Cover -- Title Page -- Copyright -- Contents -- Preface -- Introduction -- I.1 Nonlinearity of Gases and Liquids -- I.2 Nonlinearity of Homogeneous Solids -- I.3 Micro-inhomogeneous Solids. General Considerations -- References -- Chapter 1 Nonlinear Wave Processes in Homogeneous Media -- 1.1 A Progressive Approximation Approach: The Second Harmonic Generation in an Unbounded Medium -- 1.2 Generation of the Wave at a Difference Frequency: Parametric Array, Degenerate Interaction of Waves -- 1.3 Generation of the Wave at Second Harmonic Frequency in Resonators -- 1.4 Simple Waves and Formation of Discontinuities -- 1.5 Exact Solutions of the Burgers Equation -- 1.6 Nonlinear Wave Processes in Relaxing Media -- 1.7 Spherical and Cylindrical Waves -- References -- Chapter 2 Physical Models and Mechanisms of the Structure Nonlinearity of Micro-inhomogeneous Media with Cracks and Cavities -- 2.1 Contact Mechanism of Nonlinearity for Cracks with Rough and Smooth Surfaces -- 2.2 Capillary and Viscous Mechanisms of Nonlinearity for Cracks Partially Filled with Liquid -- 2.2.1 The Equilibrium State of a Crack Partially Filled with Liquid -- 2.2.2 The Equation of State for a Crack Partially Filled with a Perfect Liquid -- 2.2.3 The Equation of State for a Crack Partially Filled with a Viscous Liquid -- 2.3 Acoustic Nonlinearity of Porous Water-like Materials with Cylindrical Cavities Partially Filled with Viscous Liquid -- 2.4 An Adhesion Mechanism of Hysteretic Nonlinearity for Cracks -- References -- Chapter 3 Elastic Waves in Media with Strong Acoustic Nonlinearity -- 3.1 Nonlinear Propagation and Interaction of Acoustic Waves in Media with Cracks Possessing Adhesion -- 3.2 Acoustic Waves in Media with Bimodular Nonlinearity.

3.3 Acoustic Waves in Media with Bimodular Nonlinearity and Linear Dissipation -- 3.4 Doubling of Acoustic Wave Frequency by a Nonlinear Layer -- 3.5 Propagation of High-Frequency Pulses in Media with Dissipative Nonlinearity -- 3.6 Interaction of Counter-Propagating Acoustic Waves in Media with Dissipative Nonlinearity -- References -- Chapter 4 Wave Processes in Micro-inhomogeneous Solids with Hysteretic Nonlinearity -- 4.1 Hysteretic Equations of State for Solids: Phenomenological Models -- 4.2 Nonlinear Waves in an Unbounded Medium -- 4.2.1 Propagation of Unipolar Acoustic Pulses -- 4.2.2 Self-Demodulation of High-Frequency Acoustic Pulses -- 4.2.3 Nonlinear Travelling Waves in a Ring Resonator -- 4.3 Vibrations of Rods Composed of Materials with Hysteretic Nonlinearity and Linear Dissipation -- 4.4 Propagation of Unipolar Strain Pulses in Media with Hysteretic Nonlinearity of an Arbitrary Power-Law -- References -- Chapter 5 Wave Processes in Nonlinear Micro-inhomogeneous Media with Relaxation -- 5.1 Rheological Model and Dynamic Equation of State of Nonlinear Micro-inhomogeneous Media with Relaxation -- 5.1.1 Second Harmonic Generation -- 5.1.2 Generation of the Difference Frequency Wave -- 5.1.3 Self-Demodulation of Pulses with a High-Frequency Carrier -- 5.2 Evolution of Acoustic Waves in Micro-inhomogeneous Media with Quadratic Elastic Nonlinearity and Relaxation -- 5.2.1 Stationary Symmetric Shock Waves -- 5.2.2 Evolution Equations for Low-Frequency and High-Frequency Acoustic Waves -- 5.2.3 Evolution of Initially Harmonic Waves -- 5.3 Wave Processes in Micro-inhomogeneous Elastic Media with Hysteretic Nonlinearity and Relaxation -- 5.3.1 Equation of State of Micro-inhomogeneous Medium with Hysteretic Nonlinearity and Relaxation.

5.3.2 Nonlinear Propagation of a Quasi-Harmonic Wave -- 5.3.3 Frequency Dependencies of Nonlinear Coefficients for a Medium with Defects having Different Distribution over Relaxation Frequencies -- 5.4 Simulation of the Dynamic Hystereses in Micro-inhomogeneous Media Characterized by Imperfect Elasticity and Relaxation -- 5.5 Nonlinear Wave Processes in Media Containing Cracks Partially Filled with a Viscous Liquid -- 5.5.1 Equation of State for a Rod Containing Cracks Partially Filled with a Viscous Liquid -- 5.5.2 Nonlinear Propagation and Interaction of Elastic Waves in a Rod with Cracks -- 5.5.3 Analysis of the Wave Processes in a Rod with Identical Cracks -- 5.5.4 Analysis of the Wave Processes in a Rod with Cracks Distributed over the Radii -- References -- Chapter 6 Wave Processes in Polycrystalline Solids with Dissipative and Reactive Nonlinearity Caused by Dislocations -- 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 -- 6.2 Attenuation of High-Frequency Pulses and the Phase Delay of its Carrier Frequency under the Action of a Low-Frequency Wave -- 6.3 Amplitude-Phase Self-Action Phenomena in the High-Frequency Wave of Finite Amplitude -- References -- Chapter 7 Experimental Studies of Nonlinear Acoustic Phenomena in Polycrystalline Rocks and Metals -- 7.1 Experimental Setup -- 7.2 Nonlinear Shift in Resonance Frequency in a Glass Rod with Artificial Cracks -- 7.3 Low-Frequency Amplitude-Dependent Internal Friction and High-Frequency Dissipative Nonlinearity of Coarse-Grained Sandstone.

7.3.1 Phenomena of LF Hysteretic Nonlinearity: Amplitude-Dependent Losses and Shifts of Resonant Frequencies -- 7.3.2 Nonlinear Attenuation of an Ultrasonic Pulse under the Action of a LF Wave -- 7.4 Effect of an Intense Sound Wave on the Acoustic Properties of a Fine-Grained Sandstone Rod Resonator -- 7.5 Nonlinear Acoustic Phenomena in Limestone -- 7.5.1 Phenomena of LF Hysteretic Nonlinearity -- 7.5.2 Manifestation of the HF Dissipative Nonlinearity -- 7.6 Oscillograms of the Free Boundary Nonlinear Oscillations of a Magnesite Resonator -- 7.7 High-Frequency Nonlinear Acoustic Phenomena in Marble -- 7.7.1 Attenuation and Phase Delay of the Carrier Frequency of Weak Ultrasonic Pulses under the Action of a LF Powerful Wave -- 7.7.2 Self-Action of Finite-Amplitude Ultrasonic Pulses -- 7.8 Sound by Sound Damping of Polycrystalline Zinc -- 7.9 Modulation of Sound by Sound in Copper Subjected to Different Degrees of Annealing -- References -- Chapter 8 Experimental Studies of Nonlinear Acoustic Phenomena in Granular Media -- 8.1 Self-Demodulation of Acoustic Pulses in Partially Water-Saturated River Sand -- 8.1.1 Experimental Setup -- 8.1.2 Experimental Results -- 8.2 Self-Action of Acoustic Waves in Systems with Dissipative Nonlinearity -- 8.2.1 Description of the Experiment -- 8.2.2 Analytical Description of the Phenomenon of Self-Brightening -- 8.3 Amplification of Sound by Sound in Systems with Dissipative Nonlinearity -- 8.4 Self-Action of a Low-Frequency Acoustic Wave and Generation of the Second Harmonic in Dry and Water-Saturated River Sand -- 8.4.1 Experimental Scheme and Method of Measurement -- 8.4.2 Measurement Results -- 8.4.3 Analytical Description of the Phenomena of Self-Action and Generation of the Second Harmonic.

8.5 Amplitude Modulation of Sound by Sound in Water-Saturated River Sand -- References -- Chapter 9 Nonlinear Phenomena in Seismic Waves -- 9.1 Static Deformation of the Earth's Surface Near the Harmonic Source of Seismic Vibrations -- 9.2 Amplitude Modulation of Sound by Sound in Sandy Soil -- 9.3 Self-Action of the Seismic Wave in Sandy Soil -- 9.4 Amplitude-Phase Modulation of a Seismo-Acoustic Wave under Diurnal Tides -- References -- Index -- EULA.