Nonlinear Acoustic Waves in Micro-inhomogeneous Solids

Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives.

The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book.

The subsequent eight chapters covering: Physical models and mechanisms of the structure nonlinearity of micro-inhomogeneous media with cracks and cavities; Elastic waves in media with strong acoustic nonlinearity; Wave processes in micro-inhomogeneous media with hysteretic nonlinearity; Wave processes in nonlinear micro-inhomogeneous media with relaxation; Wave processes in the polycrystalline solids with dissipative and elastic nonlinearity caused by dislocations; Experimental studies of the nonlinear acoustic phenomena in polycrystalline rocks and metals; Experimental studies of nonlinear acoustic phenomena in granular media; and Nonlinear phenomena in seismic waves are dedicated to the theoretical and experimental research of nonlinear processes, caused by longitudinal elastic waves propagation and interaction in the micro-inhomogeneous media with a strong acoustical nonlinearity of different types (elastic, hysteretic, bimodular, elastic quadratic and non-elastic).

This valuable monograph is intended for graduate students and researchers in applied physics, mechanical engineering, and applied mathematics, as well as those working in a wide spectrum of disciplines in materials science.

Autorentext

Veniamin E. Nazarov from the Institute of Applied Physics, Russian Academy of Science, began resonance experiments in solids with microstructure as early as in the mid-1980s when the concept of contact nonlinearity in acoustic was completely new. Andrey V. Radostin is a senior scientific associate at the Institute of Applied Physics, Russian Academy of Science.

Zusammenfassung
Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives.

The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book.

The subsequent eight chapters covering: Physical models and mechanisms of the structure nonlinearity of micro-inhomogeneous media with cracks and cavities; Elastic waves in media with strong acoustic nonlinearity; Wave processes in micro-inhomogeneous media with hysteretic nonlinearity; Wave processes in nonlinear micro-inhomogeneous media with relaxation; Wave processes in the polycrystalline solids with dissipative and elastic nonlinearity caused by dislocations; Experimental studies of the nonlinear acoustic phenomena in polycrystalline rocks and metals; Experimental studies of nonlinear acoustic phenomena in granular media; and Nonlinear phenomena in seismic waves are dedicated to the theoretical and experimental research of nonlinear processes, caused by longitudinal elastic waves propagation and interaction in the micro-inhomogeneous media with a strong acoustical nonlinearity of different types (elastic, hysteretic, bimodular, elastic quadratic and non-elastic).

This valuable monograph is intended for graduate students and researchers in applied physics, mechanical engineering, and applied mathematics, as well as those working in a wide spectrum of disciplines in materials science.

Inhalt
Preface ix

I. Introduction 1

I.1 Nonlinearity of Gases and Liquids 2

I.2 Nonlinearity of Homogeneous Solids 2

I.3 Micro-inhomogeneous Solids. General Considerations 6

References 9

1. Nonlinear Wave Processes in Homogeneous Media 11

1.1 A Progressive Approximation Approach: The Second Harmonic Generation in an Unbounded Medium 14

1.2 Generation of the Wave at a Difference Frequency: Parametric Array, Degenerate Interaction of Waves 15

1.3 Generation of the Wave at Second Harmonic Frequency in Resonators 17

1.4 Simple Waves and Formation of Discontinuities 19

1.5 Exact Solutions of the Burgers Equation 25

1.6 Nonlinear Wave Processes in Relaxing Media 27

1.7 Spherical and Cylindrical Waves 32

References 34

2. Physical Models and Mechanisms of the Structure Nonlinearity of Micro-inhomogeneous Media with Cracks and Cavities 37

2.1 Contact Mechanism of Nonlinearity for Cracks with Rough and Smooth Surfaces 38

2.2 Capillary and Viscous Mechanisms of Nonlinearity for Cracks Partially Filled with Liquid 43

2.2.1 The Equilibrium State of a Crack Partially Filled with Liquid 43

2.2.2 The Equation of State for a Crack Partially Filled with a Perfect Liquid 45

2.2.3 The Equation of State for a Crack Partially Filled with a Viscous Liquid 46

2.3 Acoustic Nonlinearity of Porous Water-like Materials with Cylindrical Cavities Partially Filled with Viscous Liquid 50

2.4 An Adhesion Mechanism of Hysteretic Nonlinearity for Cracks 58

References 63

3. ElasticWaves in Media with Strong Acoustic Nonlinearity 65

3.1 Nonlinear Propagation and Interaction of Acoustic Waves in Media with Cracks Possessing Adhesion 65

3.2 Acoustic Waves in Media with Bimodular Nonlinearity 68

3.3 Acoustic Waves in Media with Bimodular Nonlinearity and Linear Dissipation 70

3.4 Doubling of Acoustic Wave Frequency by a Nonlinear Layer 76

3.5 Propagation of High-Frequency Pulses in Media with Dissipative Nonlinearity 79

3.6 Interaction of Counter-Propagating Acoustic Waves in Media with Dissipative Nonlinearity 80

References 81

4. Wave Processes in Micro-inhomogeneous Solids with Hysteretic Nonlinearity 83

4.1 Hysteretic Equations of State for Solids: Phenomenological Models 84

4.2 Nonlinear Waves in an Unbounded Medium 88

4.2.1 Propagation of Unipolar Acoustic Pulses 95

4.2.2 Self-Demodulation of High-Frequency Acoustic Pulses 96

4.2.3 Nonlinear Travelling Waves in a Ring Resonator 97

4.3 Vibrations of Rods Composed of Materials with Hysteretic Nonlinearity and Linear Dissipation 99

4.4 Propagation of Unipolar Strain Pulses in Media with Hysteretic Nonlinearity of an Arbitrary Power-Law 103

References 107

5. Wave Processes in Nonlinear Micro-inhomogeneous Media with Relaxation 111

5.1 Rheological Model and Dynamic Equation of State of Nonlinear Micro-inhomogeneous Media with Relaxation 112

5.1.1 Second Harmonic Generation 116

5.1.2 Generation of the Difference Frequency Wave 120

5.1.3 Self-Demodulation of Pulses with a High-Frequency Carrier 124

5.2 Evolution of Acoustic Waves in Micro-inhomogeneous Media with Quadratic Elastic Nonlinearity and Relaxation 127

5.2.1 Stationary Symmetric Shock Waves 127

5.2.2 Evolution Equations for Low-Frequency and High-Frequency Acoustic Waves 129

5.2.3 Evolution of Initially Harmonic Waves 130

5.3 Wave Processes in Micro-inhomogeneous Elastic Media with Hysteretic Nonlinearity and Relaxation 132

5.3.1 Equation of State of Micro-inhomogeneous Medium with Hysteretic Nonlinearity and Relaxation 133

5.3.2 Nonlinear Propagation of a Quasi-Harmonic Wave 133

5.3.3 Frequency Dependencies of Nonlinear Coefficients for a Medium with Defects having Different Distribution over Relaxation Frequencies 135

5.4 Simulation of the Dynamic Hystereses in Micro-inhomogeneous Media Characterized by Imperfect Elasticity and Relaxation 138 5.5 Nonlinear Wave Proces…