Veniamin Nazarov, Andrey Radostin

Nonlinear Acoustic Waves in Micro-inhomogeneous Solids (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 264
• Erscheinungstermin: 17. November 2014
• Englisch
• ISBN-13: 9781118698327
• Artikelnr.: 41838844

Autorenporträt

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.

Inhaltsangabe

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 Processes in Media Containing Cracks
Partially Filled with a Viscous Liquid 142 5.5.1 Equation of State for a
Rod Containing Cracks Partially Filled with a Viscous Liquid 142 5.5.2
Nonlinear Propagation and Interaction of Elastic Waves in a Rod with Cracks
144 5.5.3 Analysis of the Wave Processes in a Rod with Identical Cracks 147
5.5.4 Analysis of the Wave Processes in a Rod with Cracks Distributed over
the Radii 148 References 150 6. Wave Processes in Polycrystalline Solids
with Dissipative and Reactive Nonlinearity Caused by Dislocations 153 6.1
Modification of the Linear Part of the Granato-Lücke Dislocation Theory of
Absorption and Equation of State with Resonance Dissipative and Reactive
Nonlinearity for Polycrystalline Solids 154 6.2 Attenuation of
High-Frequency Pulses and the Phase Delay of its Carrier Frequency under
the Action of a Low-Frequency Wave 158 6.3 Amplitude-Phase Self-Action
Phenomena in the High-Frequency Wave of Finite Amplitude 160 References 163
7. Experimental Studies of Nonlinear Acoustic Phenomena in Polycrystalline
Rocks and Metals 165 7.1 Experimental Setup 166 7.2 Nonlinear Shift in
Resonance Frequency in a Glass Rod with Artificial Cracks 166 7.3
Low-Frequency Amplitude-Dependent Internal Friction and High-Frequency
Dissipative Nonlinearity of Coarse-Grained Sandstone 167 7.3.1 Phenomena of
LF Hysteretic Nonlinearity: Amplitude-Dependent Losses and Shifts of
Resonant Frequencies 168 7.3.2 Nonlinear Attenuation of an Ultrasonic Pulse
under the Action of a LF Wave 173 7.4 Effect of an Intense Sound Wave on
the Acoustic Properties of a Fine-Grained Sandstone Rod Resonator 176 7.5
Nonlinear Acoustic Phenomena in Limestone 180 7.5.1 Phenomena of LF
Hysteretic Nonlinearity 180 7.5.2 Manifestation of the HF Dissipative
Nonlinearity 186 7.6 Oscillograms of the Free Boundary Nonlinear
Oscillations of a Magnesite Resonator 187 7.7 High-Frequency Nonlinear
Acoustic Phenomena in Marble 189 7.7.1 Attenuation and Phase Delay of the
Carrier Frequency of Weak Ultrasonic Pulses under the Action of a LF
Powerful Wave 189 7.7.2 Self-Action of Finite-Amplitude Ultrasonic Pulses
192 7.8 Sound by Sound Damping of Polycrystalline Zinc 195 7.9 Modulation
of Sound by Sound in Copper Subjected to Different Degrees of Annealing 199
References 203 8. Experimental Studies of Nonlinear Acoustic Phenomena in
Granular Media 205 8.1 Self-Demodulation of Acoustic Pulses in Partially
Water-Saturated River Sand 206 8.1.1 Experimental Setup 206 8.1.2
Experimental Results 207 8.2 Self-Action of Acoustic Waves in Systems with
Dissipative Nonlinearity 212 8.2.1 Description of the Experiment 213 8.2.2
Analytical Description of the Phenomenon of Self-Brightening 216 8.3
Amplification of Sound by Sound in Systems with Dissipative Nonlinearity
221 8.4 Self-Action of a Low-Frequency Acoustic Wave and Generation of the
Second Harmonic in Dry and Water-Saturated River Sand 222 8.4.1
Experimental Scheme and Method of Measurement 222 8.4.2 Measurement Results
223 8.4.3 Analytical Description of the Phenomena of Self-Action and
Generation of the Second Harmonic 226 8.5 Amplitude Modulation of Sound by
Sound in Water-Saturated River Sand 228 References 231 9. Nonlinear
Phenomena in Seismic Waves 233 9.1 Static Deformation of the Earth's
Surface Near the Harmonic Source of Seismic Vibrations 233 9.2 Amplitude
Modulation of Sound by Sound in Sandy Soil 237 9.3 Self-Action of the
Seismic Wave in Sandy Soil 237 9.4 Amplitude-Phase Modulation of a
Seismo-Acoustic Wave under Diurnal Tides 242 References 245 Index 249