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. The book is a valuable reference for students, researchers and professionals who expect an understandable and comprehensive discussion of the theory, analytical methods and related research results.

Chapter 1 Fundamentals of Elastodynamics

1.1       Basic hypothesis of Elastodynamics

1.1.1        Continuity hypothesis

1.1.2        Elasticity hypothesis

1.1.3        Small deformation hypothesis

1.1.4        Homogeneous hypothesis

1.1.5        Isotropic hypothesis

1.1.6        Zero initial stress hypothesis

1.2       Basic conservation laws of Elastodynamics

1.2.1        Law of mass conservation

1.2.2        Law of conservation of momentum

1.2.3        The law of conservation of energy

1.3       Variational principle of elastodynamics

1.4       The initial-boundary value problem of elastodynamics

1.5       Transient and steady-state problems

Chapter 2 Elastic waves in an infinite medium

2.1 Scalar potential and vector potential

2.2 Solution of wave equation

2.3 Properties of plane waves

2.3.1 Propagation mode of plane waves

2.3.2 The stress distribution on the wavefront

2.3.3 The energy flow density of a plane wave

2.4 Inhomogeneous plane wave

2.5 Spectrum analysis of plane wave

Chapter 3 Reflection and transmission of elastic waves at interfaces

3.1 Classification of interfaces and plane waves

3.1.1 Perfect interface and imperfect interface

3.1.2 P wave?S wave and SH wave

3.2 Reflection of elastic waves on free surfaces

3.2.1 Reflection of P waves on free surfaces

3.2.2 Reflection of SH waves on free surfaces 

3.2.3 Reflection of SV waves on free surfaces

3.2.4 Incident P wave and SV wave simultaneously

3.3 Reflection and transmission of elastic waves at the interface

3.3.1 Reflection and transmission of P waves at the interface

3.3.2 Reflection and transmission of SH waves at the interface

3.3.3 Reflection and transmission of SV waves at the interface

3.3.4 P wave and SV wave incidence simultaneously

3.4 Reflection and transmission of waves at the periodic corrugated interface

Chapter4 Reflection and transmission of elastic waves in multilayer media

4.1 Simultaneous interface conditions method

4.2 Transfer matrix method

4.3 Stiffness matrix method

4.4 Multiple reflection/transmission method

4.5 Super-interface method

4.6 The state transfer equation method

4.7 Bloch waves in periodic layered structures

Chapter 5.  Surface wave and interface wave

5.1 P-type surface waves and SV-type surface waves

5.2 Rayleigh wave

5.2.1  Wave function Rayleigh wave

5.2.2  Rayleigh equation

5.2.3 The displacement field of the Ryleigh wave

5.3 Love waves

5.3.1 The displacement distribution of Love waves

5.3.2  The dispersion equation of Love wave

5.4 Stoneley waves

5.4.1  Wave function of Stoneley wave

5.4.2  Stoneley equation

5.5 Torsional surface waves

Chapter 6  Guided waves

6.1 Flexural waves in beams

6.2 Flexural waves in plates

6.3 Guided waves in a Plate (Lamb wave)

6.3.1 Mixed boundary condition

6.3.2 Free boundary conditions

6.3.3 Fixed boundary condition

6..3.4 Liquid load on both sides

6.4 Guided Waves in Cylindrical Rod

6.4.1 Axisymmetric Torsional Waves

6.4.2Axisymmetric Compression Waves

6.4.3 Non-axisymmetric guided Waves (Bending Waves)

6.4.4 Surface with Liquid Load

6.5 Wave in Cylindrical Tube

6.5.1Axisymmetric Torsional Waves

6.5.2 Axisymmetric Compression Waves

6.5.3 Non-axisymmetric Waves (bending Waves)

6.5.4 Inner and Outer Surfaces with Liquid Load

6.6 Guided Waves in a Spherical Shell

6.6.1 Inner and outer free surfaces

6.6.2 Inner and outer surfaces with liquid loads

References    

Dr. Peijun Wei received his Ph.D. from the Institute of Mechanics, Chinese Academy of Sciences in 1999. He was a visiting scholar at the University of Taxas, Arlington, the USA. He is currently a Professor and Dean of the Department of Applied Mechanics at the School of Mathematics and Physics, the University of Science and Technology Beijing. His research interests include the theory of elastic wave propagation in complex media, the elastic wave bandgap theory of phononic crystals, acoustic metamaterials and the acoustic stealth theory, inverse problems of wave and vibration and damage detection. He received the First Prize in Natural Sciences Awards by the Ministry of Education of China for his research in the theory of elastic waves.