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 raduate–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 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.

Preface

Introduction

1. Nonlinear Wave Processes in Homogeneous media

1.1 A progressive approximation approach: the second harmonic generation in an unbounded medium

1.2 A generation of the wave at a difference frequency: parametric array, degenerate interaction of waves

1.3 A generation of the wave at second harmonic frequency in resonators

1.4 Simple waves and formation of discontinuity

1.5 The exact solutions of the Burgers equation

1.6 Nonlinear wave processes in relaxing media

1.7 Spherical and cylindrical waves

References

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 particularly filled with 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

2.3 Elastic nonlinearity of water–like materials with partially liquid–filled capillaries

2.4 An adhesion mechanism of the hysteretic nonlinearity of cracks

References

3. Elastic Waves in Media with Strong Acoustic Nonlinearity

3.1 Nonlinear propagation and interaction of acoustic waves in media with cracks possessing an 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 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

4. Wave Processes in Micro–inhomogeneous Media with Hysteretic Nonlinearity

4.1 Hysteretic equations of state for solids with an imperfect elasticity Phenomenological models

4.2 Nonlinear waves in an unbounded medium

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

5. Wave Processes in Nonlinear Micro–inhomogeneous Media with Relaxation

5.1 Rheological model and dynamic equation of state of a micro–inhomogeneous medium with relaxation

5.2 Evolution of acoustic waves in micro–inhomogeneous media with quadratic elastic nonlinearity and relaxation

5.3 Wave processes in micro–inhomogeneous elastic media with hysteretic nonlinearity and relaxation

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

References

6. Wave Processes in the Polycrystalline Solids with Dissipative and Elastic Nonlinearity Caused by Dislocations

6.1 Modification of the linear part of the dislocation theory of absorption Granato–Lücke and equation of state with resonance dissipative and reactive nonlinearity for polycrystalline solid

6.2 Attenuation of high–frequency pulses and 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

7. Experimental Studies of the Nonlinear Acoustic Phenomena in Polycrystalline Rocks and Metals

7.1 The experimental set–up

7.2 Nonlinear resonance frequency shift in the glass resonator with artificial cracks

7.3 Low–frequency amplitude dependent internal friction and high–frequency dissipative nonlinearity of the coarse–grained sandstone

7.4 Effect of an Intense sound wave on the acoustic properties of fine–grained sandstone rod resonator

7.5 Nonlinear acoustical phenomena in limestone

7.6 Oscillograms of the free boundary nonlinear oscillations of a magnesite resonator

7.7 High–frequency nonlinear acoustic phenomena in a marble

7.8 Sound by sound damping of Polycrystalline zinc

7.9 Modulation of sound by sound in copper subjected to the different degree of annealing

References

8. Experimental Studies of Nonlinear Acoustic Phenomena in Granular Media

8.1 Self–demodulation of acoustic pulses in partially water–saturated river sand

8.2 Self–action of acoustic waves in systems with dissipative nonlinearity

8.3 Amplification of sound by sound in the systems with dissipative nonlinearity

8.4 Self–action of a LF acoustic wave and generation of the second harmonic in dry and water–saturated river sand

8.5 Sound amplitude modulation of sound by sound in water–saturated river sand

References

9. Nonlinear Phenomena in Seismic Waves

9.1 A static deformation of the Earth surface near the harmonic source of the seismic vibrations

9.2 Amplitude modulation of sound by sound in the sandy soil

9.3 Self–action of seismic wave in the sandy soil

9.4 Amplitude–phase modulation of a seismo–acoustic wave under diurnal tides

References

Index