excitation Frequencies xo X Higher Accuracy X Nonmodal Damping In general larger models may be solved more efficiently in modal frequency response because the numerical solution is a solution of a smaller syste
426. sults should be close to the static results any difference is due to mode truncation If the 0 0 Hz results do not match the static results check the LSEQ and DAREA entries Also use OLOAD to print the applied force in order to compare the loads 10 11 Transient Response Analysis Several factors are important in computing accurate transient response These factors include the number of retained modes for modal transient response the integration time step At the time duration of the computed response and damping The guidelines are only approximate but are nevertheless useful Running a normal modes analysis first helps to compute transient response Number of Retained Modes In modal transient response analysis a larger number of modes produces a more accurate response although at the expense of increased run times The number of modes must be large enough to cover the frequency range of interest The term range of interest means the range of frequencies whose response is to be computed as well as the range of frequencies for which the loading is applied As a general rule there should be enough modes to cover a range up to about two times the highest frequency of interest For example if response needs to be computed to 100 Hz then enough modes should be used in the transient response to cover up to at least 200 Hz As another general rule you should use enough modes to cover a range up to two to ten times the dominant frequency
427. t S PLOT COMMANDS FOR BAR MODAL FREQUENCY RESPONSE REAL IMAGINARY Executive Case Control S OUTPUT REQUESTS S REAL IMAGINARY DISPLACEMENT PLOT ALL S 9 STRUCTURE PLOTS OUTPUT PLOT S DEFINE ELEMENTS IN PLOT SET CSCALE 1 8 SET 333 ALL PLOT AXES R Z S X T Y AXES MZ X Y VIEW 0 0 0 FIND SCALE ORIGIN 5 SET 333 S PLOT UNDEFORMED SHAPE PLOT SET 399 ORIGIN 5 S PLOT DEFORMED SHAPE REAL PLOT FREQ DEFORM 0 RANGE 2 05 2 051 SET 333 PLOT DEFORMED SHAPE IMAGINARY PLOT FREQ DEFORM 0 RANGE 2 05 2 051 PHASE LAG 90 BEGIN BULK REQUIRED FOR FREQUENCY FROZEN PARAM DDRMM 1 PARAM CURVPLOT 1 STRUCTURE PLOTS rest of Bulk Data ENDDATA SET 01925 Figure 9 5 Frequency Response Structure Plot Commands for the Bar Model Real Imaginary Undeformed Shape Max Def 0 185 Frequency 2 05 Phase 0 Max Def 0 348 Frequency 2 05 Phase 90 00 Figure 9 6 Frequency Response Structure Plots for the Bar Model Real Imaginary NX Nastran Basic Dynamic Analysis User s Guide 9 5 Chapter 9 Plotted Output Figure 9 7 shows the structure plotting commands applied to a modal transient response analysis of the cantilever beam model PARAM DDRMM 1 is required in the Bulk Data in order to create structure plots at various times and or frequencies Note that PARAM DDRMM 1 generally increases the amount of computer time and is not recommended unless ot
428. t Some vectors must be present to perform this reduction For the system solution an exit 1s taken 1f eigenvalues are requested but not eigenvectors Reset the range of frequency and or the number desired on the EIGR or EIGRL entry If the superelement does not have any eigenvalues in the range of interest remove the CMS request for that particular superelement This message is also issued when the eigenvectors calculated with a transformation method do not pass internal orthogonality checks This 1s indicative of a modeling error This message can also be issued if insufficient memory is available for the Lanczos method with sparse decomposition This could occur with UFM 5401 and be related to UWM 5411 UFM 4407 USER FATAL MESSAGE 4407 MR MATRIX HAS NULL DIAGONAL TERM The MR matrix contains the rigid body mass matrix of the structure as measured at the degrees of freedom listed on the SUPORT entry If any of these degrees of freedom have null mass they result in invalid eigenvectors Specify enough masses to define all rigid body modes and check attachments between the SUPORT and the rest of the model UIM 4415 USER INFORMATION MESSAGE 4415 THE FOLLOWING A SET DEGREES OF FREEDOM HAVE EITHER NULL MASSES OR NULL MASSES AND STIFFNESSES If the listed degrees of freedom have null mass for the HOU or MHOU methods they are automatically omitted For direct frequency or direct transient response the null degrees of fre
429. t of a mechanism and that elements do not have excessive stiffness In SOLs 100 and higher this condition causes run termination PARAM BAILOUT may be used to continue the run See the NX Nastran Numerical Methods User s Guide USER FATAL MESSAGE 4421 NO FREQUENCY RESPONSE LIST AVAILABLE A frequency response dynamic analysis was requested but no frequency data is available Include frequency data FREQ FREQ1 FREQ2 in the Bulk Data USER FATAL MESSAGE 4501 RLOADi CARD SELECTED IN TRANSIENT ANALYSIS USE TLOADi RLOADji entries are used in frequency response analysis These entries have no meaning in transient analysis Replace RLOADi with TLOADo entries USER WARNING MESSAGE 4561 INSUFFICIENT MEMORY FOR MODE ORTHOGONALITY CHECKS The amount of memory needed for eigenvector orthogonalization is 1 2 number of eigenvectors number of eigenvectors 1 2 BUFFSIZE number of eigenvalues If this equation is not met the modes are orthogonalized but the checking function is not performed However all outputs from the module are provided If the check is desired you should either increase memory or decrease the number of eigenvectors to satisfy the above equation USER FATAL MESSAGE 4562 TSTEP TIME STEPS DATA IS MISSING Transient analysis requires the time step data Add a TSTEP Bulk Data entry and select it with a TSTEP Case Control command USER WARNING MESSAGE 4582 LSEQ CARD SID RE
430. tanks NX Nastran Basic Dynamic Analysis User s Guide 11 5 Chapter 11 Advanced Dynamic Analysis Capabilities Virtual Fluid Mass Small motions of incompressible fluids may be coupled directly to the structure with this option Fluids may be coupled to the interior and exterior surfaces with infinite fluid boundaries There is no explicit fluid model only the wetted structural elements ELIST have to be defined Although free surfaces are allowed no gravity effects are included directly Since the fluid is represented by a coupled mass matrix attached directly to the structural points this capability is allowed in all dynamic solution sequences This capability may be used to model a wide variety of fluid structure interaction problems Some examples are fuel tanks nuclear fluid containers drilling platforms and underwater devices Coupled Acoustics You may analyze the dynamics of compressible fluids contained within arbitrarily shaped structures with the coupled fluid structure method You would model a three dimensional fluid with conventional solid elements CHEXA etc using acoustic property and material data Each grid point in the fluid defines the pressure at its location as its degree of freedom The fluid is automatically connected to the structure via the geometry and ACMODL Bulk Data inputs You can connect acoustic absorber elements CHACAB to the structural surfaces to simulate soundproofing material In addition the CAA
431. te to its deformed position Capturing this behavior requires the iterative update techniques of nonlinear analysis ne ae eg i oi a at lt atta utut Figure 11 2 Follower Forces on a Cantilever Beam Material Nonlinearity Material nonlinear analysis can be used to analyze problems where the stress strain relationship of the material is nonlinear In addition moderately large strain values can be analyzed Examples of material nonlinearities include metal plasticity materials such as soils and concrete and rubbery materials where the stress strain relationship is nonlinear elastic Various yield criteria such as von Mises or Tresca for metals and Mohr Coulomb or Drucker Prager for frictional materials such as soils or concrete can be selected Three hardening rules are available in NX Nastran isotropic hardening kinematic hardening or combined isotropic and kinematic hardening With such generality most plastic material behavior with or without the Bauschinger effect can be modeled In addition gaps can be used to model the effects due to structural separation Contact Contact occurs when two or more structures or portions of structures collide Contact can be modeled as point to point contact CGAP or as contact along a line BLSEG Nonlinear Elastic Transient Response Analysis There are numerous structures that contain nonlinear elastic elements These elements possess nonlinear force deflection relationships yet
432. te a rigid body mass matrix M k D Maal F F M Iv Maal Wri Equation 4 6 NX Nastran Basic Dynamic Analysis User s Guide 4 5 Chapter 4 Rigid Body Modes To improve the quality of the rigid body mode shapes orthogonalization is applied to create a diagonal mass matrix M by M 6 M 0 Equation 4 7 where f is a transformation matrix This transformation matrix is used to construct the final set of rigid body mode shape vectors by DO Oriol LW io ILO b Equation 4 8 such that T LO 50 A aal lOni 0 Equation 4 9 I i Orig IM MOI Mo Equation 4 10 where Mo Care must be taken when selecting SUPORT DOFs Each SUPORT DOF must be able to displace independently without developing internal stresses In other words the SUPORT DOFs must be statically determinate The SUPORT is used only to facilitate the calculation of rigid body vectors If you do not specify the r set DOFs the rigid body modes are calculated directly by the method selected for the flexible frequency modes If an insufficient number of r set DOFs are specified the calculation of rigid body modes is unreliable is a diagonal matrix As a modeling aid NX Nastran calculates equivalent internal strain energy work for each rigid body vector as follows 4 6 NX Nastran Basic Dynamic Analysis User s Guide Rigid Body Modes Ki K D X D r K i Es L Equation 4 11 which can
433. tead of a large mass In that case the applied load is NX Nastran Basic Dynamic Analysis User s Guide 7 3 Chapter 7 Enforced Motion p Ku Equation 7 6 where k is the stiffness of the stiff spring and u is the enforced displacement The large stiffness method certainly works but the large mass method is preferred because it is easier to estimate a good value for the large mass than to estimate a good value for the stiff spring In addition and more importantly the large mass method 1s far superior when modal methods are used If very stiff springs are used for modal analysis rather than very large masses the vibration modes corresponding to the very stiff springs have very high frequencies and in all likelihood are not included among the modes used in the response analysis This is the main reason that large masses should be used instead of stiff springs The stiff spring method is advantageous in the case of enforced displacement because it avoids the roundoff error that occurs while differentiating the displacement to obtain acceleration in the large mass method The stiff spring method also avoids the problem of rigid body drift when applying enforced motion on statically determinate support points Rigid body drift means that the displacement increases continuously with time which is often caused by the accumulation of small numerical errors when integrating the equations of motion 7 3 The Large Mass Method in Modal Transient a
434. tember 1993 Wang B P Caldwell S P Smith C M Improved Eigensolution Reanalysis Procedures in Structural Dynamics The MSC 1990 World Users Conf Proc Vol II Paper No 46 March 1990 Wang B P Chang Y K Lawrence K L Chen T Y Optimum Design of Structures with Multiple Configurations with Frequency and Displacement Constraints 31st AIAA ASME ASCE AHS ASC Structures Structural Dynamics and Materials Conf Part 1 pp 378 384 April 1990 Wang B P Caldwell S P Reducing Truncation Error in Structural Dynamic Modification The MSC 1991 World Users Conf Proc Vol I Paper No 11 March 1991 Wang B P Caldwell S P Improved Approximate Method for Computting Eigenvector Derivatives Finite Elements in Analysis and Design v 14 n 4 Nov 1993 Watanabe Masaaki Computation of Virtual Mass to Rigid Body Structure by MSC NASTRAN The First MSC NASTRAN User s Conf in Japan October 1983 in Japanese Wijker J J Differential Stiffness in Conjunction with Dynamics NASTRAN User s Conf June 1981 Wijker J J Acoustic Effects on the Dynamic Behaviour of Lightweight Structures Proc of the MSC NASTRAN Eur Users Conf Paper No 3 April 1985 Wilhelmy Dr Viktor Dynamic Analysis with Gaps The 1989 MSC World Users Conf Proc Vol II Paper No 40 March 1989 Woytowitz P J Jiang K C Bhat K P Dynamic Analysis of Optical Beam Pointing The MSC 1988 World Users Conf Proc
435. thesis Methods for Space Vehicle Dynamic Analysis NASTRAN User s Conf May 1979 Everstine Gordon C Marcus Melvyn S Finite Element Prediction of Loss Factors for Structures with Frequency Dependent Damping Treatments Thirteenth NASTRAN Users Colloq pp 419 430 May 1985 NASA CP 2373 Gibson W C Johnson C D Optimization Methods for Design of Viscoelastic Damping Treatments ASME Design Engineering Division Publication Vol 5 pp 279 286 September 1987 Gibson Warren C Austin Eric Analysis and Design of Damped Structures Using MSC NASTRAN The MSC 1992 World Users Conf Proc Vol I Paper No 25 May 1992 Johnson Conor D Keinholz David A Prediction of Damping in Structures with Viscoelastic Materials Using MSC NASTRAN MSC NASTRAN Users Conf Proc Paper No 17 March 1983 Kalinowski A J Modeling Structural Damping for Solids Having Distinct Shear and Dilational Loss Factors Seventh NASTRAN Users Colloq pp 193 206 October 1978 NASA CP 2062 NX Nastran Basic Dynamic Analysis User s Guide l 17 Appendix References and Bibliography Kalinowski A J Solution Sensitivity and Accuracy Study of NASTRAN for Large Dynamic Problems Involving Structural Damping Ninth NASTRAN Users Colloq pp 49 62 October 1980 NASA CP 2151 Kienholz Dave K Johnson Conor D Parekh Jatin C Design Methods for Viscoelastically Damped Sandwich Plates AIAA ASME ASCE AHS 24th Structure
436. they are elastic since they load and unload along the same force deflection curve Examples of the nonlinear elastic force deflection curves are shown in Figure 11 3 These types of elements are common in many mechanical and structural systems including piping systems supported by nonlinear springs chains stiffness in tension only or constant force devices base mounted equipment and structure supported by nonlinear shock isolation systems structures with gaps piping systems and buildings and soil or NX Nastran Basic Dynamic Analysis User s Guide 11 7 Chapter 11 Advanced Dynamic Analysis Capabilities concrete structures which only exhibit stiffness when in compression Other systems exhibit nonlinearities that are proportional to the velocity such as seat belts and piping supports Force Jispla emer isplacement a Bilinear Spring b Preload Constant Force Device with Hard Stop Displacement Displacement 3 Force c Gap and Spring in d Stiffness in Compression Series Only Force D ispla cement Di splacement lanl e Softening D Hardening SVstem stem Figure 11 3 Examples of Nonlinear Elastic Systems There are several methods in NX Nastran for solving nonlinear elastic problems A general nonlinear solution scheme can be used in which the material properties are specified as nonlinear elastic NLELAST on the MATS1 entry Nonlinear element stiffness matrices are generated
437. time steps are to be output The TSTEP Bulk Data entry is selected by the Set ID referenced on the TSTEP Case Control command The integration time step must be small enough to represent accurately the variation in the loading The integration time step must also be small enough to represent the maximum frequency of interest The maximum frequency of interest is often called the cutoff frequency It is recommended to use at least ten solution time steps per period of response for the cutoff frequency For a given integration time step integration errors increase with increasing natural frequency because there is an upper limit to the frequency that can be represented by a given time step Also integration errors accumulate with total time In both direct and modal transient analysis the cost of integration is directly proportional to the number of time steps For example doubling the load duration doubles the integration effort In specifying the duration of the analysis on the TSTEP entry it is important to use an adequate length of time to properly capture long period low frequency response In many cases the peak dynamic response does not occur at the peak value of load nor necessarily during the duration of the loading function A good rule is always solve for at least one cycle of response for the lowest frequency mode after the peak excitation You may change At during a run but doing so causes the dynamic matrix to be redecomposed
438. ting Mode Shapes Based on Modal Assurance Criterion The MSC 1992 World Users Conf Proc Vol I Paper No 21 May 1992 Tokuda Naoaki Mitikami Shinsuke Sakata Yoshiuki Accuracy of Vibration Analysis for Thin Cylindrical Shell by MSC NASTRAN MSC NASTRAN Users Conf Proc Paper No 28 March 1984 Vaillette David Evaluation of the Modal Response of a Pressure Vessel Filled with a Fluid The MSC 1991 World Users Conf Proc Vol I Paper No 24 March 1991 Vance Judy M Bernard James E Approximating Eigenvectors and Eigenvalues Across a Wide Range of Design Finite Elements in Analysis and Design v 14 n 4 Nov 1993 Vandepitte D Wijker J J Appel S Spiele H Normal Modes Analysis of Large Models and Applications to Ariane 5 Engine Frame Proc of the 18th MSC Eur Users Conf Paper No 6 June 1991 Wamsler M Komzsik L Rose T Combination of Quasi Static and Dynamic System Mode Shapes Proc of the 19th MSC European Users Conf Paper No 13 September 1992 Wang B P Cheu T C Chen T Y Optimal Design of Compressor Blades with Multiple Natural Frequency Constraints ASME Design Engineering Division Publication Vol 5 pp 113 117 September 1987 Wang B P Lu C M Yang R J Topology Optimization Using MSC NASTRAN MSC 1994 World Users Conf Proc Paper No 12 June 1994 NX Nastran Basic Dynamic Analysis User s Guide l 27 Appendix References and Bibliography W
439. ting the Effect of Multiple Cross Correlated Excitations on the Response of Linear Systems to Gaussian Random Excitations The MSC 1988 World Users Conf Proc Vol I Paper No 18 March 1988 l 28 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Palmieri F W A Method for Predicting the Output Cross Power Spectral Density Between Selected Variables in Response to Arbitrary Random Excitations The MSC 1988 World Users Conf Proc Vol I Paper No 19 March 1988 Parthasarathy Alwar Elzeki Mohamed Abramovici Vivianne PSDTOOL A DMAP Enhancement to Harmonic Random Response Analysis in MSC NASTRAN The MSC 1993 World Users Conf Proc Paper No 36 May 1998 Robinson J H Chiang C K Rizzi S A Nonlinear Random Response Prediction Using MSC NASTRAN National Aeronautics and Space Administration Hampton VA Langley Research Center October 1993 Robinson Jay H Chiang C K An Equivalent Linearization Solution Sequence for MSC NASTRAN The MSC 1993 World Users Conf Proc Paper No 35 May 1993 Schwab H L Caffrey J Lin J Fatigue Analysis Using Random Vibration MSC 1995 World Users Conf Proc Paper No 17 May 1995 Shieh Niahn Chung Investigation of Swept Sine on Random Load The 4th MSC Taiwan Users Conf Paper No 18 November 1992 in Chinese Zins J Random Vibration and Acoustic Analysis Using ARI RANDOM a NASTRAN Postprocessor Proc of the MSC NAS
440. tion 3 20 Since the matrices are symmetric only the lower or upper triangular portion of the matrices need to be provided via the DMIG entries The corresponding input file is shown in Figure 3 33 3 40 FILE bd03dmi dat DMIG EXAMPLE CHAPTER 3 NORMAL MODES 2 SOL 103 NORMAL MODES ANALYSIS TIME 10 CEND TITLE DMIG TO READ STIFFNESS AND MASS FOR ELEM 5 SUBTITLE PLANAR PROBLEM SPC 10 SPECIFY K2GG AND M2GG K2GG EXSTIF M2GG EXMASS S METHOD 10 BEGIN BULK S SEIGRL SID V1 V2 ND EIGRL 10 2 S CBAR 1 1 1 2 10 CBAR 2 1 2 3 10 CBAR 3 1 3 4 10 CBAR 4145 10 HEADER ENTRY FOR STIFFNESS DMIG EXSTIF 06 1 S DMIG EXSTIF 5 3 5 3 500099 000001 0000015 5 250019 6 3 500039 4000002 0000026 5 250019 000003 2 DMIG EXSTIF 5 5 5 5 166680 4000004 0000046 3 250019 6 5 83340 000005 S NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis DMIG EXOTLE 6 3 6 3 500039 4000006 0000066 5 250019 000007 S DMIG EXSTIF 6 5 6 5 166680 HEADER ENTRY FOR MASS DMIG EXMASS 0 6 1 S DATA ENTRIES FOR MASS 2 DMIG EXMASS 5 3 5 3 3 5829 DMIG EXMASS 6 3 6 3 3 5829 S GRID 1 0 0 0 1249 GRID 2 1 0 0 1246 GRID 3 2 0 0 1246 GRID 4 3 0 0 1246 GRID 5 4 0 0 1246 GRID 6 5 0 0 4 0s Oe I246 GRID 10 0 0 10 123456 MATI 1 7 1 10 33 2700 PBAR 1 1 2 654 3 5 869 7 SPC1 10 123456 1 ENDDATA Figure 3 33 Input F
441. tion 7 11 For constant displacement u W it may be easiest to use the TABLED4 entry because the frequency dependent term 2nf can be specified directly NX Nastran Basic Dynamic Analysis User s Guide 7 7 Chapter 7 Enforced Motion Transient Response For transient response the type of enforced motion displacement velocity or acceleration is specified with the TYPE field field 5 on the TLOAD1 and TLOAD2 Bulk Data entries TLOAD1 Format oa 2 83 4 5 e ee s w TLOAD2 Format d BE j d T d 1 1 1 TYPE 0 or blank applied force default TYPE 1 enforced displacement TYPE 2 enforced velocity TYPE 3 enforced acceleration NX Nastran converts enforced displacements and velocities into accelerations by differentiating once for velocity and twice for displacement Note that for enforced acceleration you can specify either force TYPE 0 or blank or acceleration TYPE 3 they are the same for the large mass method You still need to use the large mass when specifying any type of enforced motion in transient response analysis 7 5 Examples This section provides several examples showing the input and output These examples are Analysis Type Enforced Motion dO7two Frequency Response Constant Acceleration dO 7bari Transient Response Ramp Acceleration bdO7bar2 Transient Response Ramp Displacement Ramp Displacement Discard Transient Response Rigid Body Mode These examples are
442. tor N denotes the nonlinear forces which are added to the right hand side of Equation 11 2 and hence are treated as additional applied loads The nonlinear forces are evaluated at the end of one time step for use in the successive time step The equations of motion therefore become the following M t c C altr I amp tu t iPr E 1NGO AD Equation 11 3 Note that the nonlinear force lags the true solution by a time step which may require using small integration time steps 1 e smaller than those required for a purely linear analysis Equation 11 3 can be solved in physical or modal coordinates the nonlinearity itself must be expressed in terms of physical coordinates A nonlinear force can be used in conjunction with a linear elastic element to produce the desired force deflection curve as illustrated 1n Figure 11 4 The nonlinear dynamic force 1s formulated using a NOLINi entry and a TABLEDi entry which contains a force versus deflection table describing the nonlinear force For desired force deflection curves more complicated than the bilinear stiffness shown in the figure the nonlinear force 1s made correspondingly more complex Force Force i Displacement Displacement Displacement Nonlinear _ Elastic Nonlinear Element Element Force Figure 11 4 Formulation of a Nonlinear Element Nonlinear Normal Modes Analysis There are times when normal modes need to be calculated for a nonlinear
443. ts between the translational mass terms MO is partitioned into four 3x3 matrices as shown in Equation G 12 G 10 NX Nastran Basic Dynamic Analysis User s Guide Grid Point Weight Generator f ir M M M0 A rt r M M Equation G 12 where the superscripts and r refer to translation and rotation respectively For this example the translational mass partition 1s given by B 9 25 933 0 M 933 1075 0 0 0 20 Equation G 13 A check is made for coupling as follows int 0 Mij i j f 2 JY Oli i Equation G 14 If c dis greater than 001 then excessive coupling exists preventing the basic coordinate system from being used for the principal mass directions and User Warning Message 3042 is 5 925 10752 20 9333 02 02 printed For this problem 9 25 10 75 and 7 355 0 0 l The ratio c d 038 agrees with the System Warning Message 3042 shown in Figure G 2 If needed the principal mass directions are computed by performing an eigensolution with t M the translational mass components The eigenvectors of are the columns of the transformation matrix S 5 te4r 1e 5 1631 Equation G 15 Using this eigenvector matrix the partitions of the rigid body mass matrix with respect to the principal mass direction are computed by Equation G 16 NX Nastran Basic Dynamic Analysis User s Guide G 11 Appendix G Grid Point Weight Generator M
444. tural mass so that the oscillator does not influence the dynamic behavior of the base structure Once a spectrum is computed it can be used for the dynamic response analysis of an NX Nastran model of the component For example the spectrum generated for a floor in a building that is subjected to an earthquake can then be applied to a complex model of a piece of equipment attached to that floor The peak response of each mode of the equipment model is obtained from the spectrum and these peak modal responses are combined to create the overall response Because the peak responses do not all occur at the same time and only the magnitude of peak responses are computed various methods are used to combine the peak responses into the overall response The combination methods implemented in NX Nastran are SRSS square root of the sum of the squares ABS absolute values and NRL U S Navy shock design modal summation The typical response quantities computed are grid point displacements and element stresses 11 4 NX Nastran Basic Dynamic Analysis User s Guide Advanced Dynamic Analysis Capabilities 11 5 Random Vibration Analysis Random vibration is vibration that can be described only in a statistical sense The instantaneous magnitude is not known at any given time rather the magnitude is expressed in terms of its statistical properties such as mean value standard deviation and probability of exceeding a certain value Examples of rand
445. uch as these in conjunction with element strain energies help to illustrate each of the mode shapes Figure 3 25 Mode Shapes for Modes 7 8 9 and 10 Test Fixture Model This example is an aluminum test fixture which is shown in Figure 3 26 The model is comprised of 8157 grid points 5070 CHEXA elements and 122 CPENTA elements The primary plates are 1 inch thick and the gusset plates are 0 5 inch thick The base of the fixture is constrained to have no vertical y motion and the bolt holes at the base are constrained to also have no horizontal x and z motion 3 34 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis i Tid tp Pe ae Td LCL AT EG a SA on a EEEE pU ee ee es ee et ee e ar i REOR RR c e M L Betapace ee eras Y SS eS SN 3 yc mute ER mom m noe mI Re CR RR g S ore ay ey eB on chm th Jmm me m um E Lien aur perp ramen Eep g i l iwl Cn E T a Eume Sp me e e a a oa aa i m e e e Ue ce eee 1 EUER I SS LE E x eet oo XL Di er e a A eee ia CET III LACK REL neut it ua D d 2 p 4 x d M cd d ee DE TE E T s TEI Om OER eee Figure 3 26 Test Fixture Model FILE bd03fix dat TEST FIXTURE CHAPTER 3 S Data entry removes the rotational DOFs 456 from the analysis since the solid elements have no A portion of the input file is shown in Figure 3 27 The Lanczos method is used to compute the rotational sti
446. uest additional output Partial output is shown at the bottom of Figure 8 11 Note that the maximum displacement at grid point 11 is the same as in run number 5 as expected since you are asking for data recovery on the same point due to the same loading condition bd08bar5 dat This is a transient restart run from the modes saved in Version 3 The applied load is a unit step function The modes calculated in run number 3 are also saved at the end of this run Since the calculation of the modes is the most expensive 112 operatio mina l 4 None dynamic analysis it is probably a good idea to save Version 3 once you have confidence in the results This way you can always restart from this version Partial output is shown at the top of Figure 8 11 A 1 critical damping value is applied to the structure This is another 4 transient restart run NX Nastran Basic Dynamic Analysis User s Guide 8 9 Chapter 8 Restarts in Dynamic Analysis Table 8 3 Typical Series of Restart Runs Run Sequence Name of Input File Number bdO8bar7 dat Solution Sequence Description of Number Runs Version Created Version Deleted This is another restart run from Version 6 with a different load condition triangular pulse Partial output is shown in Figure 8 12 In this case you can just as easily restart from Version 3 This is a database directory printout run As shown in Figure 8 14 there are seven versio
447. uide for detailed descriptions and the defaults for these keywords filenamef This 1s the physical name of the FORTRAN file STATUS Specifies whether the FORTRAN file will be created STATUS new or is an existing file STATUS old UNIT Specifies the FORTRAN unit e g UNIT 12 FORM Specifies whether the file written is in ASCII FORM FORMATTED or binary FORM UNFORMATTED format DELETE Requests that filenamef be deleted if it exists before the start of the run Example ASSIGN OUTPUT2 sample out STATUS NEW UNIT 11 FORM FORMATTED DELETE This example creates a new FORTRAN file to be used for OUTPUT2 operations This file is in ASCII format with a physical filename of sample out and is assigned to unit 11 EXPAND Purpose Concatenates files into an existing DBset in order to increase the allowable disk space The EXPAND statement is normally used in a restart run when you run out of disk space in your previous run Format EXPAND DBset name LOGICAL log namei max sizei Logical name of the DBset to be expanded by the addition of new members to this existing DBset Logical name of the i th member of the DBset An ASSIGN statement should DBset name log namei be used to point this logical name to a physical file E Maximum allowable number of NX Nastran blocks that may be written to max sizei the i th member Example The original run creates a database with a name dyn1 DBALL This database
448. uidelines described earlier the other primary factor in eigenvalue analysis is the proper selection of the eigenvalue solution method The Lanczos method is the best overall method and is the recommended method to use The automatic Householder method is useful for small dense matrices The SINV method is useful when only a few modes are required The other methods should be regarded as backup methods Carefully examine the computed frequencies and mode shapes Viewing only one or the other is usually not enough to verify accuracy of your model Modes with 0 0 Hz or computational zero frequencies indicate rigid body or mechanism modes If these modes are unintended then there is a mistake in boundary conditions or connectivity The existence and cause of unintended zero frequency modes can also be ascertained from the mode shapes In addition mode shape plots are useful for assessing local modes in which a group of one or a few grid points displaces and the rest of the structure does not Local modes may also be unintended and are often the result of incorrect connectivity or element properties 10 10 Frequency Response Analysis Several factors are important for computing accurate frequency response results These factors include the number of retained modes for modal frequency response analysis the frequency NX Nastran Basic Dynamic Analysis User s Guide 10 9 Chapter 10 Guidelines for Effective Dynamic Analysis increment Af and da
449. uire positive definite mass matrices Inserting inertia data into the wrong fields can result in nonpositive definite systems which are not physically realistic for normal modeling practices Reduce the size of the off diagonal terms to provide a positive definite determinant USER FATAL MESSAGE 4346 FREQUENCY RESPONSE SET ID TS UNDEFINED Define the set of frequencies to be used for the analysis USER FATAL MESSAGE 4391 NONUNIQUE DAREA SET HAS BEEN SPECIFIED FOR LSEQ DEFINED VECTOR Each LSEQ Bulk Data entry must define a unique DAREA set specification USER FATAL MESSAGE 4392 CONTINUATION CARD ERRORS EXPLANATIONS FOLLOW LIST OF CARDS IN ERROR ERROR NUMBER 1 2 83 Input echo EXPLANATION OF ERROR CODES ABOVE FOLLOWS 1 FIELD 1 IS NOT UNIQUE 2 MORE THAN ONE CARD HAS FIELD 10 WHICH IS THE SAME AS FIELD 1 OF THIS CARD 3 CARD IS AN ORPHAN I E NO PARENT CARD EXISTS NX Nastran Basic Dynamic Analysis User s Guide H 5 Appendix H Diagnostic Messages for Dynamic Analysis Continuation mnemonics in field 10 of a parent entry and field 1 of its continuation entry must be unique Each continuation entry must have a parent entry Check all continuation mnemonics UFM 4405 USER FATAL MESSAGE 4405 NO EIGENVECTORS COMPUTED FOR COMPONENT MODE SYNTHESIS OR SYSTEM SOLUTION The eigenvectors computed in component mode synthesis CMS are used to approximate the motion of the componen
450. uld examine the eigenvalue analysis summary output to determine whether NX Nastran has sufficient memory to use an efficient block size A smaller block size may be more efficient when only a few roots are requested The minimum recommended block size 1s 2 The SHFSCL field allows a user designated shift to be used to improve performance especially when large mass techniques are used in enforced motion analysis see Enforced Motion Large mass techniques can cause a large gap between the rigid body see Rigid body Modes 3 14 NX Nastran Basic Dynamic Analysis User s Guide Real Eigenvalue Analysis and flexible frequencies which can degrade performance of the Lanczos method or cause System Fatal Message 5299 When SHFSCL is used its value should be set close to the expected first nonzero natural frequency The Lanczos method normalizes i e scales the computed eigenvectors using the MASS or MAX method These methods are specified using the NORM field new for Version 68 The MASS method normalizes to a unit value of the generalized mass 1 e m 1 0 The MAX method normalizes to a unit value of the largest component in the a set see Advanced Dynamic Analysis Capabilities The default is MASS You can use the continuation entry to specify V1 V2 ND MSGLVL MAXSET SHFSCL and NORM if you have not specified them on the parent entry To apply the continuation entry use the following format option i value 1 e g ND
451. ultiplied by the element volume determined from the geometry and physical properties For a MATI entry a mass density for steel of 7 76E 4 IbesecZ in is entered as follows Ta Ds ps 3I I D I L I o Grid point masses can be entered using the CONM1 CONM2 and CMASSi entries The CONMI entry allows input of a fully coupled 6x6 mass matrix You define half of the terms and symmetry is assumed The CONM2 entry defines mass and mass moments of inertia for a rigid body The CMASSi entries define scalar masses Nonstructural Mass An additional way to input mass is to use nonstructural mass which is mass not associated with the geometric cross sectional properties of an element Examples of nonstructural mass are insulation roofing material and special coating materials Nonstructural mass is input as mass length for line elements and mass area for elements with two dimensional geometry Nonstructural mass is defined on the element property entry PBAR for example 2 3 Damping Input Damping is a mathematical approximation used to represent the energy dissipation observed in structures Damping is difficult to model accurately since it is caused by many mechanisms including e Viscous effects dashpot shock absorber e External friction slippage in structural joints e Internal friction characteristic of the material type e Structural nonlinearities plasticity gaps 2 8 NX Nastran Basic Dynamic Analysis User s Guide
452. uneo Ship Vibration Analysis Using Modal Synthesis Technique MSC NASTRAN Users Conf Proc Paper No 23 March 1984 Nasu Syouichi Modal Synthesis of Experimental Vibration Characteristics Using MSC NASTRAN Results as the Reference Model The Sixth MSC NASTRAN User s Conf in Japan October 1988 in Japanese Nefske D J Sung S H Duncan A E Applications of Finite Element Methods to Vehicle Interior Acoustic Design Proc of the 1984 Noise and Vibration Conf Paper No 8407743 1984 Ookuma Masaaki Nagamatsu Akio Comparison of Component Mode Synthesis Method with MSC NASTRAN Nippon Kikai Gakkai Ronbunshu C Hen Vol 49 No 446 pp 1883 1889 October 1983 in Japanese Ookuma Masaaki Nagamatsu Akio Comparison of Component Mode Synthesis Method with MSC NASTRAN Bulletin of the JSME Vol 27 No 228 pp 1294 1298 June 1984 I 16 NX Nastran Basic Dynamic Analysis User s Guide References and Bibliography Parekh Jatin C Harris Steve G The Application of the Ritz Procedure to Damping Prediction Using a Modal Strain Energy Approach Damping 89 Paper No CCB November 1989 Philippopoulos V G Dynamic Analysis of an Engine Transmission Assembly Superelement and Component Mode Synthesis Proc of the Conf on Finite Element Methods and Technology Paper No 3 March 1981 Reyer H Modal Synthesis with External Superelements in MSC NASTRAN Proc of the MSC NASTRAN Eur Users Conf May 1984
453. unl USROBJ runlUSRSOU The last two files are not needed and can be deleted if you do not want to store your own DMAP which 1s usually the case NX Nastran Basic Dynamic Analysis User s Guide 8 3 Chapter 8 Restarts in Dynamic Analysis Restart Run NASTRAN Statement Section This section is normally the same as your cold start run The BUFFSIZE must not be changed in a restart run File Management Section FMS This section tells NX Nastran that you are performing a restart run The RESTART statement is required in any restart run The general format for the RESTART statement is as follows RESTART VERSION a b where a is the version from which you restart default value for a is LAST and b indicates whether version a is to be kept KEEP or deleted NOKEEP at the end of the run The default value for b is NOKEEP Due to the default values the following two restart statements are identical RESTART VERSION LAST NOKEEP RESTART Whenever a restart is performed a new version number is automatically created in the database For each restart the current version number is incremented by one regardless of whether the job ran successfully or not There are two exceptions to this rule and they are discussed later on You also need to tell NX Nastran which database you want to attach to your current run There are several ways to accomplish this one way is to use the ASSIGN statement For example if you ar
454. urces Of Mechanisms osc cs cod REOR RAE O amp O OE X43 XE ORC EORR RR OR o CA F 5 Sources of Nonpositive Definite Matrices aeee F 6 Detection and Avoidance of Numerical Problems eee eee F 6 Grid Point Weight Generator cce eeeeeeoseseoeo rt s mn G 1 LIEU Lus 4 994x344 0 9 634444 532 4 14 39 39 4 33 X94 14 X xu Ed FRE EY 4 G 1 Commonly Used Features eee rs G 1 Example with Direction Dependent Masses leeren G 3 Diagnostic Messages for Dynamic Analysis cccccccccccececseveces H 1 References and Bibliography ccce eee tms I 1 og ke eK ERA OOS eS E E ae Oe es I 1 NX Nastran Basic Dynamic Analysis User s Guide 5 Contents General References cell Bibliography 6 NX Nastran Basic Dynamic Analysis User s Guide About this Book This guide describes and gives examples of the basic types of dynamic analysis capabilities available in NX Nastran including e normal modes analysis e transient response analysis e frequency response analysis e enforced motion This guide only presents theoretical derivations of the mathematics used in dynamic analysis as they pertain to the proper understanding of the use of each capability For more information on dynamic reduction response spectrum analysis random response analysis complex eigenvalue analysis nonlinear analysis control systems fluid structure coupling and the Lagran
455. ure 3 23 Output from the Grid Point Weight Generator EIGENVALUE ANALYSIS BLOCK SIZE USED NUMBER OF DECOMPOSITIONS NUMBER OF ROOTS FOUND TERMINATION MESSAGE NUMBER OF SOLVES REQUIRED SUMMARY 7 ee 1 she Sashes 1 3 2 1 REQUIRED NUMBER OF EIGENVALUES FOUND TOTAL ENERGY OF ALL ELEMENTS IN PROBLEM TOTAL ENERGY OF ALL ELEMENTS IN SET CYCLES 709540E 00 200551E 00 771934E 00 083335E 01 134184E 01 466106E 01 665805E 01 681600E 01 879240E 01 633622E 01 810133E 01 963736E 01 N ALL ELEMENTS IN PROBLEM ALL ELEMENTS IN SET N REAL EIGENVALUES MODE EXTRACTION EIGENVALUE RADIANS NO ORDER 1 1 2 346479E 03 4 844047E 01 7 2 2 2 6054886E 03 5 152559E 01 8 3 3 3 769821E 03 6 139887E 01 9 4 4 4 633242E 03 6 8067 92E 0 1 1 5 5 5 078395E 03 7 126286E 01 d 6 6 8 485758ET03 9 211817E 01 1 7 7 2 805541E 04 1 674975E 02 2 8 8 5 350976E 04 2 313218E 02 3 9 9 5 940912E 04 2 437399E 02 3 10 10 8 476198E 04 2 911391E 02 4 11 11 9 134271E 04 3 022296E 02 4 12 12 9 726959E 04 3 118807E 02 4 ELEMENT ST RAI ELEMENT TYPE ELAS2 TOTAL ENERGY OF MODE 1 TOTAL ENERGY OF ELEMENT ID STRAIN ENERGY 1002 2 735009E 02 1003 4 059090E 02 1012 2 685884E 02 1013 3 240471E 02 1021 8 017746E 02 1022 2 833448E 02 1023 Se OOS k2Z SES OW 1031 7 903841E 02 1032 2 781467E 02 033 3 573737E 01 TYPE ELAS2 SUBTOTAL 1 104569E 03 ELEMENT STRA I ELEMENT TYPE ELAS2 MODE ELEMENT ID STRAIN ENERGY 10
456. utter is the oscillatory aeroelastic instability that occurs at some airspeed at which the energy extracted from the airstream during a period of oscillation is exactly dissipated by the hysteretic damping of the structure The motion is divergent in a range of speeds above the flutter speed Flutter analysis utilizes complex eigenvalue analysis to determine the combination of airspeed and frequency for which the neutrally damped motion is sustained see Figure 11 8 0 2 1st Mode O ai E 2nd Mode oi 0 1 V4 s 5D z d E 4 00K i waa Te z i na d i A ri C bi zm LL 2 X w i N Flutter Divergence 0 1 E 0 2 0 500 1000 1500 2000 Velocity ft sec Figure 11 8 Flutter Stability Curve Three methods of flutter analysis are provided in NX Nastran the American flutter method called the K method in NX Nastran an efficient K method called the KE method for rapid flutter evaluations and the British flutter method called the PK method for more realistic representation of the unsteady aerodynamic influence as frequency dependent stiffness and damping terms Complex eigenvalue analysis is used with the K method and the QR transformation method is used with the KE and PK methods NX Nastran Basic Dynamic Analysis User s Guide 11 13 Chapter 11 Advanced Dynamic Analysis Capabilities Dynamic Aeroelastic Response The aeroelastic dynamic response problem determines the response of the airc
457. which can be costly in direct transient response analysis The TSTEP Bulk Data entry has the following format 1 2 3 4 5 6 7 8 9 10 TSTEP sD I A NOI j MEM M NO j j NEN S Field Contents SID Set ID specified by a TSTEP Case Control command Ni Number of time steps of value At At Integration time step NOI Output every NOi th time step 6 7 Transient Excitation Considerations A number of important considerations must be remembered when applying transient loads The averaging of applied loads 6 3 in the integration smooths the force and decreases the apparent frequency content Very sharp spikes in a loading function induce a high frequency transient response If the high frequency transient response is of primary importance in an analysis a very small integration time step must be used It is also important to avoid defining discontinuous forcing functions when describing applied loads The numerical integration of discontinuous forcing functions may cause different results for the same analysis run on different computers because of slight numerical differences on different computer types If the analysis calls for loadings with sharp impulses it is best to smooth the impulse over at least one integration time increment NX Nastran Basic Dynamic Analysis User s Guide 6 23 Chapter 6 Transient Response Analysis The loading function must
458. y generator for static load entries 5 18 NX Nastran Basic Dynamic Analysis User s Guide Frequency Response Analysis DLOAD LOADSET Case Control Bulk Data Y RLOADi LSEQ NZ N Cynamic Load DAREA Static Load Entries Te nporal Reference Link Spatial Distribution Distribution Figure 5 6 Relationship of Dynamic and Static Load Entries LSEQ Example Suppose the following commands are in the Case Control Section LOADSET 27 DLOAD 25 and the following entries are in the Bulk Data Section ROAD ps ms Jj y bse it 26 te 9 In the above the LOADSET request in Case Control selects the LSEQ Set ID 27 entry The DLOAD request in Case Control selects the RLOAD1 Set ID 25 entry This RLOAD1 entry refers to a TABLED1 ID 29 which is used to define the frequency dependent variation in the loading DAREA Set ID 28 links the LSEQ and RLOAD1 entries In addition the LSEQ entry refers to static Load Set ID 26 which is defined by FORCE and PLOAD1 entries The FORCE and PLOAD1 entries define the spatial distribution of the dynamic loading and through the DAREA link refer to the RLOAD1 TABLED1 combination for the frequency varying characteristics of the load Note that there is no DAREA entry Dynamic Load Set Combination DLOAD One of the requirements of frequency dependent loads is that RLOAD1s and RLOAD2s must have unique SIDs If they are to be applied in the same analysis th
459. y stressed across many or all modes will probably be highly stressed when dynamic loads are applied Modal strain energy is a useful quantity in identifying candidate elements for design changes to eliminate problem frequencies Elements with large values of strain energy in a mode indicate the location of large elastic deformation energy These elements are those which most directly affect the deformation in a mode Therefore changing the properties of these elements with large strain energy should have more effect on the natural frequencies and mode shapes than if elements with low strain energy were changed Structures with two or more identical eigenvalues are said to have repeated roots Repeated roots occur for structures that have a plane of symmetry or that have multiple identical pieces such as appendages The eigenvectors for the repeated roots are not unique because many sets of eigenvectors can be found that are orthogonal to each other An eigenvector that is a linear combination of the repeated eigenvectors is also a valid eigenvector Consequently small changes in the model can make large changes in the eigenvectors for the repeated roots Different computers can also find different eigenvectors for the repeated roots Rigid body modes see Rigid body Modes represent a special case of repeated roots 3 4 Methods of Computation Seven methods of real eigenvalue extraction are provided in NX Nastran These methods are numer
460. y w although similar notation is used This equation of motion is solved to obtain u t Asinw t Bcosqo t E sinet l w w i n Initial Condition Steady State Solution Solution Equation 1 17 where u t wp k A gt W i 2 1 2 n l o w w B u t Again A and B are the constants of integration based on the initial conditions The third term in Equation 1 17 is the steady state solution This portion of the solution is a function of the applied loading and the ratio of the frequency of the applied loading to the natural frequency of the structure The numerator and denominator of the third term demonstrate the importance of the relationship of the structural characteristics to the response The numerator p k is the static displacement of the system In other words if the amplitude of the sinusoidal loading is applied as a static load the resulting static displacement u is p k In addition to obtain the steady state solution the static displacement is scaled by the denominator The denominator of the steady state solution contains the ratio between the applied loading frequency and the natural frequency of the structure Dynamic Amplification Factor for No Damping The term NX Nastran Basic Dynamic Analysis User s Guide 1 9 Chapter 1 Fundamentals of Dynamic Analysis 1 1 w w is called the dynamic amplification load factor This term scales the static response to create an amplitude f
461. yk A Analytical and Experimental Study of Two Concentric Cylinders Coupled by a Fluid Gap NASTRAN Users Exper pp 249 258 September 1975 NASA TM X 3278 Murthy P L N Chamis C C Dynamic Stress Analysis of Smooth and Notched Fiber Composite Flexural Specimens National Aeronautics and Space Administration April 1984 NASA TM 83694 Murthy P L N Chamis C C Dynamic Stress Analysis of Smooth and Notched Fiber Composite Flexural Specimens Composite Materials Testing and Design Seventh Conf ASTM pp 368 391 1986 ASTM STP 893 Neal M Vibration Analysis of a Printed Wiring Board Assembly Proc of the MSC NASTRAN Eur Users Conf May 1984 Nefske D J Sung S H Power Flow Finite Element Analysis of Dynamic Systems Basic Theory and Application to Deams American Soc of Mechanical Engineers Noise Control and Acoustics Division Vol 3 pp 47 54 December 1987 Nowak Bill The Analysis of Structural Dynamic Effects on Image Motion in Laser Printers Using MSC NASTRAN The MSC 1988 World Users Conf Proc Vol I Paper No 10 March 1988 Nowak Bill Structural Dynamics Analysis of Laser Printers Sound and Vibration Vol 23 No 1 pp 22 26 January 1989 Nowak William J Dynamic Analysis of Optical Scan Systems Using MSC NASTRAN Proc of the Conf on Finite Element Methods and Technology Paper No 10 March 1981 Nowak William James Courtney Dynamic Modeling and Analysis of Spin
462. ynamic Analysis User s Guide S FILE bd08bar6 dat S THIS IS ANOTHER TRANSIENT RESTART RUN THE PURPOSE S OF THIS RUN IS TO REQUEST ADDITIONAL OUTPUT RESTART ASSIGN MASTER bd08barl MASTER ID CANT BEAM eol q12 TIME 10 CEND TITLE SUBTITLE SPG 1 METHOD SET 1 SET 2 ACCE SUBCASE S DAMP TSTEP DLOAD 10 11 10 1 100 100 100 PLOT RESULTS X Y plot commands EGIN BULK X X UJ Xn 4 Xn Xn xn Xn ENDDATA Restarts in Dynamic Analysis INPUT Figure 8 7 Input File for an Additional Output Request FILE bd08bar7 dat THIS IS ANOTHER TRANSIENT RESTART RUN USING A DIFFERENT LOAD CONDITION NOTE THAT SINCE THERE ARE NO MODEL CHANGES THE SAME MODES WERE USED FROM THE DATABASE FOR THE RESPONSE CALCULATIONS UY dV oU XU X Xo V RESTART ASSIGN MASTER bd08barl MASTER ID CANT BEAM SOL 112 TIME 10 CEND S NOTE THAT TITLE CHANGES HAVE NO EFFECT S ON SOLUTION PROCESS THEY ONLY CHANGE THE PRINTOUT TITLE S TITLE TRANSIENT RESTART SUBTITLE TRIANGLE PULSE 1 0 AT T 0 AND 0 0 AFTER SPC 1 METHOD 10 SET 1 11 DISP 1 SUBCASE 1 SDAMP 100 TSTEP 100 DLOAD 300 S m PLOT RESULTS NX Nastran Basic Dynamic Analysis User s Guide 2 SEC 8 13 Chapter 8 Restarts in Dynamic Analysis 8 14 S 9er plot commands S BEGIN BULK S S SID DAREA DELAY TYPE TID TLOAD1 300 301 202 S DAREA 301 11 3 1 0 S TABLED 2 B07 Y apt TBL3 TRBhSrx04054020739042514105 40
463. you can specify a good value for the large mass es 10 7 Loads Because of their time or frequency varying nature it is more complicated to apply dynamic loads than it is to apply static loads Therefore it is important to verify that the dynamic loads are correctly specified and that there are no discontinuous loads The best way to verify proper dynamic load specification is to plot the loads as a function of time or frequency Another way to verify proper dynamic load specification is to print the loads as a function of time or frequency Use the OLOAD Case Control command to plot or print the loads 10 8 Meshing An adequate element mesh is required to create an accurate model For static analysis the mesh density is primarily controlled by the load paths the element mesh must be fine enough so that there is a smooth transition of stress from one element to another in the region of interest Load paths are also important for dynamic analysis but there is an additional consideration the mesh must be fine enough to accurately represent the deformed shape of the modes of interest If many modes are to be considered in the analysis then the model must be fine enough to accurately represent the mode shapes of the highest modes of interest Table 10 1 shows the frequencies resulting from several cantilever beam models each column represents the same structure but with a different number of elements Note that the frequencies are closer to th
464. you select a set of dynamic DOFs called the a set these are the retained DOFs that form the analysis set The complementary set is called the o set and is the set of DOFs that are omitted from the dynamic analysis through a reduction process The process distributes the o set mass stiffness and damping to the a set DOFs by using a transformation that is based on a partition of the stiffness matrix hence the term static condensation This reduction process is exact only for static analysis which leads to approximations in the dynamic response The a set DOFs are defined by the ASET or ASET1 Bulk Data entries and the o set DOFs are defined by the OMIT or OMIT1 Bulk Data entries It is emphasized that dynamic reduction is an optional technique and is best left to the dynamic analysis specialist Whereas dynamic reduction was required in the days of small computer memory and disk space now it is no longer required due to increased computer resources and better eigenanalysis methods in particular the Lanczos method 11 3 Complex Eigenvalue Analysis Complex eigenvalue analysis is used to compute the damped modes of structures and assess the stability of systems modeled with transfer functions including servomechanisms and rotating systems Complex eigenvalue analysis solves for the eigenvalues and mode shapes based on the following equation in operator notation b M pB K ul 0 Equation 11 1 where p acit This equation is simil

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