Structural Acoustics and Vibration: Mechanical Models, Variational Formulations and Discretization
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Table of contents
- Cover
- Contentsv
- Prefacexi
- Chapter I. A Strategy for Structural-Acoustic Problems1
- 1. Introduction1
- 2. Structural-acoustic master system2
- 3. Concept of fuzzy structure and structural-acoustic fuzzy system2
- 4. LF, MF and HF frequency ranges3
- 5. Strategy used for the LF and MF ranges4
- 6. Excitations and responses5
- 7. Organization of the book6
- Chapter II. Bask Notions on Variational Formulations9
- 1. Introduction9
- 2. Boundary value problem9
- 3. Strong solution of the boundary value problem10
- 4. Variational formulation and weak solution of the boundary value problem11
- 5. Converse12
- 6. Associated linear operator equation13
- 7. Ritz-Galerkin approximation and finite element method14
- 8. Bibliographical comments17
- Chapter III. Linearized Vibrations of Conservative Structures and Structural Modes19
- 1. Introduction19
- 2. Conservative elastodynamic boundary value problem in a bounded medium with initial Cauchy conditi20
- 3. Associated spectral problem: eigenfrequencies and structural modes23
- 4. Variational formulation of the spectral problem23
- 5. Associated linear operators and algebraic properties25
- 6. Basic properties of the eigenfrequencies and structural modes for a structure fixed on ***28
- 7. Basic properties of the eigenfrequencies and structural modes for a free structure29
- 8. Cases of structures with symmetry properties33
- 9. Finite element discretization and generalized symmetric matrix eigenvalue problem40
- 10. Dynamic substructuring procedures for calculation of the structural modes41
- Chapter IV. Dissipative Constitutive Equation for the Master Structure51
- 1. Introduction51
- 2. Notation for the Fourier transform52
- 3. Damping model with frequency-independent coefficients52
- 4. Model with frequency-dependent coefficients based on the linear theory of viscoelasticity53
- 5. Summary57
- Chapter V. Master Structure Frequency Response Function61
- 1. Introduction61
- 2. Equations in the frequency domain62
- 3. Variational formulation65
- 4. Linear operators and algebraic properties66
- 5. Frequency response function70
- 6. Finite element discretization75
- 7. Boundary impedance operator76
- Chapter VI. Calculation of the Master Structure Frequency Response Function in the LF Range85
- 1. Introduction85
- 2. FRF model in the LF range86
- 3. Projection of the FRF on the elastic structural modes of the associated conservative system87
- 4. Remark on a nonviscoelastic model diagonalized by the elastic structural modes90
- 5. Introduction of quasi-static correction terms94
- 6. Frequency-by-frequency construction of the FRF95
- Chapter VII. Calculation of the Master Structure Frequency Response Function in the MF Range97
- 1. Introduction97
- 2. FRF model in the MF range98
- 3. Definition of an MF narrow band99
- 4. Class of MF narrow band excitation force fields100
- 5. Approximation of the FRF on an MF narrow band due to the frequency-dependent damping and stiffnes101
- 6. Analytical processing of the short time scale in the frequency domain and numerical processing of102
- 7. Construction of the FRF on an MF broad band106
- 8. Finite element discretization107
- Chapter VIII. Reduced Model in the MF Range109
- 1. Introduction109
- 2. Definition of a narrow MF band110
- 3. Energy properties of a simple-linear-oscillator response110
- 4. Variational formultaion of the master structure in the MF range117
- 5. Construction of an appropriate functional basis for the reduced model in the MF range119
- 6. Construction of a reduced model in the MF range123
- 7. Finite element discretization124
- 8. Construction of the dominant eigensubspace using the subspace iteration method127
- Chapter IX. Response to Deterministic and Random Excitations129
- 1. Introduction129
- 2. Operator-valued FRF and associated linear filter in the time domain129
- 3. LF and MF deterministic cases: time-periodic excitation134
- 4. LF and MF deterministic cases: time square integrable excitation138
- 5. LF and MF random cases: time stationary stochastic excitation141
- 6. Random case: nonstationary stochastic excitation153
- Chapter X. Linear Acoustic Equations169
- 1. Introduction169
- 2. Inviscid acoustic fluid169
- 3. Dissipative acoustic fluid179
- Chapter XI. Internal Acoustic Fluid Formulation for the LF and MF Ranges189
- 1. Introduction189
- 2. Statement of the internal acoustic problem190
- 3. Boundary value problem190
- 4. Variational formulation and linear operator equation192
- 5. Frequency response function195
- 6. Finite element discretization195
- 7. Acoustic modes of the acoustic cavity197
- 8. Finite element discretization and generalized symmetric matrix eigenvalue problem199
- 9. FRF calculation in the LF range199
- 10. FRF calculation in the MF range205
- 11. Case of a zero pressure condition on part of the boundary209
- 12. Particular case of an axisymmetric acoustic cavity214
- 13. Response to deterministic and random excitations214
- Chapter XII. External Acoustic Fluid. Boundary Integral Formulation for the LF and MF Ranges215
- 1. Introduction215
- 2. Statement of the external acoustic problem217
- 3. Exterior Neumann problem related to the Helmholtz equation218
- 4. Acoustic impedance boundary operator and radiation impedance operator221
- 5. Free-space Green's function and solution of the inhomogeneous Helmholtz equation224
- 6. Response to prescribed wall displacement, acoustic source density and incident plane wave226
- 7. Results of potential theory: single- and double-layer potentials231
- 8. Helmholtz integral representations and their normal derivatives233
- 9. Boundary integral equations for the exterior Neumann problem related to the Helmholtz equation237
- 10. Acoustic impedance boundary operator construction: appropriate symmetric boundary integral metho244
- 11. Construction of the radiation impedance operator and asymptotic formula for the radiated pressur246
- 12. Symmetric boundary element method valid for all real values of the frequency249
- 13. Case of a free surface253
- Chapter XIII. Structural-Acoustic Master System in the LF range255
- 1. Introduction255
- 2. Statement of the structural-acoustic problem in the frequency domain256
- 3. Boundary value problem of the structural-acoustic master system259
- 4. Variational formulation of the structural-acoustic problem261
- 5. Finite element discretization269
- 6. Symmetric reduced matrix model in the LF range272
- 7. FRF calculation in the LF range278
- 8. Location of the resonant frequencies of the coupled system282
- 9. Structural-acoustic modes of the master structure coupled with an internal acoustic fluid283
- 10. Case of a master structure coupled with an external acoustic fluid288
- 11. Structure coupled with an external and an internal acoustic fluid. Case of a zero pressure condi296
- 12. Case of an axisymmetric structural-acoustic master system304
- 13. Response to deterministic and random excitations305
- Chapter XIV. Structural-Acoustic Master System in the MF Range307
- 1. Introduction307
- 2. Statement of the structural-acoustic problem in the frequency domain308
- 3. Boundary value problem of the structural-acoustic master system311
- 4. Variational formulation of the structural-acoustic problem313
- 5. Finite element discretization320
- 6. FRF calculation in the MF range323
- 7. Case of a master structure coupled with an external acoustic fluid329
- 8. Structure coupled with an external and an internal acoustic fluid. Case of a zero pressure condit333
- 9. Case of an axisymmetric structural-acoustic master system340
- 10. Response to deterministic and random excitations341
- 11. Bibliographical comments341
- Chapter XV. Fuzzy Structure Theory343
- 1. Introduction343
- 2. Statement of the problem344
- 3. Fuzzy structure theory stated as an inverse problem348
- 4. Random equation of the master structure coupled with fuzzy substructures in terms of the displace353
- 5. Homogeneous model of a fuzzy substructure355
- 6. Construction of a homogeneous fuzzy impedance law for a fuzzy substructure and for a local direct358
- 7. Solving method for the random equation of the master structure coupled with fuzzy substructures372
- 8. Ritz-Galerkin approximation and finite element discretization377
- 9. Identification method for the parameters of type I and type II fuzzy impedance laws381
- 10. Case of a real structure constituted by a master structure coupled with a very large number of s391
- Appendix: Mathematical Notations393
- References415
- Subject Index417
- Symbol Index423
Structural Acoustics and Vibration presents the modeling of vibrations of complex structures coupled with acoustic fluids in the low and medium frequency ranges. It is devoted to mechanical models, variationalformulations and discretization for calculating linear vibrations in the frequency domain of complex structures. The book includes theoretical formulations which are directly applicable to develop computer codes for the numerical simulation of complex systems, and gives a general scientific strategy to solve various complex structural acoustics problems in different areas such as spacecraft, aircraft, automobiles, and naval structures. The researcher may directly apply the material of the book to practical problems such as acoustic pollution, the comfort of passengers, and acoustic loads induced by propellers.
Structural Acoustics and Vibration considers the mechanical and numerical aspects of the problem, and gives original solutions to the predictability of vibrations of complex structures interacting with internal and external, liquid and gaseous fluids. It is a self-contained general synthesis with a didactic presentation and fills the gap between analytical methods applied to simple geometries and statistical methods, which are useful in high frequency structural acoustic problems.
Key Features
* Provides for the first time complex structures in scientific literature
* Presents a self-contained general synthesis with a didactic presentation
* Integrates the most advanced research topics on the subject
* Enables the researcher to solve complex structural acoustics problems in areas such as spacecraft, aircraft, automobiles, and naval structures
* Fills the gap between analytical methods applied to simple geometries and statistical methods
Contains advanced mechanical and numerical modeling
* Provides appropriate formulations directly applicable for developing computer codes for the numerical simulation of complex systemssystems
Structural Acoustics and Vibration considers the mechanical and numerical aspects of the problem, and gives original solutions to the predictability of vibrations of complex structures interacting with internal and external, liquid and gaseous fluids. It is a self-contained general synthesis with a didactic presentation and fills the gap between analytical methods applied to simple geometries and statistical methods, which are useful in high frequency structural acoustic problems.
Key Features
* Provides for the first time complex structures in scientific literature
* Presents a self-contained general synthesis with a didactic presentation
* Integrates the most advanced research topics on the subject
* Enables the researcher to solve complex structural acoustics problems in areas such as spacecraft, aircraft, automobiles, and naval structures
* Fills the gap between analytical methods applied to simple geometries and statistical methods
Contains advanced mechanical and numerical modeling
* Provides appropriate formulations directly applicable for developing computer codes for the numerical simulation of complex systemssystems