Wave Processes in Solids With Microstructure

by Erofeyev, Vladimir I.

• ISBN13: 9789812382276
• ISBN10: 9812382275
• Format: Hardcover
• Copyright: 2003-08-01
• Publisher: World Scientific Pub Co Inc

Summary

This book systematically discusses the modern theory of propagation and interaction of elastic waves in solids with microstructure. Mathematical models of solids taking into account microstructure, geometrical and physical nonlinearity, damage media, interaction of deformation and magnetic field are obtained. Different wave effects characteristic of solids with microstructure are studied. The opportunity to use these effects in problems of ultrasonic testing of materials and devices of constructions is considered.

Table of Contents

Preface	p. vii
Introduction	p. ix
The Fundamental Hypothesis of Microstructured Elastic Solids. Structural-Phenomenological Model	p. 1
Mathematical Models of Solids with Microstructure	p. 1
Micromorphic media	p. 1
Cosserat continuum	p. 3
Cosserat pseudocontinuum	p. 5
Gradient Elasticity Media (Le Roux continuum)	p. 6
Two-component mixture of solids	p. 9
Definition of Material Constants	p. 12
Gradient Elasticity Media. Dispersion. Dissipation. Non-Linearity	p. 19
Dynamic Equations. Energy and Momentum Variation Law	p. 19
Dispersion Properties of Longitudinal and Shear Waves. Surface Rayleigh Waves	p. 21
Dissipative Properties	p. 25
Nonlinear Plain Stationary Waves	p. 27
Longitudinal waves	p. 27
Shear waves	p. 30
Quasi-Plain Wave Beams	p. 41
Parabolic approximation in the linear theory of diffraction	p. 41
Longitudinal waves	p. 46
Shear waves	p. 48
Self-Modulation of Quasi-Harmonic Shear Waves	p. 50
Resonant Interaction of Quasi-Harmonic Waves	p. 57
Nonlinear resonant interaction of elastic waves	p. 57
Three-wave interaction of longitudinal and shear waves	p. 59
Four-frequency interaction of shear waves	p. 66
Noise Waves	p. 68
Gradient Elasticity Media. Damaged Medium. Magnetoelasticity	p. 73
Waves in Damaged Medium with Microstructure	p. 73
Basic terms	p. 73
Longitudinal waves	p. 77
Shear waves	p. 80
Magneto-Elastic Waves in the Medium with Microstructure	p. 83
Nonlinear magneto-elastic equations	p. 84
Dispersion characteristics	p. 85
Medium without microstructure	p. 86
Medium with microstructure	p. 89
Stationary magnetoelastic waves	p. 91
Longitudinal waves	p. 91
Shear waves	p. 97
Cosserat Continuum	p. 101
Basic Equations of Micropolar Elasticity Theory	p. 101
Dispersion Properties of Volume Waves	p. 105
Wave Reflection from the Free Interface of Micropolar Halfspace. Rayleigh Surface Waves	p. 109
Normal Waves in a Micropolar Layer	p. 113
Nonlinear Resonant Interaction of Longitudinal and Rotation Waves	p. 119
Interaction of longitudinal waves and longitudinal rotation waves	p. 119
Interaction of longitudinal waves and shear-rotation waves	p. 127
Waves in Cosserat Pseudocontinuum	p. 131
Waves in the Cosserat Continuum with Symmetric Stress Tensor	p. 143
Waves in Two-Component Mixture of Solids	p. 149
Dispersion Properties	p. 149
Some Nonlinear Wave Effects	p. 151
Stationary waves	p. 153
Resonant interactions of quasi-harmonic waves	p. 154
Waves in Micromorphic Solids	p. 159
Dynamics Equations	p. 159
Different Types of Volume Waves and their Dispersion Properties	p. 167
Microoscilations	p. 167
Equations describing one-dimension wave processes	p. 168
Dispersion relations	p. 171
Low-frequency approximation	p. 173
Surface Shear Waves in the Gradient-Elastic Half-Space with Surface Energy	p. 176
Elasto-Plastic Waves in the Medium with Dislocations	p. 191
Equations of Dynamics	p. 191
Dispersion Properties	p. 193
Some Nonlinear Problems	p. 198
Longitudinal waves	p. 200
Shear waves	p. 202
Correlation of Elasto-Plastic Continuum and Cosserat Continuum	p. 204
Example of Research of the Influence of Dislocations on Dispersion and Damping of Ultrasound in Solid Body	p. 205
Wave Problems of Micropolar Hydrodynamics	p. 211
Rotational Waves in Micropolar Liquids	p. 211
Shear Surface Wave at the Interface of Elastic Body and Micropolar Liquid	p. 215
Shear Surface Wave at the Interface Between Elastic Half-Space and Conducting Viscous Liquid in a Magnetic Field	p. 223
Bibliography	p. 233
Index	p. 253
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