Theoretical Acoustics of... | Buy

This important book provides an account of the linear acoustics of basic isotropic/anisotropic structures excited by time-harmonic and transient mechanical forces and acoustic sources. Many examples are given to aid physical insight and to provide benchmark computations of sound radiation and sound scattering. The theoretical methods, developed originally for naval noise control problems, should find civil application in the acoustic modelling of structures fabricated from both fibre-reinforced and isotropic materials, such an endeavour being increasingly desirable and necessary in this noisy world.

PREFACE

xi

(2)

ACKNOWLEDGEMENTS

xiii

INTRODUCTION

1

(6)

1 MATHEMATICAL METHODS

7

(36)

1.1 Fourier Series

7

(2)

1.2 Fourier Transforms

9

(2)

1.3 Delta Functions

11

(3)

1.4 Vector and Scalar Identities

14

(4)

1.5 Integral Theorems

18

(1)

1.6 Bessel Functions

19

(4)

1.7 Spherical Bessel Functions

23

(3)

1.8 Legendre Functions

26

(2)

1.9 Stationary Phase

28

(2)

1.10 Matrices

30

(4)

1.11 Numerical Integration

34

(9)

2 RESPONSE OF DYNAMICAL SYSTEMS

43

(18)

2.1 Time-Harmonic Response

43

(4)

2.2 Transient Response

47

(8)

2.3 Time-Harmonic Power Flow

55

(6)

3 ACOUSTIC EQUATIONS

61

(22)

3.1 Differential Equation

61

(5)

3.2 Plane Wave Solutions

66

(1)

3.3 Green's Function in Cartesian Coordinates

67

(3)

3.4 Green's Function in Cylindrical Coordinates

70

(3)

3.5 Green's Function in Spherical Coordinates

73

(2)

3.6 Arbitrary Source Distribution

75

(2)

3.7 Arbitrary Boundaries

77

(1)

3.8 Helmholtz Integral Equation

77

(6)

4 SCATTERING FROM HARD AND SOFT STRUCTURES

83

(32)

4.1 Planar Surface

83

(5)

4.2 Spherical Surface

88

(4)

4.3 Cylindrical Surface

92

(5)

4.4 Axisymmetric Slender Body

97

(9)

4.5 Monopole in Axisymmetric Channel

106

(9)

5 ACOUSTIC FINITE ELEMENTS

115

(18)

5.1 Variational Principle

115

(4)

5.2 Finite Element Discretization

119

(2)

5.3 Acoustic Finite Elements

121

(2)

5.4 Radiation Boundary Condition

123

(2)

5.5 Sources of Sound

125

(1)

5.6 Axisymmetric Elements

126

(7)

6 ELASTIC EQUATIONS AND CONSTITUTIVE RELATIONS

133

(30)

6.1 Strain and Stress

133

(3)

6.2 Isotropic Displacement Equations

136

(4)

6.3 Finite Element Variational Principle

140

(4)

6.4 Fluid Constants

144

(1)

6.5 Isotropic Elastic Constants

144

(4)

6.6 Anisotropic Solid

148

(2)

6.7 Unidirectional Fibre Reinforcement

150

(1)

6.8 Thin Layered Composite

151

(4)

6.9 Local to Global Transformation

155

(4)

6.10 Effective Constants of Symmetric Stack

159

(4)

7 ACOUSTICS OF SPHERICAL SHELL

163

(16)

7.1 Equations of Motion

163

(2)

7.2 Mechanical Excitation

165

(6)

7.3 Acoustical Excitation

171

(8)

8 ACOUSTICS OF THIN PLATE

179

(62)

8.1 Equations of Motion

179

(1)

8.2 Mechanical Excitation

180

(9)

8.3 Monopole Excitation

189

(2)

8.4 Plane Wave Excitation

191

(2)

8.5 Transient Sound Radiation

193

(5)

8.6 Frame and Bulkhead Stiffened Plate

198

(9)

8.7 Orthogonally Stiffened Plate

207

(6)

8.8 Plate with Point Attachments

213

(8)

8.9 Parallel Plates with Attachments

221

(7)

8.10 Plate with Periodic Resonators

228

(13)

9 ACOUSTICS OF CYLINDRICAL SHELL

241

(42)

9.1 Equations of Isotropic Shell

241

(3)

9.2 Equations of Anisotropic Shell

244

(2)

9.3 Mechanical Excitation

246

(7)

9.4 Monopole Excitation

253

(6)

9.5 Plane Wave Excitation

259

(4)

9.6 Periodic Rib Stiffening

263

(10)

9.7 Axisymmetric Attachments

273

(5)

9.8 Fluid Coating

278

(5)

10 SPHERICALLY LAYERED MEDIA

283

(18)

10.1 Introduction

283

(1)

10.2 Acoustic Fluid Layer

284

(3)

10.3 Isotropic Elastic Layer

287

(4)

10.4 Viscous Fluid Layer

291

(2)

10.5 Assembly of Elements

293

(1)

10.6 Mechanical Excitation

294

(1)

10.7 Acoustical Excitation

295

(2)

10.8 Numerical Examples

297

(4)

11 PLANAR LAYERED MEDIA

301

(42)

11.1 Introduction

301

(2)

11.2 Acoustic Fluid Layer

303

(2)

11.3 Isotropic Elastic Layer

305

(6)

11.4 Orthotropic Elastic Layer

311

(6)

11.5 Viscous Fluid Layer

317

(2)

11.6 Assembly of Elements

319

(1)

11.7 Mechanical Excitation

320

(5)

11.8 Monopole Excitation

325

(4)

11.9 Plane Wave Excitation

329

(4)

11.10 Low Frequency Sound Propagation

333

(10)

12 CYLINDRICALLY LAYERED MEDIA

343

(30)

12.1 Introduction

343

(2)

12.2 Acoustic Fluid Layer

345

(2)

12.3 Isotropic Elastic Layer

347

(7)

12.4 Orthotropic Elastic Layer

354

(5)

12.5 Viscous Fluid Layer

359

(2)

12.6 Assembly of Elements

361

(1)

12.7 Mechanical Excitation

362

(4)

12.8 Monopole Excitation

366

(3)

12.9 Plane Wave Excitation

369

(4)

13 SIMPLY SUPPORTED CYLINDER

373

(22)

13.1 Isotropic Thin Cylinder

373

(3)

13.2 Point Force Excitation

376

(5)

13.3 Plane Wave Excitation

381

(4)

13.4 Anisotropic Layered Cylinder

385

(10)

14 FINITE AXISYMMETRIC STRUCTURE

395

(34)

14.1 Introduction

395

(2)

14.2 Fourier Series

397

(1)

14.3 Helmholtz Integral Equation

397

(6)

14.4 Far Field Acoustics

403

(3)

14.5 Fluid-Structure Equations

406

(2)

14.6 Conical Shell Finite Element

408

(6)

14.7 Axisymmetric Solid Finite Element

414

(6)

14.8 System Dynamic Stiffness

420

(3)

14.9 Numerical Examples

423

(6)

LIST OF COMMONLY OCCURRING SYMBOLS

429

(4)

INDEX

433

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