Nonlinear Acoustical Imaging

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
4.7 The Laws of Momentum and Energy for Matter, as a Consequence of the Gravitational Field Equations
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
5.2 Gauge Invariance Formulation of Electron–Phonon Interaction
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 B/A Nonlinear Parameter Acoustical Imaging
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
8.2 Definition and History of Chaos
8.3 Definition of Fractal
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
8.6.3 Other Definitions
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
8.13 Hounsfield Method
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 Nonclassical Nonlinear Acoustical Imaging
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 Modulation Method of Nonlinear Acoustical Imaging
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 Applications of Nonlinear Acoustical Imaging and Conclusions
11.1 Introduction