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1. 00 3 2 Pressure amplitude over boundary of duct 3 3 Sound pressure along the centre of duct side vi 5 1 5 2 5 3 5 4 5 9 5 6 5 7 5 8 5 9 5 10 5 11 5 12 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 6 11 7 1 7 2 7 3 7 4 7 5 7 6 T T Creating the base of the r00M Defining the room base as a surface 0 4 Translating the surface in the z direction Resultant 3 dimensional room a oao a a x 0 plane is clearly visible pd raid dork ee ad ke ee Addition of a rectangle to define the source Defining the source surface 2 2 a ee Correct orientation of the surface normals Assigning a velocity boundary condition to the source surface Defining the problem data catas e ees ee Sere lt Meshing the boundary of the room Pressure amplitude over the boundary of the room Imported car geometry o da a 4G eek eR Beh oS es Listing the point coordinates 2 Listing the point coordinates in one window Scaling the model esos cath ee ee ale Gye ee ee es Checking the point coordinates after rescaling Checking the surface normals 0004 All surface normals are oriented correctly Implementing the velocity boundary condition Problem data for car a oa o a te io ee ee ee Wished car boundary e cot2. The only boundary conditions required for this problem are velocity boundary conditions A velocity of 1 0i is needed over the entire surface of the sphere To do this select Data gt Conditions Click on Velocity Set the real velocity component to 1 and the imaginary velocity components to zero Click on assign Type lt gt in the command line to select all surfaces and select finish and then Close The boundary conditions have now been set Select Data gt Problem data Give the project a title of lt sphere gt Ensure the boundary type is selected to be external symmetry is set to Y 7 density is set to 1 speed of sound is set to 6 2832 freq start to 0 1 freq stop to 7 and freq int to 0 1 see Figure 7 5 Click Accept data and Close to leave the problem data environment 60 Problem Data El Figure 7 5 Selecting the problem data 61 7 EXAMPLE SIX PULSATING SPHERE The next step is to mesh the semi sphere surface Select Meshing gt Generate A dialog box will appear asking you to Enter the size of elements to be generated Type in lt 0 2 gt and press OK A dialog box will appear which states that 568 triangle elements have been created Press OK and the mesh will appear Figure 7 6 Files View Geometry Utilities Data Meshing Calculate Help Z2OSS AG YOSSIAQ 4 GiD Veron PIV IF BAINOIZ NOs O Changed size automatica
3. 0 733737 1 587281 1 278 2 0 733737 1 587281 1 278 0 751207 0 924000 1 213 0 751207 0 924000 1 2131 D 700000 0 650000 0 200 D 700000 0 650000 0 000 D 700000 1 190042 0 000 0 700000 1 444821 0 700 9 D 700000 1 231985 0 700 10 0 700000 1 050000 0 20 11 0 100000 1 050000 0 20 12 0 100000 0 650000 0 20 13 0 100000 1 231985 0 70 14 0 100000 1 444821 0 70 15 0 100000 1 190042 0 0 16 0 100000 0 650000 0 00 on non kom a ols sds Go View text Close Figure 6 5 Checking the point coordinates after rescaling 46 The next step is to ensure that all of the surface normals are facing in the correct direction Select Utilities gt Draw Normals gt Surfaces To select all surfaces type lt gt in the command line and then press enter Due to there being 36 separate surfaces it is very difficult to see which surface normals are directed correctly To rectify this problem right click the mouse select Contextual and then Color All of the outward pointing surfaces will be coloured green and all of those pointing inwards will be coloured yellow To check all the surfaces you will need to rotate the object View gt Rotate gt Trackball All surfaces should be orientated correctly but if they are not see Figure 6 6 you will need to right click the mouse and select Contextual gt Swap some Click on all of the yellow surfaces once to reorientate them in the correct direction see Fig
4. ROIG USA le le ABUSBAAADI AMOS z 9 Added 1 new surfaces to the selection Enter more surfaces ESC to leave j Changed sense to 1 entities Can continue y Command f Figure 2 6 All normals are oriented correctly for an internal BEM problem 13 2 EXAMPLE ONE STANDING WAVE IN A DUCT The next step is to define the problem as a Helm3D BEM problem To do this select Data gt Problem type gt helm3d A dialog window warning the user that all data information will be lost will appear Select OK Once the problem type has been chosen the boundary conditions need to be defined The only boundary conditions required for the standing wave ie magnitude 1 phase problem are velocity boundary conditions A velocity of 1 0i is needed to mimic the piston at the entrance of the tube All other surfaces need to be set to zero velocity To do this select Data gt Conditions Click on Velocity Set both the real and imaginary velocity components to zero Click on assign Type lt gt in the command line to select all surfaces and select finish Change the real velocity component to 1 Click on assign and select the surface at z 0 as depicted in Figure 2 7 Select finish The boundary conditions have now been set lex Files View Geometry Utilities Data Meshing Calculate Help OB B BMGIOOSS Gil eson Conditions Velocity E 2 Normal Velocity Re 1
5. are asking the user to hit the enter or escape key on the keyboard respectively If the user is asked to select something enclosed in quotations then they need to click on the appropriate button using the mouse For example select OK is asking the user to use the mouse to click on the OK button on the screen Chapter 2 Example One Standing Wave in a Duct The first example see Figure 1 1 a is a simple model of a 1D standing wave in a rigid walled duct A 1D standing wave is created when a source of constant velocity is operated at one end of a closed tube The sound emitted from the source experiences multiple reflections from each end of the tube The resulting forward and back propagating waves combine to form a standing wave of high amplitude This problem introduces the very simple geometry of a long rectangle One of the dimensions is much larger than the other two enabling the assumption of 1D plane propagating waves to be valid which simplifies the theoretical analysis at low frequencies below the cut on frequency of higher order modes Velocity boundary conditions the required direction of normals and meshing are introduced How the accuracy of results can be affected by mesh resolution is also demonstrated Results obtained from the numerical model are then compared to the analytical solution Open up a new project Files gt New and save it Files gt Save in your working directory as stand gid Th
6. A 3dimensional prism should have been constructed To fit the prism in the frame select View gt Zoom gt Frame see Figure 5 4 Copy Entities type Surfaces Transformation Translation First point Num x 0 0 ma y 0 0 Pick 0 0 Second point Num x joo oo Duplicate entities Do extrude Surfaces I Create contacts I Maintain layers Multiple copies f Select Cancel Figure 5 3 Translating the surface in the z direction 30 Project room View Geometry Utilities Data Meshing Calculate Help G Files ZA ROOMS SSA la Gil amp 6 Z gt a A q ao pod LA E A Selected 1 surfaces 4 Geometry has 5 new surfaces 8 new lines 4 new points Leaving Y Command f Figure 5 4 Resultant 3 dimensional room 31 5 EXAMPLE FOUR SPEAKER IN A ROOM Rotate the view so that the x 0 plane is clearly visible using View gt Rotate gt Trackball see Figure 5 5 Files Yiew Geometry Utilities Data Meshing Calculate Help ROIG ISA le GiD Veron PIV IF BAINO IZ AMOS dez Pick LEFTMOUSE to rotate ESC to quit Pick LEFTMOUSE to rotate ESC to quit y Command Figure 5 5 x 0 plane is clearly visible 32 The next step is to define the source region Chose the option of creating a line Geometry gt Create gt Line Type lt 0 0 1 0 1 gt in the command line and then press
7. Change the real velocity component to 1 Click on assign and select only the source surface at x 0 see Figure 5 9 Select finish and then Close The boundary conditions have now been set 18 xi il S Conditions El Velocity Normal Y PIS IF SAINO IT MO Lo Enter Surfaces with new values 3 y Added 1 new surfaces to the selection Enter more surfaces ESC to leave Command f Figure 5 9 Assigning a velocity boundary condition to the source surface 36 Select Data gt Problem data Give the project a title of lt room gt Ensure the boundary type is selected to be internal and that the density and speed of sound are selected to be 1 21 and 343 respectively Set the frequency start and frequency stop to be 68 5 corresponding to a wave length of 5 m the longest room dimension and then click Accept data and Close see Figure 5 10 Problem Data Figure 5 10 Defining the problem data 37 5 EXAMPLE FOUR SPEAKER IN A ROOM The next step is to mesh the boundary of the room Rather than using the default triangular meshing elements this time you ll use quadrilateral elements To do this select Meshing gt Element type gt Quadrilat eral An information window will appear asking you to select the surfaces to which this element type should be assigned Click OK type lt gt in the command
8. enter lt 0 0 1 0 3 gt enter lt 0 0 3 0 3 gt enter and lt 0 0 3 0 1 gt enter To connect the last point to the original point type lt join gt and press enter Using the mouse click on the point located at 0 0 1 0 1 You should now have a rectangle which will be used to define the source see Figure 5 6 Press esc Files View Geometry Utilities Data Meshing Calculate Help Z2OSB AGIYOSSIA 4 GiD vere R 5 9 A a Q i Sil Qu pa LA Y Leaving line creation 4 new lines 4 new points y Enter points to define line ESC to leave Command Figure 5 6 Addition of a rectangle to define the source 33 5 EXAMPLE FOUR SPEAKER IN A ROOM The surface of the prism on which the source lies needs to be divided into two surfaces the entire surface minus the source rectangle and the source rectangle by itself To do this select Geometry gt Edit gt Divide gt Surfaces gt Split Select the surface on the x 0 plane Using the mouse select the four lines defining the exterior of this surface as well as the four lines defining the source location Press esc The surface should now have been subdivided see Figure 5 7 lr Lo Enter name of the project Layer to use Layer0 y Command f Figure 5 7 Defining the source surface 34 The next step is to ensure that all of the surface normals are facing in the correct directi
9. 4 Max 422 9 Command Figure 3 2 Pressure amplitude over boundary of duct 23 3 EXAMPLE Two TRAVELLING WAVE IN A DUCT During the generation of the solution a file entitled output dat would have been written to your working folder This can be opened and read using your preferred text editor The file lists the density speed and sound and frequency of analysis The nodal points element connectivity and boundary conditions are all listed within Following this the sound pressure on the boundary VN on the boundary and the field point solution are listed for each frequency interval The analytical pressure at any point in the duct of a travelling plane wave is given by the equation p x pee 3 1 where x is the distance from the point of excitation along the duct Using your preferred graphing package try comparing the real and com plex pressures of the travelling wave obtained by reading the BEM values of sound pressure along the centre of on of the duct sides from output dat with the analytical solution You should obtain a graph which looks simi lar to Figure 3 3 the actual sound pressure you obtain depends upon the analysis frequency chosen 500 400 gt N Q O O O O O O 100 200 300 400 500 0 2 4 6 8 10 distance along duct m Re theory Re BEM Im theory Im BEM sound pressure Pa gt Figure 3 3 Sound pressure
10. Audio Engineering Society Los Angeles California October 2002 Cited on page 1 T H Hodgson and R L Underwood BEM computations of a finite length acoustic horn and comparison with experiment In Computa tional Acoustics and its Environmental Applications pages 213 222 WIT Press 1997 Cited on page 1 P M Juhl The boundary element method for sound field calculations PhD thesis Technical University of Denmark 1993 Cited on page 1 R D Ciskowski and C A Brebbia editors Boundary element methods in Acoustics Computational Mechanics Publications Co published with Elsevier Applied Science 1991 Cited on page 1 O von Estorff editor Boundary Elements in Acoustics Advances and Applications WIT Press 2000 Cited on page 1 R C Morgans External acoustic analysis using comet Technical re port Internal Report The University of Adelaide 2000 Cited on page 1 T W Wu editor Boundary Element Acoustics Fundamentals and Computer Codes WITPress 2000 Cited on pages 1 and 2 R C Morgans A C Zander and C H Hansen Fast boundary ele ment models for far field pressure prediction In Australian Acoustical Society Conference Acoustics 2004 2004 Cited on page 1 L G Copley Fundamental results concerning integral representations in acoustic radiation Journal of the Acoustical Society of America 44 1 28 82 July 1968 Cited on page 63 73 REFERENCES 10 H A Schenck Improv
11. Geometry Utilities Data Meshing Calculate Help 2OSS MGIOOSSIA 4 GiD vere y R a PIS IF SAINO Z WOSewr rs LK z Saved OK Leaving Saving backup file backup gid Saved y Command f Figure 2 4 Constructing the prism surfaces 11 2 EXAMPLE ONE STANDING WAVE IN A DUCT The next step is to check the surface normals Select Utilities gt Draw Normals gt Surfaces To select all surfaces type lt gt in the command line and then press enter or select the entire model by clicking and dragging the mouse from one corner to the diagonally opposite corner of the screen Some of the surfaces may point into the prism whilst others may be pointing out see Figure 2 5 Files Yiew Geometry Utilities Data Meshing Calculate Help 2OSS HMGIOSSFSIA 4 GiD Veron y R a PIV IF BAINO TZ AMOR gt Added 6 new surfaces to the selection Enter more surfaces ESC to leave F y Command f Figure 2 5 Draw Normals environment 12 For an internal boundary element problem all surfaces must face out Whilst still in the Draw Normals mode right click the mouse and select Contextual gt Swap some Click on all of the surfaces that have an inward pointing normal until all surfaces are oriented in the correct direction see Figure 2 6 Hit esc to leave the Draw Normals mode NS G Files View Geometry Utilities Data Meshing Calculate Help
12. a reasonable size and many useful acoustic problems can be solved It is highly recommended that those who are unfamiliar with GiD should download the GiD user manual from the website http gid cimne upc es 1 2 How to install Helm3D and GiD Both the pre and postprocessor GiD and the BEM code Helm3D are re quired Although GiD can be operated using Linux Windows is currently the only platform supported Please contact the authors if Linux compati bility is required The book Boundary Element Acoustics Fundamentals and Com puter Codes 7 including a CD containing a PC executable of Helm3d helm3d exe as well as F77 source code is available from WITPress http www witpress com acatalog 5709 html The program GiD can be downloaded from its homepage http gid cimne upc es The program will be downloaded as an executable To unpack and install GiD on your computer simply run the executable file and follow the step by step instructions of the setup procedure Helm3D zip can be downloaded from the University of Ade laide Active Noise and Vibration Control ANVC Group homepage http www mecheng adelaide edu au anve publications php Once you have downloaded GiD you need to unzip Helm3D zip into the GiD prob lem types folder GiD Gid7 2 problemtypes A folder entitled helm3d gid containing the contents of the zip file should be created The helm3D ex ecutable helm3d exe obtained from the CD accompanying the aforeme
13. codes whilst readily available with the purchase of the book have not gained widespread use for a number of reasons the interface has traditionally been command file driven and requires access to some form of pre and postprocessor and there is a limited availability of suitable tutorial material Thus it was realised that there was a need for e an easy to use freely available interface to an acoustic BEM code and e a well written step by step tutorial on the use of BEM to solve simple relevant acoustic problems A GUI interface to Helm3D within the GiD environment has been devel oped meeting the first requirement This tutorial satisfies the second re quirement presenting step by step instructions that teach the user funda 1 INTRODUCTION mental acoustic concepts BEM concepts and how to use the GUI interface to solve BEM problems 1 1 GiD GiD is a general purpose fully featured finite element pre and post proces sor developed over a number of years by the International Centre for Numer ical Methods in Engineering CIMNE in Barcelons Spain It has exten sive geometry creation features as well as CAD import IGES and others supports the meshing of many different element types the application of boundary conditions and has a postprocessing capability for viewing results The academic version of this program is freely downloadable the only restriction being limited to 700 3D elements Fortunately for BEM this is
14. 0990 751 207473 924 000000 1 751 207473 924 000000 1 700 000000 650 000000 z 700 000000 650 000000 700 000000 1190 041508 700 000000 1444 820672 g 700 000000 1231 985117 10 700 000000 1050 00000 11 100 000000 1050 00000 12 100 000000 650 000000 13 100 000000 1231 98511 14 100 000000 144482067 15 100 000000 1190 04150 co y Ma mn E an Go View text Close Figure 6 3 Listing the point coordinates in one window 44 Select Utilities gt Move A window will appear Within this window select Entities type to be Surfaces Transformation to be Scale and the Scale factors to be 0 001 in the x y and z directions Click Select see Figure 6 4 and select the entire model by typing lt gt in the command line and pressing enter Select finish for the transformation to occur and then close the move window by clicking the cross in the top right hand corner Figure 6 4 Scaling the model 45 6 EXAMPLE FIVE SOUND IN A CAR It may appear as though the car has disappeared but this is only because it is 1 1000th of its original size To rescale the image select View gt Zoom gt Frame An image of the car similar to that in Figure 6 1 should appear To check that the scaling has been correctly implemented you can once more list the nodes by selecting Utilities gt List gt Points and List see Figure 6 5 List Entities Tot x Select entity
15. 7 5 EXAMPLE FOUR SPEAKER IN A ROOM Project UNNAMED Files Yiew Geometry Utilities Data Meshing Calculate Help ROIG OIEA le GiD Veron 00 U BAIADIJIMO LE E a a join Pick an existing point y Command f Figure 5 1 Creating the base of the room 28 Save the project in your working folder as room gid To change to a 3D view select View gt Rotate gt Isometric To zoom to the best fit of the image in the window select View gt Zoom gt Frame To create a surface out of the rectangle select Geometry gt Create gt NURBS surface gt By contour Type lt gt in the command line to select all lines and press esc see Figure 5 2 le xi 2OSB BG OO FS A 4 Al dl PIV IF SAINO IZ ANOS w y Created one new planar NURBS surface You can continue gt Enter lines to define NurbSurface ESC to leave y Command Figure 5 2 Defining the room base as a surface 29 5 EXAMPLE FOUR SPEAKER IN A ROOM The surface can now be translated via extrusion by 5 units in the z direction To do this type ctrl c A copy dialog box will appear on the screen Select the Entities type to be Surfaces the Second point z coor dinate to be 5 0 and Do extrude to be Surfaces see Figure 5 3 Click Select and type lt gt in the command line and press esc to select all sur faces Type Finish and then Cancel
16. Normal Velocity Im O Finis 4 y Enter Surfaces with new values Added 1 new surfaces to the selection Enter more surfaces ESC to leave y Command f Figure 2 7 Setting the z 0 velocity boundary condition 14 Select Data gt Problem data Give the project a title of lt stand gt Ensure the boundary type is selected to be internal and that the density and speed of sound are selected to be 1 21 and 343 respectively Set the frequency start and frequency stop to be 25 725 corresponding to the second resonance frequency of the tube and then click Accept data and Close see Figure 2 8 Problem Data stand me Moe na o o o CEA 2006 Figure 2 8 Defining the problem data 15 2 EXAMPLE ONE STANDING WAVE IN A DUCT The next step is to mesh the boundary of the tube Select Meshing gt Generate A dialog box will appear asking you to Enter the size of elements to be generated Type in lt 2 gt A dialog box will appear which states that 52 triangle elements have been created Press OK and the mesh will appear Figure 2 9 Figure 2 9 View of the meshed tube 16 A solution to the problem can now be generated by selecting Calculate gt Calculate A dialog box will appear telling you once the solution is done Figure 2 10 Click OK Process info xj Process stand started
17. THE UNIVERSITY OF ADELAIDE AUSTRALIA DUE cruce LUN Faculty of Engineering Computer and Mathematical Sciences SCHOOL OF MECHANICAL ENGINEERING Learning Acoustics and the Boundary Element Method Using Helm3D and GiD TUTORIAL MATERIAL November 28 2005 Laura A Brooks and Richard C Morgans email laura brooksCmecheng adelaide edu au iTemail rick morgansOgmail com MAYBE VLL START l WITH THE ACKNOW LEDGEMENTS JORGE CHAM THE STANFORD DAIL phdstanford edo comics source Piled Higher and Deeper by Jorge Cham www phdcomics com Learning Acoustics and the Boundary Ele ment Method Using Helm3D and GiD Brooks L A amp Morgans R C November 2005 Active Noise and Vibration Control Group School of Mechanical Engineering The University of Adelaide SA 5005 Australia Typeset by the authors with the ATRX 2 doc ument preparation system Please submit and er rors suggestions or modifications to the authors Printed in Australia Copyright 2005 The University of Adelaide South Australia Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advan tage and that copies bear this notice and the full citation on the first page To copy otherwise to re publish to post on servers or to redistribute to lists requires prior specific permission of th
18. along the centre of duct side 24 Chapter 4 Example Three Side Branch Resonator The third example see Figure 1 1 c is the addition of a side branch res onator to the travelling wave duct This example is currently a work in progress and will be avail able soon 25 Chapter 5 Example Four Speaker in a Room The fourth example see Figure 1 1 d is a model of a speaker in the corner of a rigid walled room This problem introduces the excitation of modes in a 3D environment The first step is to construct the rectangular room This will be done using a method different to that used to construct the rectangular tubes of examples 1 through 3 showing that there are multiple ways to construct similar geometry The room to be modelled is 3 metres wide 5 metres long and 2 5 me tres high Open up a new project Chose the option of creating a line Geometry gt Create gt Line Type lt 0 0 gt in the command line and then press enter A point at 0 0 will appear Type in lt 2 5 0 gt and press enter A point at this location and a line connecting it to the previous point will appear Type lt 2 5 3 gt press enter type lt 0 3 gt and press en ter To connect the last point to the original point type lt join gt and press enter You will be asked to pick an existing point Using the mouse click on the point located at 0 0 You should now have a rectangle see Figure 5 1 Press esc 2
19. at Fri Oct 07 16 20 23 has finished Postprocess Figure 2 10 Process information dialog box To review the results once must enter the postprocessor To do this select Files gt Postprocess To display the pressure over the bound ary of the duct select View results gt Contour fill gt Press amp Figure 2 11 cio Project stand laj xi Files View Utilities Docuts View results Options Windows Help Z2eCeeslRAg QVoGsla a re Sea XS K 3 IED E la Pres amp 460 9 21 By 417 45 373 99 330 54 287 09 243 64 200 18 156 73 113 28 x 69 83 vw Enter variable name Contour Fill Pres_amp Min 69 83 Max 460 9 z Contour Fill of Pres amp Command Figure 2 11 Pressure amplitude over boundary of duct 17 2 EXAMPLE ONE STANDING WAVE IN A DUCT As expected a standing wave corresponding to the second resonance frequency of the tube is observed To see how the real and imaginary pressure components vary along the tube or to see the total sound pressure level in dB select View results gt Contour fill and chose the desired parameter Although the BEM problem was solved only at one frequency the so lution can be swept over a frequency range in order to see the frequency dependance of the solution To do this you first need to return to the pre processor Files gt Preprocess The frequency range can then be changed
20. dent Try solving the BEM problem at other frequencies and compare the pressure plot to that obtained at 100Hz To do this leave the preprocessor redefine the problem data frequency to that which you desire remesh and then resolve the problem Note how at certain frequencies very high pressure amplitudes are obtained at various locations across the car interior boundary How could this present itself as a problem in a real situation and what feasible solutions could you implement to ameliorate this problem 93 Chapter 7 Example Six Pulsating Sphere The first exterior problem is the classical fundamental radiation problem of a pulsating sphere see Figure 1 1 f Key concepts covered are modelling symmetry and how this affects computational efficiency appropriate direc tion of normals for an external problem and the use of CHIEF points in the interior to improve the condition number of the matrix To model a complete sphere select Geometry gt Create gt Object gt Sphere You will be asked to enter a centre for the sphere In the command line type lt 0 0 0 gt and press enter You will then be asked to enter a radius for the sphere Type lt 1 gt and press enter A sphere should appear on the screen To enlarge the view select View gt Zoom gt Frame see Figure 7 1 59 7 EXAMPLE SIX PULSATING SPHERE ROOSCB HGIYO FSA 4 GiD veer amp 0 Z N O Q o lt I bia Oe 3 Created 1 new volum
21. e fdat files gen erated with no CHIEF point a CHIEF point at the sphere centre and a CHIEF point at half the sphere radius graphically using your preferred graphing package by graphing the pressure as a function of frequency or ka where k is the wavelength and a is the sphere radius You should obtain a plot similar to Figure 7 7 Surface Pressure no CHIEF CHIEF r 0 CHIEF r 0 5 gt analytical Figure 7 7 Surface pressure of a pulsating sphere The BEM solution with no CHIEF point shows poor agreement with the analytical solution at ka and ka 2 where k is the wavenumber and a is the radius of the source This is due to poor conditioning of the matrix The placement of a CHIEF point at r a 0 5 where r is the radial location from the centre of the sphere ameliorates the problem at ka however poor agreement at ka 2 still occurs due to the CHIEF point being on the interior nodal surface corresponding to the characteristic eigenfrequency ka 2 meaning that this resonance cannot be cancelled Placing the CHIEF point at the sphere centre ensures that it does not lie on a nodal surface The resulting solution is therefore in good agreement with the analytical solution When using BEM to analyse more complex geometries the user 64 generally has no prior knowledge of the optimal CHIEF point location and therefore multiple CHIEF points randomly distributed within the volume are used 65 Chapter 8 Exa
22. e Authors Pr cis The Boundary Element Method BEM is a powerful tool which has be come an important and useful numerical technique applied to problems in acoustics It is particularly useful for analysing sound radiation and acoustic scattering problems Numerous commercial BEM codes with graphical user interfaces GUIs and mesh generators exist however these are relatively expensive which discourages their use by academic institutions and smaller companies Helm3D is a three dimensional BEM code available with pur chase of a relatively inexpensive book but the command file driven interface is difficult to learn and some mechanism to generate the mesh is required In addition there is a limited availability of suitable tutorial material so the uptake of BEM throughout the acoustics community has so far been limited A GUI interface to a low cost commercial mesh generator GiD has been developed for the Helm3D code This tutorial material guides the user through the use of the GUI to solve BEM problems Step by step instructions which explain how to input each model apply boundary con ditions and postprocess the results are given Comparisons with analytical solutions are given when possible ill Contents Pr cis ili List of Tables vi List of Figures vi 1 Introduction 1 ANA o o rs Sat Gk Sie ae Gow wi ky WER A E des 2 1 2 How to install Helm3D and GiD ais ota ge RSA eS 2 hed Tutorial SUCRE E A 3 TAS Nomenclature 0 a
23. e os ere ats ae te eo cla Te ace ts Pressure magnitude on car interior Generated Spheres Ent A Beth A ed Deleting sphere surfaces in the negative x coordinate region Model of half a sphere ia wea dd 4 Ak Ake Kom ae Se Orienting the surface normals in the correct direction Selecting the problem data oa cas tota 3 Meshed semi sphere o Surface pressure of a pulsating sphere vil Chapter 1 Introduction The acoustic Boundary Element Method BEM has been used to solve a wide range of practical problems in acoustics such as the modelling of sound generated by loudspeakers 1 and 2 or received by microphones 3 the sound power radiated by a particular structure such as an engine valve cover 4 or a fan 5 and the sound scattered by hard structures 6 Numerous commercial codes that implement acoustic BEM exist however the licensing costs are prohibitively expensive for casual users limiting the uptake of this technology by the wider acoustics community There exist numerous non commercial acoustic BEM codes such as those associated with the book edited by Wu 7 These source codes exist as pedagogical examples for teaching the basics of BEM at an advanced undergraduate or postgraduate level They are written in Fortran 77 and are available the CD accompanying the book They are fully featured and capable of solving practical problems 8 These non commercial
24. easonable for the window size View gt Zoom gt Frame Construct a rectangular prism by joining the nodes as depicted in Fig ure 2 3 To do this select the option to create a line Geometry gt Create Line Right click the mouse and select Contextual gt Join C a or hit ctrl a Click on the points to join the lines To start a line from a point different to the finish point of the last line right click the mouse and select Contextual gt Escape or hit the esc key before clicking the first point of the new line 59 amp 9 E X Sy Q z S ui 7 R Leaving line creation 1 new lines 0 new points Enter points to define line ESC to leave Command Figure 2 3 Joining the points to form a prism 10 Now that the basic geometry has been defined the surfaces of the bound ary problem need to be defined To do this select Geometry gt Create gt NURBS surface gt By contour Click on the four lines defining the edges of one of the prism surfaces Upon selection they will be highlighted in red If an incorrect line is accidently selected it can be unselected by clicking on it once more Once the four lines are highlighted hit esc a purple rectangle will appear inside of the original boundary indicating the existence of a surface Use the same procedure to define each of the other five prism surfaces as depicted in Figure 2 4 igen Project stand MATES Files View
25. ed integral formulation for acoustic radiation problems Journal of the Acoustical Society of America 44 1 41 58 1968 Cited on page 63 11 A J Burton and G F Miller The application of integral equation methods to the numerical solutions of some exterior boundary value problems Proceedings of the Royal Society of London A 323 201 210 1971 Cited on page 63 74
26. es 4 new surfaces 4 new lines and 2 new points Can continue y y Enter a center for the sphere Command f Figure 7 1 Generated sphere 56 Since the sphere is symmetrical it can be modelled using half a sphere with a symmetry boundary condition Half the sphere must therefore be deleted Select Geometry gt Delete gt Volume click on the blue lines defining the spherical volume and press esc Select Geometry gt Delete gt Surface click on the two surfaces in the negative x coordinate region see Figure 7 2 and press esc iJ Gio Project UNNAMED lB x Files View Geometry Utilities Data Meshing Calculate Help 2ACeslR GlOYoVslaQ la i R SHBNSBAAADI MORRIS J Added 1 new surfaces to the selection Enter more surfaces ESC to leave bo Added 1 new surfaces to the selection Enter more surfaces ESC to leave y Command f Figure 7 2 Deleting sphere surfaces in the negative x coordinate region 57 7 EXAMPLE SIX PULSATING SPHERE Select Geometry gt Delete gt Line click on the line in the negative x coordinate region and press esc You should be left with a semi sphere as depicted in Figure 7 3 Project UNNAMED Files View Geometry Utilities Data Meshing Calculate Help Z2OSB AGIYO SSI le Gil Veron PIS IF BAINOT Z NOS Added 1 new lines to the selection Enter more lines ESC to leave Deleted 1 lines Leaving del
27. eting function v Command f Figure 7 3 Model of half a sphere 58 Save the project in your working folder as sphere gid The next step is to check the surface normals For an external bound ary element problem all surfaces must face in Select Utilities gt Draw Normals gt Surfaces To select all surfaces type lt gt and then press enter To see the directions of both surface normals clearly you may need to change the rotation of the sphere To do this select View gt Rotate gt Trackball and rotate the view until you are happy that the normals can be clearly seen Right click the mouse and select Contextual gt Swap some Click on all of the surfaces that have an outward pointing normal until all surfaces are oriented in the correct direction see Figure 7 4 Hit esc to leave the Draw Normals mode E 18 xi Files View Geometry Utilities Data Meshing Calculate Help 2OSB AGIYOSSIR 4 Al R amp 9 Za aS S Q a Sil Qu ba LA A amp Pick LEFTMOUSE to rotate ESC to quit y Saving backup file backup gid Saved Command Figure 7 4 Orienting the surface normals in the correct direction 99 7 EXAMPLE SIX PULSATING SPHERE The next step is to define the problem as a Helm3D BEM problem To do this select Data gt Problem type gt helm3d A dialog window warning the user that all data information will be lost will appear Select OK
28. g CAD data into GiD for meshing flipping surface normals meshing the geometry applying boundary conditions solving the problem through the GiD interface to Helm3d and post processing results through GiD Nomenclature Figure 1 1 shows the breakdown of the tutorials Two application areas are addressed interior acoustics and external acoustic radiation Simple problems with analytical solutions are introduced The power of BEM is then demonstrated through application to more realistic problems Step by step instructions on how to solve each of the eight tutorial problems are given in the subsequent chapters BEM interior exterior problems problems L ae O f pulsating sphere b travelling wave in tube 3 PP O g model loudspeaker a speaker in room Em c side branch resonator e sound in a car i A h actual loudspeaker Figure 1 1 Breakdown of the tutorial problems 1 4 Nomenclature Within this tutorial instructions written in bold text indicate that the user should select from the main title bar at the top of the screen For example Meshing gt Generate is asking the user to select Meshing from the title bar using the mouse and then to scroll down to Generate and then select this Commands enclosed in triangle brackets are to be typed on the 1 INTRODUCTION keyboard For example lt gt is asking the user to type a colon Commands to hit or press enter or esc
29. g box will appear which states that 490 triangle elements have been created Press OK and the mesh will appear Figure 6 10 Gio Project car k la x Files view Geometry Utilities Data Meshing Calculate Help Z Oe olasl9o Sele 4 amp 9 A Zi N 2 Sepa 5 ZS ia Op DD 2 Changed size automatically to 174 entities Mesh Generated To see it use command meshview X Command ff Figure 6 10 Meshed car boundary 5l 6 EXAMPLE FIVE SOUND IN A CAR A solution to the problem can now be generated by selecting Calculate gt Calculate A dialog box will appear telling you once the solution is done Click OK To review the results once must enter the postprocessor Select Files gt Postprocess To display the pressure over the boundary of the car select View results gt Contour fill gt Press amp Fig ure 6 11 18 xi Files View Utilities Docuts View results Options Windows Help 2OSS MGIOSSSIA 4 lr y R a IW oars A IA K SIRP p la Pres amp 503 4 448 12 392 85 337 57 282 29 227 02 171 74 116 46 61 186 5 914 z Contour Fill of Pres amp Enter variable name Contour Fill Pres_amp Min 5 914 Max 503 4 v Command Figure 6 11 Pressure magnitude on car interior 52 Extension 6 1 Extension The pressure over the car interior is highly frequency depen
30. h will maintain the 0 04 m s volume velocity Make sure that the centroid of the source location remains at approximately the same location within the room How does changing the source geometry affect the results you obtain What would happen if you changed the volume velocity The room that you analysed in this problem had three different axial dimensions What would happen if this were not the case Try modelling rooms with two or even three of the room dimensions being identical See how this affects the sound pressure over the boundary both at resonance by selecting a frequency corresponding to the ratio between the speed of sound and the repeated dimension f c A and off resonance What can you conclude from this If you were to design a room do you think it would be a good idea to use identical dimensions along each axis or should you purposely use unequal dimensions What would be the effect of having a sloped roof or alcove 40 Chapter 6 Example Five Sound in a Car The final interior problem the interior of a car see Figure 1 1 e gives an example of how BEM can be applied to a practical 3D problem The geometry of this problem is more complicated than that of the previous problems and as such would be cumbersome to construct within the GiD environment More complex shapes should be drawn using another drawing package and then imported into GiD Open up a new project Files gt New and save it Files gt Save in your w
31. he project a title of lt trav gt Set the problem data parameters to be exactly the same as for example one The next step is to mesh the duct Rather than using the default tri angular meshing elements this time you ll use quadrilateral elements To do this select Meshing gt Element type gt Quadrilateral An infor mation window will appear asking you to select the surfaces to which this element type should be assigned Click OK type lt gt in the command line to select all surfaces press enter and then esc to leave the selection environment Select Meshing gt Generate A dialog box will appear asking you to Enter the size of elements to be generated Type in lt 0 5 gt A dialog box will appear which states that 168 quadrilateral elements have been created Press OK and the mesh will appear Generate a solution and review the results in exactly the same manner as for example one The pressure amplitude pattern obtained should differ considerably from that of the standing wave This time the amplitude should decrease continuously the the piston to the duct exit Figure 3 1 zix Files View Utilities Docuts View results Options Windows Help ROIG IS lA le GiD Veron a D jee n Pres amp E 422 9 E 421 51 9 420 12 pe 418 73 417 34 415 96 414 57 413 18 411 79 y 410 4 A Contour Fill of Pres amp Enter variable name Contour Fill Pres_amp Min 410
32. ich is the pressure amplitude in Pascals of the field point in our case the point of excitation As the boundary condition at the point of excitation necessitates unit velocity amplitude at this location the specific acoustic impedance which is the ratio between the acoustic pressure and the particle velocity is simply the magnitude of the pressure at this point The theoretical resonance frequencies of the system are simply the res onances of an open closed duct and are given by ne h 2 1 18 Problem Data xi Lae Project title stand Analysis type Internal Symmetry None Density f 21 Speed of sound 343 Frequency start j Frequency stop f 10 Frequency interval 1 Field point x lo Field point y fo Field point z fo TP Dutput node i Reference pressure 20e 6 Accept data Close Figure 2 12 Altering the problem data to sweep over a frequency range where n is the mode number c is the speed of sound and is the length of the duct The analytical specific acoustic impedance at the excitation location is Z 0 ipccot kl E 2 2 v where i y 1 pis the density of the medium k is the wavenumber p acoustic pressure and v is the particle velocity By solving the BEM problem over a range of frequencies as you have done the theoretical specific acoustic impedance and the BEM specific acoustic impedance the ratio between the acoustic pressure and the particle vel
33. is will create a folder in which all of the files generated using GiD will automatically be saved The first step is to construct the rectangular tube depicted in Figure 2 1 Open up an auxiliary window from which coordinates can be easily entered Utilities gt Graphical gt Coordinates Window Chose the option of creating a point Geometry gt Create gt Point Enter the eight points in Table 2 1 by typing their coordinates in the coordinate window 2 EXAMPLE ONE STANDING WAVE IN A DUCT Figure 2 1 Rectangular tube Table 2 1 Coordinates of the duct vertices point coordinates 0 0 0 1 0 0 1 1 0 0 1 0 1 0 10 1 1 10 0 1 10 0 0 10 o Nn oan AWUN Click apply after entering the coordinates of each point see Figure 2 2 Click close once all points have been entered Project stand Files View Geometry Utilities Data Meshing Calculate Help R OSBl HGIYS SSA Gi een y fg E C System Cartesian o New point ask Change Use tab Shift tab and Return Entered point 7 Enter point jo Entered point 8 Enter point a Command Figure 2 2 Entering the point coordinates 2 EXAMPLE ONE STANDING WAVE IN A DUCT Using the trackball View gt Rotate gt Trackball rotate the coor dinate system until all eight points can clearly be seen in a 3D view Centre the image and ensure that the zoom is r
34. line to select all surfaces press enter and then esc to leave the selection environment Select Meshing gt Generate A dialog box will appear asking you to Enter the size of elements to be generated Type in lt 0 4 gt A dialog box will appear which states that 498 quadrilateral elements have been created Press OK and the mesh will appear Fig ure 5 11 A Files View Geometry Utilities Data Meshing Calculate Help O8 B B GIOOSSIA 4 Gilson PIS IF SAINO II MOR va j NE AOS NN i i l iW 1 TEELLA D AEE FAS a Mesh Generated To see it use command meshview 3 Y Saving backup file backup gid Saved Command Figure 5 11 Meshing the boundary of the room 38 A solution to the problem can now be generated by selecting Calculate gt Calculate A dialog box will appear telling you once the solution is done Click OK To review the results once must enter the postprocessor Select Files gt Postprocess To display the pressure over the bound ary of the room select View results gt Contour fill gt Press amp Figure 5 12 18 x Gi Files View Utilities Docuts Viewresults Options Windows Help 2OSCS MSIYO SSA le GiD Veen y R a BNO Sew Ss 7 X E Pres amp 182 8 162 75 142 71 122 66 102 61 82 566 62 519 42 472 22 425 y 2 38 dy ARIS IEY mus ZnS E E W ANS Contour Fill of P
35. lly absorbed no reflections resulting in a travelling wave Either the previous example stand gid can be loaded up or a com pletely new model can be made To make changes to example one load up stand gid and save as trav gid To start a new model open up a new project and save it in your working folder as trav gid Follow the same steps as outlined in the first example up to and including the step where the velocity boundary conditions are defined Prior to leaving the boundary condition environment ie after the as signment of unit velocity to mimic the piston but before selecting finish absorption needs to be added to the downstream end of the duct To do this click on Impedance Set the real normal impedance to 415 03 the product of the speed of sound in air and the density of air 343 and 1 21 respectively and leave the imaginary normal impedance as 0 Click as sign and then using the mouse select the surface at z 10 the far end of the duct see Figure 3 1 Select finish to complete the assignment of boundary conditions 21 3 EXAMPLE Two TRAVELLING WAVE IN A DUCT GiD Project trav w o E e el g DS y ES ISBAIADI MOD Enter Surfaces with new values Added 1 new surfaces to the selection Enter more surfaces ESC to leave Command Figure 3 1 Adding an impedance to the duct 22 Select Data gt Problem data Give t
36. lly to 5 entities Mesh Generated To see it use command meshview v Command f Figure 7 6 Meshed semi sphere 62 A solution to the problem can now be generated by selecting Calculate gt Calculate A dialog box will appear telling you once the solution is done Click OK The file sphere fdat will have been created in your working directory You can open this using a text editor to review your results Numerous columns of data appear each labelled with a heading in the first row Each row of data corresponds to one calculation frequency Of particular interest are the first second and ninth columns the frequency condition number and pressure amplitude respectively The condition number is important as it gives an indication of how well conditioned the matrix to be inverted is The closer the condition number is to unity the better the conditioning The higher the condition number the more poorly conditioned the matrix is and hence the results obtained at these frequencies are more likely to be incorrect Note that at certain frequencies the condition number is high Save the file in a separate folder for comparative puposes which will be explained later One disadvantage to the direct BEM approach is that if the Kirchoff Helmholtz integral equation is used to represent the sound field on the exterior of a finite volume at the natural frequencies of the interior of the finite volume the exterior problem b
37. mple Seven Model Loudspeaker The second exterior problem is of a spherical volume with an external ve locity over a proportion of its surface representing a simplified model of a loudspeaker in a rigid walled box see Figure 1 1 g This problem highlights the frequency dependance of radiation This example is currently a work in progress and will be avail able soon 67 Chapter 9 Example Eight Actual Loudspeaker The final exterior problem applies external BEM to a more realistic situa tion by analysing radiation from a speaker of more realistic geometry see Figure 1 1 4 This example is currently a work in progress and will be avail able soon 69 Chapter 10 Conclusion The tutorial material described within this document covered some funda mental acoustic problems and how these would be solved using the newly developed BEM interface The tutorials should have equipped the user with the necessary understanding and tools required for reliable application of BEM to other more complex systems Modelling of systems that have complexities beyond the limitations of the Helm3D BEM code will require the use of larger commercial BEM codes however the BEM and acoustic fundamentals obtained using Helm3D will form a solid basis for any future acoustic BEM analyses regardless of the chosen program 71 References J A Pederson and G Munch Driver directivity control by sound redistibution In 113th Convention of the
38. n 2 Tutorial structure tioned BEM book also needs to be copied and placed within the helm3d gid folder 1 3 Tutorial structure The tutorial guides the user through BEM modelling with eight problems each introducing different aspects of e fundamental concepts in acoustics e BEM specific concepts and e using the GiD Helm3d interface The tutorial material comprises step by step instructions which explain how to input each model apply boundary conditions and postprocess the re sults Comparisons with analytical solutions are given when possible By the end of the tutorial the user should have had an introduction to these fundamental concepts in acoustics e one dimensional standing waves e one dimensional travelling waves e impedance sound absorbing boundary conditions e modes in a rectangular room e modes in more complex spaces e one dimensional spherical waves e sound radiation from a sphere and e sound radiation from more complex shapes The user should understand these BEM specific concepts e advantages and disadvantages when compared to other techniques e interior versus exterior problems e element types e mesh size 6 elements per wavelength 1 INTRODUCTION non uniqueness difficulty CHIEF points symmetry and direction of normals The user should also have a working knowledge of these GiD Helm3d inter face concepts inputting the geometry into GiD directly importin
39. ocity at the point of excitation can be obtained An example comparing the theory and BEM solutions was 19 2 EXAMPLE ONE STANDING WAVE IN A DUCT constructed using Matlab see Figure 2 13 o a specific acoustic impedance kgs Tm o o 20 40 60 80 100 frequency Hz theory BEM Figure 2 13 Harmonic response of an open closed acoustic duct at the point of excitation Try comparing your BEM results with the theoretical solution using your preferred graphing package 2 1 Extension An important point to consider in BEM problems is mesh size In order for a BEM solution to be accurate there must be a sufficient number of elements per wavelength Hence at higher frequency the mesh density must be greater Try experimenting with your mesh density and analysis frequency to see how these affect your solution Compare the BEM results with the theoretical result for each case It has been proposed that for accurate BEM results to be obtained there should be a minimum of six elements per wavelength Does this hypothesis hold true for the case of an open closed duct 20 Chapter 3 Example Two Travelling Wave in a Duct The second example see Figure 1 1 b is a simple model of a 1D travelling wave in a rigid walled duct This problem introduces the concept of impedance by the addition of absorption to the downstream end of the duct studied in the first example The wave is fu
40. on Select Utilities gt Draw Normals gt Surfaces To select all surfaces type lt gt in the command line and then press enter Right click the mouse and select Contextual gt Swap some Click on all of the surfaces that have an inward pointing normal until all surfaces are oriented in the correct direction see Figure 5 8 Hit esc to leave the Draw Normals mode ax Files View Geometry Utilities Data Meshing Calculate Help ROCSCB HGIVO FSA 4 GiD Ves ES 0 7 N a Q x lt I a 0 a 4 E Added 1 new surfaces to the selection Enter more surfaces ESC to leave X Changed sense to 1 entities Can continue Command f Figure 5 8 Correct orientation of the surface normals 35 5 EXAMPLE FOUR SPEAKER IN A ROOM The next step is to define the problem as a Helm3D BEM problem To do this select Data gt Problem type gt helm3d A dialog window warning the user that all data information will be lost will appear Select OR The only boundary conditions required for this problem are velocity boundary conditions A velocity of 1 0i is needed to mimic the piston at the source location All other surfaces need to be set to zero velocity To do this select Data gt Conditions Click on Velocity Set both the real and imaginary velocity components to zero Click on assign Type lt gt in the command line to select all surfaces and select finish
41. orking directory as car gid Import the car geometry car igs into GiD Files gt Import gt IGES An information window specifying the read time and geometry information of the model will appear Click close The car geometry should have appeared see Figure 6 1 41 6 EXAMPLE FIVE SOUND IN A CAR GiD Project car Files View Geometry Utilities Data Meshing Calculate Help 2ROCOMGISO FSA 4 GiD Veron 9 Z a Q 2 lt I a o EA HE Enter name of IGES file to read ha leaving IGES reading a Command f Figure 6 1 Imported car geometry 42 The geometry was originally constructed in mm and hence it is necessary to scale it to metres To see the current point coordinates select Utilities gt List gt Points type lt gt in the command line to select all points and press esc A list entities window will appear listing the coordinates of each point see Figure 6 2 List Entities POINT 733 736925 1587 280990 1278 200972 Figure 6 2 Listing the point coordinates 43 6 EXAMPLE FIVE SOUND IN A CAR To list all of the coordinates in one window see Figure 6 3 select List Alternatively you can track backwards and forwards through each node by selecting Prev or Next To close the lists select Close List Entities Tot xj Select entity 733 736925 1587 280990 2 733 736925 1587 28
42. reaks down and the matrix becomes ill conditioned This is well documented 9 and many solutions have been attempted 10 11 The CHIEF method 10 is commonly used to over come the interior natural frequency problem because of its simplicity This technique solves an overdetermined system of equations formed by placing extra points CHIEF points inside the volume of interest Provided the CHIEF points are not placed at a nodal line of the interior solution this will improve the matrix condition number and allow the matrix to be solved using least squares methods Re enter the preprocessor and alter the problem data to include a CHIEF point check the CP box to indicate the inclusion of a chief point set Chief point x to be 0 and output node to be 1 Remesh and resolve the prob lem Save the newly generated fdat file for future comparison Repeat the process with Chief point x at 0 5 The analytical solution for the pressure produced by a pulsating sphere which can be derived from the spherical wave equation is r Ey 300 omikra 7 1 PO IT ika where a is the sphere radius r is the radius at which the pressure is being calculated and w is the angular frequency The characteristic eigenfrequen 63 7 EXAMPLE SIX PULSATING SPHERE cies of the sphere which are the eigenfrequencies of the interior Dirichlet problem are given by the equation sin ka 0 7 2 Compare the theoretical and BEM results saved in th
43. res amp Enter variable name Contour Fill Pres_amp Min 2 38 Max 182 8 y Command f Figure 5 12 Pressure amplitude over the boundary of the room 39 5 EXAMPLE FOUR SPEAKER IN A ROOM 5 1 Extension The solution was obtained at the resonance frequency associated with one of the room dimensions Try comparing solutions obtained both at and away from the various resonances associated with the room Can you see a pattern hint The resonance frequencies of the room are given by the equation a Nez yo Mya Mero f ay GP eG TG 51 where c is the speed of sound in the media ng ny and n are the integer mode numbers in the x y and z axial directions respectively and L Ly and L are the lengths of the room in the x y and z directions respectively The axial resonances occur when two of the mode numbers are set to zero and the other is not Tangential resonances occur when one of the mode numbers is zero and oblique resonances occur when all mode numbers are non zero Try comparing sources of identical volume velocity but different shapes such as circular or rectangular sources and sizes hint the original source is 0 2 m by 0 2 m or 0 04 m in area and has a velocity of 1 m s correspond ing to a volume velocity of 0 04 m s Hence if you increase or decrease the total area of the source the velocity boundary condition of the source must be decreased or increased by an amount whic
44. s and select finish Change the real velocity component to 1 Click on assign and select only the vertical surface at the far rear end of the car see Figure 6 8 Select finish and then Close The boundary conditions have now been set 218 x Eiles View Geometry Utilities Data Meshing Calculate Help A OSB MGIYO SSA le Giron R amp gt XN Velociy E Normal Velocity Re fT NN Normal Velocity Im O ZS ESO Lips lt I a is LEY w ZI LA amp Added 1 new surfaces to the selection Enter more surfaces ESC to leave y Saving backup file backup gid Saved Command ff Figure 6 8 Implementing the velocity boundary condition 49 6 EXAMPLE FIVE SOUND IN A CAR Select Data gt Problem data Give the project a title of lt car gt Ensure the boundary type is selected to be internal and that the density and speed of sound are selected to be 1 21 and 343 respectively Set the frequency start and frequency stop to be 100 and then click Accept data and Close see Figure 6 9 Problem Data El 3 fear ed Moe JETS AC foo o o o o Moo 2088 Figure 6 9 Problem data for car 50 The next step is to mesh the surface of the car Select Meshing gt Generate A dialog box will appear asking you to Enter the size of elements to be generated Type in lt 0 4 gt and press OK A dialo
45. ts eau a aes a do 5 2 Example One Standing Wave in a Duct T Ze EXTENSION area ul dara Serge 1B dena Md NG 20 3 Example Two Travelling Wave in a Duct 21 4 Example Three Side Branch Resonator 25 5 Example Four Speaker in a Room 27 SE Extensions a As ld eR a S 40 6 Example Five Sound in a Car 41 6 AERCUSIOA eta A IA EA E 53 7 Example Six Pulsating Sphere 55 8 Example Seven Model Loudspeaker 67 9 Example Eight Actual Loudspeaker 69 10 Conclusion 71 References 73 List of Tables 2 1 Coordinates of the duct vertices List of Figures 1 1 Breakdown of the tutorial problems 2 1 Rectangular obeso d Sy cde niet amp 2 2 Entering the point coordinates 2 3 Joining the points to form a prism ei 408 444 at ed 2 4 Constructing the prism surfaces ado oa a 2 5 Draw Normals environment malaria a 2 6 All normals are oriented correctly for an internal BEM problem 2 7 Setting the z 0 velocity boundary condition 2 8 Defining the problem data ys aaa es le es 2 9 View of the meshed tube o 2 10 Process information dialog box 2 11 Pressure amplitude over boundary of duct 2 12 Altering the problem data to sweep over a frequency range 2 13 Harmonic response of an open closed acoustic duct at the point Ofexcitation e st td ee bend Bik oe Reh Oe Ae Kod a 3 1 Adding an impedance to the duct
46. ure 6 7 Press esc to leave the draw normals environment asi Files View Geometry Utilities Data Meshing Calculate Help 2OSS MGIOOSSFSIA 4 Gi Veron y R a SBE SAO NOON ZX Added 1 new surfaces to the selection Enter more surfaces ESC to leave Changed sense to 1 entities Can continue v Command Figure 6 6 Checking the surface normals 47 6 EXAMPLE FIVE SOUND IN A CAR x Files View Geometry Utilities Data Meshing Calculate Help Eep 2OVOAGIDOIS IA A amp 0 Z N a E 5 lt I Na E 2 3 zx Added 1 new surfaces to the selection Enter more surfaces ESC to leave Changed sense to 1 entities Can continue y Command f Figure 6 7 All surface normals are oriented correctly 48 The next step is to define the problem as a Helm3D BEM problem To do this select Data gt Problem type gt helm3d A dialog window warning the user that all data information will be lost will appear Select OK The only boundary conditions required for this problem are velocity boundary conditions A velocity of 1 0i is used to represent sound trans mission through the engine firewall All other surfaces need to be set to zero velocity To do this select Data gt Conditions Click on Velocity Set both the real and imaginary velocity components to zero Click on assign Type lt gt in the command line to select all surface
47. within the problem data environment Data gt Problem data Change frequency start to 1 frequency stop to 110 and frequency interval to a suitably such as 1 as depicted in Figure 2 12 the smaller the increment the higher the resolution of the result but the necessary computational effort also increases If the problem data or conditions are changed the model must always be remeshed before the new solution is obtained To do this select Meshing gt Generate A warning will appear alerting you that the old mesh will be erased and asking you whether to continue with the mesh Click OK for this and the following two dialog boxes Generate a new solution to the problem Calculate gt Calculate A greater period of time will elapse before the dialog box telling you that the solution is done appears This is due to a separate solution having to be generated at each frequency increment Once the solution is complete you can once again enter the postprocessor to review your results Files gt Postprocess The pressure at the field point 0 0 0 ie the point of excitation at each frequency can be viewed by opening the output fdat file using any simple text editor which will have appeared in your working folder the folder in which you have saved stand The first line contains the headings of each column of data Of greatest interest in this case are the first column which is the frequency and the ninth column wh
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