弹性波理论（英文）（Theory of Elastic Waves)

This book highlights a systematic introduction to the basic theory of elastic wave propagation in complex media. The theory of elastic waves is widely used in fields such as geophysical exploration, seismic survey, medical ultrasound imaging, nondestructive testing of materials and structures, phononic crystals, metamaterials and structure health monitoring. To help readers develop a systematic grasp of the basic theory, and thus its applications, the book elaborates on the theory of elastic wave propagation in isotropic solid media, covering phenomena in infinite media, interfaces, layered structure with finite thickness, Rayleigh wave and Love wave propagating along the surface of semi infinite solid and covering layer, and the guided waves and leaky waves in flat plates and in cylindrical rods. The propagation patterns and features of guided waves in cylindrical shells and spherical shells are also introduced. The author wrote the book based on a decade of teaching experience of a graduate course of the same name and two decades of research on the theory and applications.

Contents
1 Fundamentals of Elastodynamics 1
1.1 Basic Hypothesis of Elastodynamics 1
1.1.1 Continuity Hypothesis 1
1.1.2 Elasticity Hypothesis 1
1.1.3 Small Deformation Hypothesis 2
1.1.4 Homogeneous Hypothesis 2
1.1.5 Isotropic Hypothesis 2
1.1.6 Zero Initial Stress Hypothesis 3
1.2 Basic Conservation Laws of Elastodynamics 3
1.2.1 Law of Mass Conservation 3
1.2.2 Law of Conservation of Momentum 5
1.2.3 The Law of Conservation of Energy 6
1.3 Variational Principle of Elastodynamics 7
1.4 The Initial Boundary Value Problem of Elastodynamics 10
1.5 Transient and Steady-State Problems 12
2 Elastic Waves in an Infinite Medium 15
2.1 Scalar Potential and Vector Potential 15
2.2 Solution of Wave Equation 19
2.3 Properties of Plane Waves 31
2.3.1 Propagation Mode of Plane Waves 31
2.3.2 The Stress Distribution on the Wavefront 34
2.3.3 The Energy Flow Density of a Plane Wave 35
2.4 Inhomogeneous Plane Wave 51
2.5 Spectrum Analysis of Plane Wave 59
3 Reflection and Transmission of Elastic Waves at Interfaces 63
3.1 Classification of Interfaces and Plane Waves 64
3.1.1 Perfect Interface and Imperfect Interface 64
3.1.2 P Wave， S Wave and SH Wave 70
3.2 Reflection of Elastic Waves on Free Surface 73
3.2.1 Reflection of P Wave on Free Surface 73
3.2.2 Reflection of SH Waves on Free Surface 83
3.2.3 Reflection of SV Waves on Free Surface 84
3.2.4 Incident P Wave and SV Wave Simultaneously 90
3.3 Reflection and Transmission of Elastic Waves at the Interface 95
3.3.1 Reflection and Transmission of P Waves at the Interface 95
3.3.2 Reflection and Transmission of SH Waves at the Interface 103
3.3.3 Reflection and Transmission of SV Waves at the Interface 106
3.3.4 P Wave and SV Wave Incidence Simultaneously 112
3.4 Reflection and Transmission of Waves at the Periodic Corrugated Interface 128
4 Reflection and Transmission of Elastic Waves in Multilayer Media 151
4.1 Simultaneous Interface Conditions Method 151
4.2 Transfer Matrix Method 161
4.3 Stiffness Matrix Method 167
4.4 Multiple Reflection/Transmission Method 175
4.5 Super-Interface Method 179
4.6 The State Transfer Equation Method 193
4.7 Bloch Waves in Periodic Layered Structures207
5 Surface Wave and Interface Wave 225
5.1 P-type Surface Waves and SY-Type Surface Waves 225
5.2 Rayleigh Wave 228
5.2.1 Rayleigh Wave’s Wave Function 228
5.2.2 Rayleigh Equation 231
5.2.3 The Displacement Field of the Ryleigh Wave 233
5.2.4 Rayleigh Wave in Elastic Half-Space with Cover Layer 236
5.3 Love Wave 251
5.3.1 The Displacement Distribution of Love Wave 252
5.3.2 The Dispersion Equation of Love Wave 255
5.4 Stoneley Wave 258
5.4.1 Wave Function of Stoneley Wave 259
5.4.2 Stoneley Equation 262
5.5 Torsional Surface Wave 264
6 Guided Waves 283
6.1 Flexural Waves in Beams 283
6.2 Flexural Waves in Plate 299
6.3 Guided Waves in Plate (Lamb Wave) 309
6.3.1 Mixed Boundary Condition 312
6.3.2 Free Boundary Conditions 316
6.3.3 Fixed Boundary Condition 318
6.3.4 Liquid Load on Both Sides 320
6.4 Guided Waves in Cylindrical Rod 324
6.4.1 Axisymmetric Torsional Waves 326
6.4.2 Axisymmetric Compression Waves 328
6.4.3 Non-axisymmetric Guided Waves (Bending Waves) 331
6.4.4 Surface with Liquid Load 335
6.5 Waves in Cylindrical Tube 337
6.5.1 Axisymmetric Torsional Waves 337
6.5.2 Axisymmetric Compression Waves 339
6.5.3 Non-axisymmetric Waves (Bending Waves) 342
6.5.4 Inner and Outer Surfaces with Liquid Load 344
6.6 Guided Waves in Spherical Shell 346
6.6.1 Inner and Outer Free Surfaces 351
6.6.2 Inner and Outer Surfaces with Liquid Loads 355
References 359