Structural acoustics : deterministic and random phenomena

290 Pages·2011·4.04 MB·English

by  Joshua E Greenspon

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Deterministic and Random Phenomena
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Structural Acoustics: Deterministic and Random Phenomena presents
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SIMPLIFIED SOLUTIONS TO COMPLICATED PROBLEMS
Deterministic and Random Phenomena
Starting with a review of the fundamentals of acoustics and structural S
acoustics, the book discusses the response of the beams, plates, and
shells that compose most built-up structures before providing methods
for solving problems of built-up systems, including a procedure for
computing the response of an elastic or viscoelastic media without
resorting to a large computer program. Building on this analysis,
the second section develops the analysis for random loading, which
can also be applied to geophysical phenomena and viscoelastic
media. Proceeding from the fundamental aspects of simple structures G
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the area of acoustics and vibration analysis, it also includes computer
programs for acoustical analysis
K11519
available at www.crcpress.com.
JOSHUA E. GREENSPON
6000 Broken Sound Parkway, NW
Suite 300, Boca Raton, FL 33487
711 Third Avenue
an informa business New York, NY 10017
2 Park Square, Milton Park
Abingdon, Oxon OX14 4RN, UK
STRUCTURAL
ACOUSTICS
Deterministic and Random Phenomena

STRUCTURAL
ACOUSTICS
Deterministic and Random Phenomena
JOSHUA E. GREENSPON
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2011 by Taylor and Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
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Contents
Preface ......................................................................................................................xi
Acknowledgments ..............................................................................................xiii
The Author .............................................................................................................xv
Section 1 Deterministic Phenomena
1. General Overview of the Book ....................................................................3
1.1 Introduction ...........................................................................................3
1.2 Background ............................................................................................4
1.3 Overview of Random Structural Acoustics ......................................5
1.3.1 The Problems of Most Practical Interest ...............................5
1.4 Overview of Methods and Applications ...........................................6
1.4.1 Methods .....................................................................................6
1.4.2 Green’s Functions and Cross Spectrum ...............................6
1.4.3 Modal Analysis ........................................................................6
1.5 Comparison of Methods Used in the Recent Literature ..................7
1.6 Applications ...........................................................................................7
References .........................................................................................................8
2. Fundamentals of Acoustics and Structural Acoustics ............................9
2.1 Introduction ...........................................................................................9
2.2 Physical Phenomena in Linear Acoustics ..........................................9
2.2.1 Sound Propagation in Air, Water, and Solids ......................9
2.2.2 Reflection, Refraction, Diffraction, Interference,
and Scattering .........................................................................10
2.2.2.1 Reflection .................................................................10
2.2.2.2 Refraction and Transmission ................................10
2.2.2.3 Diffraction ...............................................................11
2.2.2.4 Interference .............................................................11
2.2.2.5 Scattering .................................................................11
2.2.3 Standing Waves, Propagating Waves,
and Reverberation ..................................................................11
2.2.4 Sound Radiation .....................................................................12
2.2.5 Coupling and Interaction between
Structures and the Surrounding Medium .........................12
2.2.6 Deterministic versus Random Linear Acoustics ...............12
2.3 Basic Assumptions and Equations in Linear Acoustics ................13
2.3.1 Linear versus Nonlinear Acoustics .....................................13
2.3.2 Derivation of Basic Equations ..............................................15
© 2011 by Taylor and Francis Group, LLC v
vi Contents
2.4 Intensity and Energy ..........................................................................18
2.5 Free Sound Propagation .....................................................................18
2.5.1 Ray Acoustics .........................................................................18
2.5.2 Normal Mode Theory ...........................................................20
2.5.3 Underwater Sound Propagation ..........................................23
2.5.4 Atmospheric Sound Propagation ........................................23
2.6 Sound Propagation with Obstacles ..................................................24
2.6.1 Refraction ................................................................................24
2.6.2 Reflection and Transmission ................................................24
2.6.3 Interference .............................................................................27
2.6.4 Scattering ................................................................................28
2.7 Free and Confined Waves ..................................................................29
2.7.1 Propagating Waves ................................................................29
2.7.2 Standing Waves ......................................................................30
2.7.3 Reverberation ..........................................................................30
2.7.4 Wave Guides and Ducts ........................................................31
2.8 Sound Radiation and Vibration ........................................................34
2.8.1 Helmholtz Integral, Sommerfeld Radiation,
and Green’s Function.............................................................34
2.8.2 Rayleigh’s Formula for Planar Sources ...............................38
2.8.3 Vibrating Structures and Radiation ....................................38
2.8.4 Vibration of Flat Plates in Water ..........................................42
2.9 Coupling of Structure/Medium (Interactions) ...............................43
2.9.1 Coupled versus Uncoupled Systems ...................................43
References .......................................................................................................43
Glossary ...........................................................................................................44
3. Approximations for Added Mass and Radiation Damping ................47
Definitions.......................................................................................................50
References .......................................................................................................51
4. Fundamentals of Structures and Analysis of Beams ............................53
4.1 Fundamentals of Structures ..............................................................53
4.1.1 Introduction ............................................................................53
4.2 Beams ....................................................................................................53
4.2.1 Longitudinal Vibration .........................................................53
4.2.2 Lateral Vibration ....................................................................55
4.3 Plates .....................................................................................................56
4.3.1 Differential Equations for Stretching
and Shearing ...........................................................................58
4.3.2 Differential Equation for Bending and Twisting ..............59
4.4 Shells .....................................................................................................60
4.5 Three-Dimensional Variable Bodies ................................................60
4.6 Analysis of Beams ...............................................................................61
© 2011 by Taylor and Francis Group, LLC
Contents vii
4.6.1 Bernoulli–Euler and Timoshenko Beams ...........................61
4.6.2 Green’s Function for the Constant Section
Timoshenko Beam .................................................................62
4.6.3 Addition of Water Loading ...................................................63
4.6.4 Variable Section Beam ...........................................................64
4.6.5 Approximation to the Variable Section Beam
Frequencies .............................................................................65
4.7 Computer Programs ...........................................................................66
References .......................................................................................................71
5. Unstiffened, Stiffened, Sandwich, and Composite Plates ...................73
5.1 Introduction .........................................................................................73
5.2 Unstiffened Plates ...............................................................................73
5.3 Rectangular Plates ..............................................................................78
5.4 Addition of Water Loading ................................................................81
5.5 Proposed Design Procedure for Simply Supported
or Clamped Rectangular Plates under Uniform
Impulsive Pressure .............................................................................81
5.5.1 Evaluation of Accuracy of Proposed Method ....................89
5.5.2 Discussion ...............................................................................89
5.6 Cross-Stiffened and Sandwich Plates ..............................................94
5.7 Calculation of the Characteristics of Stiffened
and Sandwich Plates ...........................................................................99
5.7.1 Energy in the Plating ...........................................................100
5.8 Composite Plates ...............................................................................105
5.9 Plate Applications .............................................................................105
References .....................................................................................................105
6. A Simplified Procedure for Built-up Structures ..................................107
6.1 General Considerations ....................................................................107
6.2 Potential Energy and Stiffness Coefficients ..................................107
6.2.1 Bending and Twisting Energy ...........................................112
6.3 Equations of Motion and Basic Matrix ..........................................112
6.4 Effect of Fluid ....................................................................................113
6.5 Modal Impedances ...........................................................................113
6.6 Calculation of the Green’s Function ...............................................113
6.7 Potential Energy of Stretching and Shearing ................................114
6.8 Potential Energy of Bending and Twisting ...................................115
6.9 Stiffness Coefficients ........................................................................116
6.10 Example Calculations .......................................................................121
References .....................................................................................................125
7. Sound Patterns from Cylindrical Shells ................................................127
7.1 Introduction .......................................................................................127
7.2 Basic Equations ..................................................................................127
7.2.1 Types of Construction .........................................................127
© 2011 by Taylor and Francis Group, LLC
viii Contents
7.3 General Equations for Shell Vibrating in Fluid
and Containing Fluid .......................................................................135
7.4 Frequencies and Mode Shapes ........................................................141
7.5 Effect of External or Internal Pressure on Natural
Frequency ...........................................................................................142
7.6 Relation to Buckling .........................................................................143
7.7 Forced Vibration ................................................................................144
7.8 Description of the Computer Program ..........................................146
7.9 Far Field Patterns for a Representative Case .................................155
References .....................................................................................................157
8. Analysis of Three-Dimensional Media with Variable
Properties .....................................................................................................159
8.1 Introduction .......................................................................................159
8.2 Physical Characteristics of the Mathematical Model ...................159
8.3 Differential Equations of the Complex Medium ..........................159
8.4 Approximate Solution ......................................................................161
8.5 Solution for Nonhomogeneous Systems ........................................165
References .....................................................................................................166
Section 2 Random Phenomena
9. Linear Systems Equations .........................................................................169
9.1 Impulse Response .............................................................................169
9.2 Frequency Response Function ........................................................171
9.3 Statistics of the Response .................................................................171
9.4 Important Quantities Derivable from
the Cross Spectrum ...........................................................................174
9.5 The Cross Spectrum in Terms of Fourier Transforms .................176
9.6 The Conceptual Meaning of Cross Correlation, Cross
Spectrum, and Coherence ................................................................177
References .....................................................................................................182
10. Statistical Acoustics ...................................................................................183
10.1 Physical Concept of Transfer Function ..........................................183
10.2 Response in Terms of Green’s Functions .......................................184
10.3 Statistical Differential Equations Governing
the Sound Field .................................................................................185
References .....................................................................................................190
11 Statistics of Structures ...............................................................................193
11.1 Integral Relation for the Response .................................................193
11.2 Computation of the Response in Terms of Modes .......................198
11.3 Coupled Structural Acoustic Systems ............................................205
References .....................................................................................................208
© 2011 by Taylor and Francis Group, LLC
Contents ix
12. Random Radiation from Cylindrical Structures .................................209
12.1 Directivity Patterns ...........................................................................209
12.2 Multipole Expansion .........................................................................212
12.3 Random Loading and Response .....................................................214
12.3.1 Far Field from Random Loading .......................................214
12.3.2 Far Field due to Turbulence Excitation .............................221
12.4 Computer Programs .........................................................................223
References .....................................................................................................239
13. Applications of Statistical Acoustics to Near Field–Far Field
Problems .......................................................................................................241
13.1 The Near Field–Far Field Problem ..................................................241
13.2 Parrent’s Solution for the Plane .......................................................241
13.3 Other Applications of the Parrent Equation .................................242
13.4 Solution Using a Single Integration with Known
Coherence ...........................................................................................243
13.5 Determination of Far Field from Near Field
Autospectrum Alone and the Inverse Far Field–Near
Field Problem .....................................................................................244
13.6 Simplification of Equations for Plane Waves ................................246
13.7 Methods for Computing Far Field from Near Field
Acceleration ........................................................................................250
13.7.1 The Direct Method...............................................................250
13.7.2 Point Force Method ..............................................................251
13.8 Application to Prediction of Radiation ..........................................252
13.8.1 Direct Method Calculations ...............................................252
13.8.1.1 Far Field Fourier Transform ................................252
13.9 Inverse Method Calculation: Development of the Field in
Terms of Point Sources .....................................................................254
13.9.1 Governing Equations ..........................................................254
13.10 Point Force Calculations ...................................................................256
References .....................................................................................................257
14. Scale Models of Random Loading and Response ................................259
14.1 Approximate Formulation of the Modeling Laws .......................259
14.2 Damping .............................................................................................263
14.2.1 Joint or Interface Damping .................................................263
14.2.2 Material and Fluid Damping .............................................263
14.3 More General Formulation of Modeling Laws .............................265
14.4 Some General Considerations in Modeling ..................................270
References .....................................................................................................271
© 2011 by Taylor and Francis Group, LLC