كتاب Sound and Structural Vibration

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Sound and Structural Vibration
Radiation, Transmission and Response
FRANK FAHY
Institute of Sound and Vibration Research
University of Southampton
Southampton, UK
PAOLO GARDONIO
Institute of Sound and Vibration Research
University of Southampton
Southampton, UK

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Contents
Preface to the First Edition xiii
Preface to the Second Edition xvii
Acknowledgements xxi
List of Permissions xxiii
Introduction xxv
1. Waves in Fluids and Solid Structures
1.1 Frequency and Wavenumber 1
1.2 Sound Waves in Fluids 8
1.3 Longitudinal Waves in Solids 11
1.4 Quasi-Longitudinal Waves in Solids 13
1.5 Transverse (Shear) Waves in Solids 14
1.6 Bending Waves in Bars 19
1.7 Bending Waves in Thin Plates 26
1.8 Dispersion Curves 27
1.9 Flexural Waves in Thin-Walled Circular Cylindrical
Shells 30
1.10 Natural Frequencies and Modes of Vibration 38
1.11 Forced Vibration and Resonance 50
viiviii CONTENTS
1.12 Modal Density and Modal Overlap 64
1.13 The Roles of Modal Density in Vibroacoustics 69
Problems 72
2. Structural Mobility, Impedance, Vibrational Energy and Power
2.1 Mobility and Impedance Representations 75
2.2 Concepts and General Forms of Mobility and Impedance
of Lumped Mechanical Elements 79
2.3 Mobility Functions of Uniform Beams in Bending 84
2.3.1 Infinite Beam 84
2.3.2 Finite Beam (Closed Form) 87
2.3.3 Finite Beam (Modal Summation) 90
2.4 Mobility and Impedance Functions of Thin Uniform
Flat Plates 102
2.4.1 Infinite Plate 102
2.4.2 Finite Plate 106
2.5 Radial Driving-Point Mobility of Thin-Walled Circular
Cylindrical Shells 110
2.6 Mobility and Impedance Matrix Models 115
2.7 Structural Power 121
2.8 Energy Density and Energy Flux of Vibrational Waves 129
Problems 134
3. Sound Radiation by Vibrating Structures
3.1 The Importance and Mechanism of Sound Radiation by
Vibrating Structures 135
3.2 The Simple Volume Source 138
3.3 Sound Radiation by a Pair of Elementary
Surface Sources 141
3.4 The Baffled Piston 143
3.5 Sound Radiation by Flexural Modes of Plates 145
3.6 Sound Radiation by Plates in Multi-Mode Flexural
Vibration 159
3.6.1 Formulation in Terms of Structural Modes 159
3.6.2 Formulation in Terms of Elementary Radiators 165
3.7 Independent Radiation Modes 168
3.7.1 Formulation in Terms of Structural Modes 169
3.7.2 Formulation in Terms of Elementary Radiators 170
3.7.3 Radiation Modes and Efficiencies 171
3.7.4 A Comparison of Self- and Mutual Radiation by
Plate Modes 172CONTENTS ix
3.8 Sound Radiation by Flexural Waves in Plates 175
3.9 The Frequency-Average Radiation Efficiency of Plates 185
3.10 Sound Radiation due to Concentrated Forces and
Displacements 195
3.11 Sound Radiation by Non-Uniform Plate Structures 204
3.11.1 Beam-Stiffened Plates 204
3.11.2 Corrugated Plates 209
3.11.3 Sandwich Plates 210
3.11.4 Composite Sound Insulation Panels 212
3.12 Sound Radiation by Curved Shells 213
3.13 Sound Radiation by Irregularly Shaped Vibrating Bodies 227
Problems 240
4. Fluid Loading of Vibrating Structures
4.1 Practical Aspects of Fluid Loading 243
4.2 Pressure Fields on Vibrating Surfaces 245
4.3 Wave Impedances of Structures and Fluids 256
4.4 Fluid Loading of Vibrating Plates 261
4.5 Natural Frequencies of Fluid-Loaded Plates 267
4.6 Effects of Fluid Loading on Sound Radiation from
Point-Excited Plates 268
4.7 Natural Frequencies of Fluid-Loaded, Thin-Walled, Circular
Cylindrical Shells 270
4.8 Effects of Fluid Loading on Sound Radiation by Thin-Walled,
Circular Cylindrical Shells 270
4.9 Damping of Thin Plates by Porous Sheets 275
Problems 275
5. Transmission of Sound through Partitions
5.1 Practical Aspects of Sound Transmission through
Partitions 277
5.2 Transmission of Normally Incident Plane Waves through
an Unbounded Partition 278
5.3 Transmission of Obliquely Incident Plane Waves through an
Unbounded Flexible Partition 284
5.4 Transmission of Diffuse Sound through a Bounded Partition
in a Baffle 296
5.5 Transmission of Sound through a Partition between
Two Rooms 299
5.6 Double-Leaf Partitions 303x CONTENTS
5.7 Transmission of Normally Incident Plane Waves through an
Unbounded Double-Leaf Partition 304
5.8 The Theoretical Effect of Cavity Sound Absorption on Normal
Incidence Transmission Loss 310
5.9 Transmission of Obliquely Incident Plane Waves through an
Unbounded Double-Leaf Partition 314
5.10 Mechanical Stiffening and Coupling of Double
Partition Leaves 323
5.11 Close-Fitting Enclosures 330
5.12 Transmission of Sound through Stiffened, Composite, Multilayer
and Non-Uniform Panels 337
5.13 Transmission of Sound through Circular
Cylindrical Shells 352
5.14 Coupling between Shell Modes and Acoustic Modes
of a Contained Fluid 353
5.15 Vibrational Response of Pipes to Internal Acoustic
Excitation 358
5.16 Transmission of Internally Generated Sound through
Pipe Walls 364
5.17 Transmission of Externally Incident Sound through
Large-Diameter, Thin-Walled Cylinders 366
Problems 372
6. Acoustically Induced Vibration of Structures
6.1 Practical Aspects of Acoustically Induced Vibration 375
6.2 Decomposition of a Sound Field 376
6.3 Response of a Baffled Plate to Plane Sound Waves 379
6.4 The Principle of Vibroacoustic Reciprocity 385
6.5 Modal Reciprocity: Radiation and Response 386
6.6 Radiation Due to Point Forces and Response to
Point Sources 391
6.7 An Application of Response Theory to
Building Acoustics 396
Problems 400
7. Acoustic Coupling between Structures and Enclosed Volumes
of Fluid
7.1 Practical Importance of the Problem 403
7.2 A Simple Case of Fluid–Structure Interaction 404CONTENTS xi
7.3 Harmonic Sound Fields in an Enclosed Volume of Fluid 408
7.4 Sound Field in a Closed Space with Rigid Surfaces 414
7.5 Interaction Analysis by Green’s Function 415
7.6 Modal-Interaction Model 418
7.7 Solutions of the Modal-Interaction Model 422
7.8 Power Flow and Statistical Energy Analysis 427
7.9 Wave Propagation in Plates Loaded by Confined
Fluid Layers 433
7.10 Wave Propagation in Fluid-Filled Tubes of Circular
Cross Section 443
Problems 447
8. Introduction to Numerically Based Analyses of Fluid–Structure
Interaction
8.1 The Role of Numerical Analysis 449
8.2 Numerical Analysis of Vibration in Solids and Fluids 451
8.3 Finite Element Analysis 453
8.4 Finite Element Analysis of Vibrations
in Solid Structures 455
8.4.1 Flexural Vibration of Slender Beams: Rayleigh–Ritz
Method 456
8.4.2 Flexural Vibration of Slender Beams: Finite Element
Analysis 461
8.4.3 Flexural Vibration of Thin Flat Plates: Finite Element
Analysis 470
8.4.4 Finite Element Models for Other Types
of Structure 478
8.5 Finite Element Analysis of Acoustic Vibrations of Fluids
in Cavities 479
8.5.1 One-Dimensional Acoustic Vibration of a Fluid in a
Uniform Straight Pipe: Rayleigh–Ritz Method 480
8.5.2 One-Dimensional Acoustic Vibration of Fluid in a
Uniform Straight Pipe: Finite Element Analysis 484
8.5.3 Acoustic Vibration of a Fluid in a Three-Dimensional
Cavity: Finite Element Analysis 489
8.6 Coupled Fluid–Structure Analysis 496
8.7 Boundary Element Analysis for Vibroacoustic Problems 503
8.7.1 Direct Boundary Element Method 505
8.8 Coupled Structure–Fluid Analysis 515
Problems 519xii CONTENTS
9. Introduction to Active Control of Sound Radiation and
Transmission
9.1 Introduction to Active Control 521
9.2 Fundamentals of Active Control Theory 522
9.2.1 Feed-Forward Control 523
9.2.2 Feedback Control 532
9.3 Sensor–Actuator Transducers 548
9.3.1 Strain Actuators 549
9.3.2 Inertial Electrodynamic Actuators 555
9.3.3 Strain Sensors 561
9.3.4 Inertial Sensors (Accelerometers) 565
9.4 From Active Noise Control to Active Structural Acoustic
Control and Active Vibration Control 569
9.4.1 Feed-Forward Active Noise Control
and Active Noise-Vibration Control 570
9.4.2 Feed-Forward Active Structural Acoustic
Control 573
9.4.3 Feedback Active Structural Acoustic Control 575
9.4.4 Decentralised Feedback Active Vibration
Control 576
9.5 Smart Panels for ASAC and AVC Systems 580
9.5.1 Models of Smart Panels 580
9.5.2 Smart Panels with Feed-Forward MIMO and SISO
Control Systems 584
9.5.3 Smart Panel with Feed-Forward SISO Control
Systems Using a Volume Velocity Distributed Sensor and
Uniform Force Distributed Actuator 588
9.5.4 Smart Panels with Feedback MIMO and SISO Control
Systems 590
9.5.5 Smart Panel with a Feedback SISO Control System
Using a Volume Velocity Sensor and Uniform Force
Actuator 595
Problems 596
Answers 597
References 607
Index

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