LMS International Numerical Acoustics
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2.9.1.3 Modal finite element model.........................................................................................................77
2.9.2 Coupled vibro-acoustic problem ........................................................................................79
2.9.2.1 Problem definition .......................................................................................................................79
2.9.2.2 Model reduction techniques.........................................................................................................80
2.10 REFERENCES.......................................................................................................................... 82
3. BOUNDARY ELEMENT MODELING FOR ACOUSTICS ..............................................86
3.1 INTRODUCTION ...................................................................................................................... 86
3.2 PROBLEM DEFINITION............................................................................................................ 87
3.3 BOUNDARY INTEGRAL FORMULATIONS ................................................................................ 89
3.3.1 Preliminary considerations ................................................................................................89
3.3.2 Direct boundary integral formulation................................................................................90
3.3.3 Indirect boundary integral formulation .............................................................................95
3.4 BOUNDARY ELEMENT METHODS ........................................................................................... 99
3.4.1 Direct collocational boundary element method.................................................................99
3.4.1.1 Surface variable approximations .................................................................................................99
3.4.1.2 Direct collocational boundary element model ..........................................................................100
3.4.2 Indirect variational boundary element method................................................................101
3.4.2.1 Variational formulation .............................................................................................................101
3.4.2.2 Surface variable approximations ...............................................................................................104
3.4.2.3 Indirect variational boundary element model............................................................................105
3.5 CONVERGENCE .................................................................................................................... 106
3.5.1 Direct boundary element method .....................................................................................106
3.5.2 Indirect boundary element method...................................................................................110
3.6 PROPERTIES ......................................................................................................................... 111
3.6.1 Direct BEM versus indirect BEM.....................................................................................111
3.6.2 BEM versus FEM..............................................................................................................111
3.7 COUPLED VIBRO-ACOUSTIC PROBLEMS............................................................................... 114
3.7.1 Problem definition ............................................................................................................114
3.7.2 Coupled FE/BE models ....................................................................................................118
3.7.2.1 Coupled FE/direct BE model.....................................................................................................118
3.7.2.2 Coupled FE/indirect BE model .................................................................................................121
3.7.3 Coupled FE/BE versus coupled FE/FE............................................................................124
3.8 REFERENCES........................................................................................................................ 125
4. ATV CONCEPT AND ATV BASED APPLICATIONS ....................................................127
4.1 ACOUSTIC TRANSFER VECTORS.......................................................................................... 127
4.1.1 Direct Collocation Approach ...........................................................................................128
4.1.2 Indirect Variational Approach .........................................................................................128
4.1.3 ATV Interpolation .............................................................................................................129
4.2 ATV-BASED ACOUSTIC FORCED RESPONSE ....................................................................... 133
4.2.1 Radiated Acoustic Pressure..............................................................................................133
4.2.2 Radiated Acoustic Power .................................................................................................134
4.3 PANEL ACOUSTIC CONTRIBUTION ANALYSIS BASED ON ACOUSTIC TRANSFER VECTORS 135
4.3.1 Panel Acoustic Contribution Analysis..............................................................................135
4.4 INVERSE NUMERICAL ACOUSTICS....................................................................................... 136
4.4.1 Fine Approach ..................................................................................................................136
4.4.2 Coarse Approach..............................................................................................................137
4.4.3 Conditioning .....................................................................................................................137
4.4.4 Singular Value Decomposition.........................................................................................138
4.5 REFERENCE: ........................................................................................................................ 139
5. ACOUSTIC TREATMENTS ................................................................................................141
5.1 BACKGROUND ..................................................................................................................... 141
5.1.1 Structure-Cavity coupling with acoustic treatments........................................................141
5.1.1.1 Local governing equations.........................................................................................................142
5.1.1.2 Weak formulation of the problem .............................................................................................143
5.1.1.3 Local Admittance Model ...........................................................................................................144
5.1.1.4 Discretization of the weak formulation. ....................................................................................144
5.1.2 Transfer Admittance between two acoustic faces ............................................................146
5.2 TRIM MODELING AS TRANSFER ADMITTANCE .................................................................... 148
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