- •Foreword
- •Preface
- •Contents
- •1 Introduction to Nonlinear Acoustics
- •1.1 Introduction
- •1.2 Constitutive Equations
- •1.3 Phenomena in Nonlinear Acoustics
- •References
- •2 Nonlinear Acoustic Wave Equations for Sound Propagation in Fluids and in Solids
- •2.1 Nonlinear Acoustic Wave Equations in Fluids
- •2.1.1 The Westervelt Equation [1]
- •2.1.2 The Burgers’ Equation [2]
- •2.1.3 KZK Equation
- •2.1.4 Nonlinear Acoustic Wave Equations for Sound Propagation in Solids
- •References
- •3 Statistical Mechanics Approach to Nonlinear Acoustics
- •3.1 Introduction
- •3.2 Statistical Energy Analysis is Transport Theory
- •3.3 Statistical Energy Analysis
- •3.4 Transport Theory Approach to Phase Transition
- •References
- •4 Curvilinear Spacetime Applied to Nonlinear Acoustics
- •4.1 Introduction and Meaning of Curvilinear Spacetime
- •4.2 Principle of General Covariance
- •4.3 Contravariant and Covariant Four-Vectors
- •4.4 Contravariant Tensors and Covariant Tensors
- •4.5 The Covariant Fundamental Tensor gμν
- •4.6 Equation of Motion of a Material Point in the Gravitational Field
- •4.8 The Euler Equation of Fluids in the Presence of the Gravitational Field
- •4.9 Acoustic Equation of Motion for an Elastic Solid in the Presence of Gravitational Force
- •Reference
- •5 Gauge Invariance Approach to Nonlinear Acoustical Imaging
- •5.1 Introduction
- •5.3 Illustration by a Unidirectional Example
- •5.4 Quantization of the Gauge Theory
- •5.5 Coupling of Elastic Deformation with Spin Currents
- •References
- •6.1 Introduction
- •6.2 The Thermodynamic Method
- •6.2.1 Theory
- •6.2.2 Experiment
- •6.3 The Finite Amplitude Method
- •6.3.1 The Wave Shape Method
- •6.3.2 Second Harmonic Measuements
- •6.3.3 Measurement from the Fundamental Component
- •6.4 B/A Nonlinear Parameter Acoustical Imaging
- •6.4.1 Theory
- •6.4.2 Simulation
- •6.4.3 Experiment [17]
- •6.4.4 Image Reconstruction with Computed Tomography
- •References
- •7 Ultrasound Harmonic Imaging
- •7.1 Theory of Ultrasound Harmonic Imaging
- •7.2 Methods Used to Isolate the Second Harmonic Signal Component
- •7.3 Advantages of Harmonic Imaging
- •7.4 Disadvantages of Harmonic Imaging
- •7.5 Experimental Techniques in Nonlinear Acoustics
- •7.6 Application of Ultrasound Harmonic Imaging to Tissue Imaging
- •7.7 Applications of Ultrasonic Harmonic Imaging to Nondestructive Testing
- •7.8 Application of Ultrasound Harmonic Imaging to Underwater Acoustics
- •References
- •8 Application of Chaos Theory to Acoustical Imaging
- •8.1 Nonlinear Problem Encountered in Diffraction Tomography
- •8.4 The Link Between Chaos and Fractals
- •8.5 The Fractal Nature of Breast Cancer
- •8.6 Types of Fractals
- •8.6.1 Nonrandom Fractals
- •8.6.2 Random Fractals
- •8.7 Fractal Approximations
- •8.8 Diffusion Limited Aggregation
- •8.9 Growth Site Probability Distribution
- •8.10 Approximating of the Scattered Field Using GSPD
- •8.11 Discrete Helmholtz Wave Equation
- •8.12 Kaczmarz Algorithm
- •8.14 Applying GSPD into Kaczmarz Algorithm
- •8.15 Fractal Algorithm using Frequency Domain Interpretation
- •8.16 Derivation of Fractal Algorithm’s Final Equation Using Frequency Domain Interpolation
- •8.17 Simulation Results
- •8.18 Comparison Between Born and Fractal Approximation
- •References
- •9.1 Introduction
- •9.2 Mechanisms of Harmonic Generation Via Contact Acoustic Nonlinearity (CAN)
- •9.2.1 Clapping Mechanism
- •9.2.2 Nonlinear Friction Mechanism
- •9.3 Nonlinear Resonance Modes
- •9.4 Experimental Studies on Nonclassical CAN Spectra
- •9.4.1 CAN Application for Nonlinear Acoustical Imaging and NDE
- •9.5 Conclusions
- •References
- •10.1 Introduction
- •10.2 Principles of Modulation Acoustic Method
- •10.3 The Modulation Mode of Method of Crack Location
- •10.4 Experimental Procedure of the Modulation Method for NDT
- •10.5 Experimental Procedures for the Modulation Mode System
- •10.6 Conclusions
- •References
- •11.1 Introduction
Contents
1 Introduction to Nonlinear Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
1 |
|
1.1 |
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
1 |
1.2 |
Constitutive Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
2 |
1.3 |
Phenomena in Nonlinear Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . |
2 |
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
2 |
|
2 Nonlinear Acoustic Wave Equations for Sound Propagation |
|
|
in Fluids and in Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
3 |
|
2.1 |
Nonlinear Acoustic Wave Equations in Fluids . . . . . . . . . . . . . . . . |
3 |
|
2.1.1 The Westervelt Equation [1] . . . . . . . . . . . . . . . . . . . . . . . . . |
4 |
|
2.1.2 The Burgers’ Equation [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . |
4 |
|
2.1.3 KZK Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
5 |
|
2.1.4 Nonlinear Acoustic Wave Equations for Sound |
|
|
Propagation in Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
6 |
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
7 |
|
3 Statistical Mechanics Approach to Nonlinear Acoustics . . . . . . . . . . . |
9 |
|
3.1 |
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
9 |
3.2 |
Statistical Energy Analysis is Transport Theory . . . . . . . . . . . . . . . |
10 |
3.3 |
Statistical Energy Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
12 |
3.4 |
Transport Theory Approach to Phase Transition . . . . . . . . . . . . . . |
14 |
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
15 |
|
4 Curvilinear Spacetime Applied to Nonlinear Acoustics . . . . . . . . . . . . |
17 |
|
4.1 |
Introduction and Meaning of Curvilinear Spacetime . . . . . . . . . . . |
17 |
4.2 |
Principle of General Covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
18 |
4.3 |
Contravariant and Covariant Four-Vectors . . . . . . . . . . . . . . . . . . . . |
19 |
4.4 |
Contravariant Tensors and Covariant Tensors . . . . . . . . . . . . . . . . . |
20 |
4.5 |
The Covariant Fundamental Tensor gμν . . . . . . . . . . . . . . . . . . . . . . |
21 |
4.6Equation of Motion of a Material Point in the Gravitational
Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
22 |
xi
xii |
Contents |
4.7The Laws of Momentum and Energy for Matter,
as a Consequence of the Gravitational Field Equations . . . . . . . . . 22
4.8The Euler Equation of Fluids in the Presence
of the Gravitational Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.9Acoustic Equation of Motion for an Elastic Solid
in the Presence of Gravitational Force . . . . . . . . . . . . . . . . . . . . . . . 24 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5 Gauge Invariance Approach to Nonlinear Acoustical Imaging . . . . . 29 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2Gauge Invariance Formulation of Electron–Phonon
Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.3 Illustration by a Unidirectional Example . . . . . . . . . . . . . . . . . . . . . 33 5.4 Quantization of the Gauge Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.5 Coupling of Elastic Deformation with Spin Currents . . . . . . . . . . 34 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6 B/A Nonlinear Parameter Acoustical Imaging . . . . . . . . . . . . . . . . . . . . |
37 |
||
6.1 |
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
37 |
|
6.2 |
The Thermodynamic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
37 |
|
|
6.2.1 |
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
37 |
|
6.2.2 |
Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
39 |
6.3 |
The Finite Amplitude Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
40 |
|
|
6.3.1 The Wave Shape Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
41 |
|
|
6.3.2 |
Second Harmonic Measuements . . . . . . . . . . . . . . . . . . . . . |
41 |
|
6.3.3 Measurement from the Fundamental Component . . . . . . . |
42 |
|
6.4 |
B/A Nonlinear Parameter Acoustical Imaging . . . . . . . . . . . . . . . . |
43 |
|
|
6.4.1 |
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
43 |
|
6.4.2 |
Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
45 |
|
6.4.3 |
Experiment [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
45 |
|
6.4.4 |
Image Reconstruction with Computed Tomography . . . . . |
46 |
References . |
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
47 |
|
7 Ultrasound Harmonic Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 7.1 Theory of Ultrasound Harmonic Imaging . . . . . . . . . . . . . . . . . . . . 49
7.2Methods Used to Isolate the Second Harmonic Signal
|
Component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
54 |
7.3 |
Advantages of Harmonic Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . |
54 |
7.4 |
Disadvantages of Harmonic Imaging . . . . . . . . . . . . . . . . . . . . . . . . |
55 |
7.5 |
Experimental Techniques in Nonlinear Acoustics . . . . . . . . . . . . . |
55 |
7.6Application of Ultrasound Harmonic Imaging to Tissue
Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
7.7Applications of Ultrasonic Harmonic Imaging
to Nondestructive Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Contents |
xiii |
7.8Application of Ultrasound Harmonic Imaging
to Underwater Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
8 Application of Chaos Theory to Acoustical Imaging . . . . . . . . . . . . . . 61
8.1Nonlinear Problem Encountered in Diffraction Tomography . . . . 61
8.2 |
Definition and History of Chaos . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
62 |
|
8.3 |
Definition of Fractal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
62 |
|
8.4 |
The Link Between Chaos and Fractals . . . . . . . . . . . . . . . . . . . . . . . |
63 |
|
8.5 |
The Fractal Nature of Breast Cancer . . . . . . . . . . . . . . . . . . . . . . . . |
64 |
|
8.6 |
Types of Fractals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
65 |
|
|
8.6.1 |
Nonrandom Fractals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
65 |
|
8.6.2 |
Random Fractals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
67 |
|
8.6.3 |
Other Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
68 |
8.7 |
Fractal Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
68 |
|
8.8 |
Diffusion Limited Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
69 |
|
8.9 |
Growth Site Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . |
69 |
|
8.10 |
Approximating of the Scattered Field Using GSPD . . . . . . . . . . . . |
71 |
|
8.11 |
Discrete Helmholtz Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . |
72 |
|
8.12 |
Kaczmarz Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
73 |
|
8.13 |
Hounsfield Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
75 |
|
8.14 |
Applying GSPD into Kaczmarz Algorithm . . . . . . . . . . . . . . . . . . . |
76 |
|
8.15 |
Fractal Algorithm using Frequency Domain Interpretation . . . . . . |
77 |
|
8.16 |
Derivation of Fractal Algorithm’s Final Equation Using |
|
|
|
Frequency Domain Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . |
77 |
|
8.17 |
Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
78 |
|
8.18 |
Comparison Between Born and Fractal Approximation . . . . . . . . |
80 |
|
References . |
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
82 |
|
9 Nonclassical Nonlinear Acoustical Imaging . . . . . . . . . . . . . . . . . . . . . . |
83 |
||
9.1 |
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
83 |
|
9.2Mechanisms of Harmonic Generation Via Contact
|
Acoustic Nonlinearity (CAN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
84 |
|
|
9.2.1 |
Clapping Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
84 |
|
9.2.2 |
Nonlinear Friction Mechanism . . . . . . . . . . . . . . . . . . . . . . . |
85 |
9.3 |
Nonlinear Resonance Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
86 |
|
9.4 |
Experimental Studies on Nonclassical CAN Spectra . . . . . . . . . . . |
88 |
|
|
9.4.1 CAN Application for Nonlinear Acoustical |
|
|
|
|
Imaging and NDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
89 |
9.5 |
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
92 |
|
References . |
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
92 |
|
10 Modulation Method of Nonlinear Acoustical Imaging . . . . . . . . . . . . . |
95 |
||
10.1 |
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
95 |
|
10.2 |
Principles of Modulation Acoustic Method . . . . . . . . . . . . . . . . . . . |
95 |
|
10.3 |
The Modulation Mode of Method of Crack Location . . . . . . . . . . |
96 |
|
xiv |
|
Contents |
10.4 |
Experimental Procedure of the Modulation Method for NDT |
. . . 97 |
10.5 |
Experimental Procedures for the Modulation Mode System . . |
. . . 99 |
10.6 |
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . . 100 |
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . 101 |
|
11 Applications of Nonlinear Acoustical Imaging and Conclusions . . . . 103 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103