Nonlinear Acoustic Waves in Micro-inhomogeneous Solids

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.

• Preface ixI. Introduction 1I.1 Nonlinearity of Gases and Liquids 2I.2 Nonlinearity of Homogeneous Solids 2I.3 Micro-inhomogeneous Solids. General Considerations 6References 91. Nonlinear Wave Processes in Homogeneous Media 111.1 A Progressive Approximation Approach: The Second Harmonic Generation in an Unbounded Medium 141.2 Generation of the Wave at a Difference Frequency: Parametric Array, Degenerate Interaction of Waves 151.3 Generation of the Wave at Second Harmonic Frequency in Resonators 171.4 Simple Waves and Formation of Discontinuities 191.5 Exact Solutions of the Burgers Equation 251.6 Nonlinear Wave Processes in Relaxing Media 271.7 Spherical and Cylindrical Waves 32References 342. Physical Models and Mechanisms of the Structure Nonlinearity of Micro-inhomogeneous Media with Cracks and Cavities 372.1 Contact Mechanism of Nonlinearity for Cracks with Rough and Smooth Surfaces 382.2 Capillary and Viscous Mechanisms of Nonlinearity for Cracks Partially Filled with Liquid 432.2.1 The Equilibrium State of a Crack Partially Filled with Liquid 432.2.2 The Equation of State for a Crack Partially Filled with a Perfect Liquid 452.2.3 The Equation of State for a Crack Partially Filled with a Viscous Liquid 462.3 Acoustic Nonlinearity of Porous Water-like Materials with Cylindrical Cavities Partially Filled with Viscous Liquid 502.4 An Adhesion Mechanism of Hysteretic Nonlinearity for Cracks 58References 633. ElasticWaves in Media with Strong Acoustic Nonlinearity 653.1 Nonlinear Propagation and Interaction of Acoustic Waves in Media with Cracks Possessing Adhesion 653.2 Acoustic Waves in Media with Bimodular Nonlinearity 683.3 Acoustic Waves in Media with Bimodular Nonlinearity and Linear Dissipation 703.4 Doubling of Acoustic Wave Frequency by a Nonlinear Layer 763.5 Propagation of High-Frequency Pulses in Media with Dissipative Nonlinearity 793.6 Interaction of Counter-Propagating Acoustic Waves in Media with Dissipative Nonlinearity 80References 814. Wave Processes in Micro-inhomogeneous Solids with Hysteretic Nonlinearity 834.1 Hysteretic Equations of State for Solids: Phenomenological Models 844.2 Nonlinear Waves in an Unbounded Medium 884.2.1 Propagation of Unipolar Acoustic Pulses 954.2.2 Self-Demodulation of High-Frequency Acoustic Pulses 964.2.3 Nonlinear Travelling Waves in a Ring Resonator 974.3 Vibrations of Rods Composed of Materials with Hysteretic Nonlinearity and Linear Dissipation 994.4 Propagation of Unipolar Strain Pulses in Media with Hysteretic Nonlinearity of an Arbitrary Power-Law 103References 1075. Wave Processes in Nonlinear Micro-inhomogeneous Media with Relaxation 1115.1 Rheological Model and Dynamic Equation of State of Nonlinear Micro-inhomogeneous Media with Relaxation 1125.1.1 Second Harmonic Generation 1165.1.2 Generation of the Difference Frequency Wave 1205.1.3 Self-Demodulation of Pulses with a High-Frequency Carrier 1245.2 Evolution of Acoustic Waves in Micro-inhomogeneous Media with Quadratic Elastic Nonlinearity and Relaxation 1275.2.1 Stationary Symmetric Shock Waves 1275.2.2 Evolution Equations for Low-Frequency and High-Frequency Acoustic Waves 1295.2.3 Evolution of Initially Harmonic Waves 1305.3 Wave Processes in Micro-inhomogeneous Elastic Media with Hysteretic Nonlinearity and Relaxation 1325.3.1 Equation of State of Micro-inhomogeneous Medium with Hysteretic Nonlinearity and Relaxation 1335.3.2 Nonlinear Propagation of a Quasi-Harmonic Wave 1335.3.3 Frequency Dependencies of Nonlinear Coefficients for a Medium with Defects having Different Distribution over Relaxation Frequencies 1355.4 Simulation of the Dynamic Hystereses in Micro-inhomogeneous Media Characterized by Imperfect Elasticity and Relaxation 1385.5 Nonlinear Wave Processes in Media Containing Cracks Partially Filled with a Viscous Liquid 1425.5.1 Equation of State for a Rod Containing Cracks Partially Filled with a Viscous Liquid 1425.5.2 Nonlinear Propagation and Interaction of Elastic Waves in a Rod with Cracks 1445.5.3 Analysis of the Wave Processes in a Rod with Identical Cracks 1475.5.4 Analysis of the Wave Processes in a Rod with Cracks Distributed over the Radii 148References 1506. Wave Processes in Polycrystalline Solids with Dissipative and Reactive Nonlinearity Caused by Dislocations 1536.1 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 1546.2 Attenuation of High-Frequency Pulses and the Phase Delay of its Carrier Frequency under the Action of a Low-Frequency Wave 1586.3 Amplitude–Phase Self-Action Phenomena in the High-Frequency Wave of Finite Amplitude 160References 1637. Experimental Studies of Nonlinear Acoustic Phenomena in Polycrystalline Rocks and Metals 1657.1 Experimental Setup 1667.2 Nonlinear Shift in Resonance Frequency in a Glass Rod with Artificial Cracks 1667.3 Low-Frequency Amplitude-Dependent Internal Friction and High-Frequency Dissipative Nonlinearity of Coarse-Grained Sandstone 1677.3.1 Phenomena of LF Hysteretic Nonlinearity: Amplitude-Dependent Losses and Shifts of Resonant Frequencies 1687.3.2 Nonlinear Attenuation of an Ultrasonic Pulse under the Action of a LF Wave 1737.4 Effect of an Intense Sound Wave on the Acoustic Properties of a Fine-Grained Sandstone Rod Resonator 1767.5 Nonlinear Acoustic Phenomena in Limestone 1807.5.1 Phenomena of LF Hysteretic Nonlinearity 1807.5.2 Manifestation of the HF Dissipative Nonlinearity 1867.6 Oscillograms of the Free Boundary Nonlinear Oscillations of a Magnesite Resonator 1877.7 High-Frequency Nonlinear Acoustic Phenomena in Marble 1897.7.1 Attenuation and Phase Delay of the Carrier Frequency of Weak Ultrasonic Pulses under the Action of a LF Powerful Wave 1897.7.2 Self-Action of Finite-Amplitude Ultrasonic Pulses 1927.8 Sound by Sound Damping of Polycrystalline Zinc 1957.9 Modulation of Sound by Sound in Copper Subjected to Different Degrees of Annealing 199References 2038. Experimental Studies of Nonlinear Acoustic Phenomena in Granular Media 2058.1 Self-Demodulation of Acoustic Pulses in Partially Water-Saturated River Sand 2068.1.1 Experimental Setup 2068.1.2 Experimental Results 2078.2 Self-Action of Acoustic Waves in Systems with Dissipative Nonlinearity 2128.2.1 Description of the Experiment 2138.2.2 Analytical Description of the Phenomenon of Self-Brightening 2168.3 Amplification of Sound by Sound in Systems with Dissipative Nonlinearity 2218.4 Self-Action of a Low-Frequency Acoustic Wave and Generation of the Second Harmonic in Dry and Water-Saturated River Sand 2228.4.1 Experimental Scheme and Method of Measurement 2228.4.2 Measurement Results 2238.4.3 Analytical Description of the Phenomena of Self-Action and Generation of the Second Harmonic 2268.5 Amplitude Modulation of Sound by Sound in Water-Saturated River Sand 228References 2319. Nonlinear Phenomena in Seismic Waves 2339.1 Static Deformation of the Earth’s Surface Near the Harmonic Source of Seismic Vibrations 2339.2 Amplitude Modulation of Sound by Sound in Sandy Soil 2379.3 Self-Action of the Seismic Wave in Sandy Soil 2379.4 Amplitude–Phase Modulation of a Seismo–Acoustic Wave under Diurnal Tides 242References 245Index 249