9780125249454

Structural Acoustics and Vibration

by ;
  • ISBN13:

    9780125249454

  • ISBN10:

    0125249454

  • Format: Hardcover
  • Copyright: 1997-10-28
  • Publisher: Elsevier Science
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Summary

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

Table of Contents

Preface xi
Chapter I. A Strategy for Structural-Acoustic Problems
1(8)
1. Introduction
1(1)
2. Structural-acoustic master system
2(1)
3. Concept of fuzzy structure and structural-acoustic fuzzy system
2(1)
4. LF, MF and HF frequency ranges
3(1)
5. Strategy used for the LF and MF ranges
4(1)
6. Excitations and responses
5(1)
7. Organization of the book
6(3)
Chapter II. Basic Notions on Variational Formulations
9(10)
1. Introduction
9(1)
2. Boundary value problem
9(1)
3. Strong solution of the boundary value problem
10(1)
4. Variational formulation and weak solution of the boundary value problem
11(1)
5. Converse
12(1)
6. Associated linear operator equation
13(1)
7. Ritz-Galerkin approximation and finite element method
14(3)
8. Bibliographical comments
17(2)
Chapter III. Linearized Vibrations of Conservative Structures and Structural Modes
19(32)
1. Introduction
19(1)
2. Conservative elastodynamic boundary value problem in a bounded medium with initial Cauchy conditions
20(3)
3. Associated spectral problem: eigenfrequencies and structural modes
23(1)
4. Variational formulation of the spectral problem
23(2)
5. Associated linear operators and algebraic properties
25(3)
6. Basic properties of the eigenfrequencies and structural modes for a structure fixed on XXX(0)
28(1)
7. Basic properties of the eigenfrequencies and structural modes for a free structure
29(4)
8. Cases of structures with symmetry properties
33(7)
9. Finite element discretization and generalized symmetric matrix eigenvalue problem
40(1)
10. Dynamic substructuring procedures for calculation of the structural modes
41(10)
Chapter IV. Dissipative Constitutive Equation for the Master Structure
51(10)
1. Introduction
51(1)
2. Notation for the Fourier transform
52(1)
3. Damping model with frequency-independent coefficients
52(1)
4. Model with frequency-dependent coefficients based on the linear theory of viscoelasticity
53(4)
5. Summary
57(4)
Chapter V. Master Structure Frequency Response Function
61(24)
1. Introduction
61(1)
2. Equations in the frequency domain
62(3)
3. Variational formulation
65(1)
4. Linear operators and algebraic properties
66(4)
5. Frequency response function
70(5)
6. Finite element discretization
75(1)
7. Boundary impedance operator
76(9)
Chapter VI. Calculation of the Master Structure Frequency Response Function in the LF Range
85(12)
1. Introduction
85(1)
2. FRF model in the LF range
86(1)
3. Projection of the FRF on the elastic structural modes of the associated conservative system
87(3)
4. Remark on a nonviscoelastic model diagonalized by the elastic structural modes
90(4)
5. Introduction of quasi-static correction terms
94(1)
6. Frequency-by-frequency construction of the FRF
95(2)
Chapter VII. Calculation of the Master Structure Frequency Response Function in the MF Range
97(12)
1. Introduction
97(1)
2. FRF model in the MF range
98(1)
3. Definition of an MF narrow band
99(1)
4. Class of MF narrow band excitation force fields
100(1)
5. Approximation of the FRF on an MF narrow band due to the frequency dependent damping and stiffness operators
101(1)
6. Analytical processing of the short time scale in the frequency domain and numerical processing of the long time scale in the time domain
102(4)
7. Construction of the FRF on an MF broad band
106(1)
8. Finite element discretization
107(2)
Chapter VIII. Reduced Model in the MF Range
109(20)
1. Introduction
109(1)
2. Definition of a narrow MF band
110(1)
3. Energy properties of a simple-linear-oscillator response
110(7)
4. Variational formultaion of the master structure in the MF range
117(2)
5. Construction of an appropriate functional basis for the reduced model in the MF range
119(4)
6. Construction of a reduced model in the MF range
123(1)
7. Finite element discretization
124(3)
8. Construction of the dominant eigensubspace using the subspace iteration method
127(2)
Chapter IX. Response to Deterministic and Random Excitations
129(40)
1. Introduction
129(1)
2. Operator-valued FRF and associated linear filter in the time domain
129(5)
3. LF and MF deterministic cases: time-periodic excitation
134(4)
4. LF and MF deterministic cases: time square integrable excitation
138(3)
5. LF and MF random cases: time stationary stochastic excitation
141(12)
6. Random case: nonstationary stochastic excitation
153(16)
Chapter X. Linear Acoustic Equations
169(20)
1. Introduction
169(1)
2. Inviscid acoustic fluid
169(10)
3. Dissipative acoustic fluid
179(10)
Chapter XI. Internal Acoustic Fluid Formulation for the LF and MF Ranges
189(26)
1. Introduction
189(1)
2. Statement of the internal acoustic problem
190(1)
3. Boundary value problem
190(2)
4. Variational formulation and linear operator equation
192(3)
5. Frequency response function
195(1)
6. Finite element discretization
195(2)
7. Acoustic modes of the acoustic cavity
197(2)
8. Finite element discretization and generalized symmetric matrix eigenvalue problem
199(1)
9. FRF calculation in the LF range
199(6)
10. FRF calculation in the MF range
205(4)
11. Case of a zero pressure condition on part of the boundary
209(5)
12. Particular case of an axisymmetric acoustic cavity
214(1)
13. Response to deterministic and random excitations
214(1)
Chapter XII. External Acoustic Fluid. Boundary Integral Formulation for the LF and MF Ranges
215(40)
1. Introduction
215(2)
2. Statement of the external acoustic problem
217(1)
3. Exterior Neumann problem related to the Helmholtz equation
218(3)
4. Acoustic impedance boundary operator and radiation impedance operator
221(3)
5. Free-space Green's function and solution of the inhomogeneous Helmholtz equation
224(2)
6. Response to prescribed wall displacement, acoustic source density and incident plane wave
226(5)
7. Results of potential theory: single- and double-layer potentials
231(2)
8. Helmholtz integral representations and their normal derivatives
233(4)
9. Boundary integral equations for the exterior Neumann problem related to the Helmholtz equation
237(7)
10. Acoustic impedance boundary operator construction: appropriate symmetric boundary integral method valid for all real values of the frequency
244(2)
11. Construction of the radiation impedance operator and asymptotic formula for the radiated pressure field
246(3)
12. Symmetric boundary element method valid for all real values of the frequency
249(4)
13. Case of a free surface
253(2)
Chapter XIII. Structural-Acoustic Master System in the LF range
255(52)
1. Introduction
255(1)
2. Statement of the structural-acoustic problem in the frequency domain
256(3)
3. Boundary value problem of the structural-acoustic master system
259(2)
4. Variational formulation of the structural-acoustic problem
261(8)
5. Finite element discretization
269(3)
6. Symmetric reduced matrix model in the LF range
272(6)
7. FRF calculation in the LF range
278(4)
8. Location of the resonant frequencies of the coupled system
282(1)
9. Structural-acoustic modes of the master structure coupled with an internal acoustic fluid
283(5)
10. Case of a master structure coupled with an external acoustic fluid
288(8)
11. Structure coupled with an external and an internal acoustic fluid. Case of a zero pressure condition on part of the internal fluid boundary
296(8)
12. Case of an axisymmetric structural-acoustic master system
304(1)
13. Response to deterministic and random excitations
305(2)
Chapter XIV. Structural-Acoustic Master System in the MF Range
307(36)
1. Introduction
307(1)
2. Statement of the structural-acoustic problem in the frequency domain
308(3)
3. Boundary value problem of the structural-acoustic master system
311(2)
4. Variational formulation of the structural-acoustic problem
313(7)
5. Finite element discretization
320(3)
6. FRF calculation in the MF range
323(6)
7. Case of a master structure coupled with an external acoustic fluid
329(4)
8. Structure coupled with an external and an internal acoustic fluid. Case of a zero pressure condition on part of the internal fluid boundary
333(7)
9. Case of an axisymmetric structural-acoustic master system
340(1)
10. Response to deterministic and random excitations
341(1)
11. Bibliographical comments
341(2)
Chapter XV. Fuzzy Structure Theory
343(50)
1. Introduction
343(1)
2. Statement of the problem
344(4)
3. Fuzzy structure theory stated as an inverse problem
348(5)
4. Random equation of the master structure coupled with fuzzy substructures in terms of the displacement field of the master structure
353(2)
5. Homogeneous model of a fuzzy substructure
355(3)
6. Construction of a homogeneous fuzzy impedance law for a fuzzy substructure and for a local direction
358(14)
7. Solving method for the random equation of the master structure coupled with fuzzy substructures
372(5)
8. Ritz-Galerkin approximation and finite element discretization
377(4)
9. Identification method for the parameters of type I and type II fuzzy impedance laws
381(10)
10. Case of a real structure constituted by a master structure coupled with a very large number of simple oscillators. Application of the fuzzy structure theory
391(2)
Appendix. Mathematical Notations 393(14)
References 407(10)
Subject Index 417(6)
Symbol Index 423

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