Theory of Elastic Waves

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

3.4 Reflection and transmission of waves at the periodic corrugated interface

Chapter4 Reflection and transmission of elastic waves in multilayer media

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

6.4 Guided Waves in Cylindrical Rod

6.4.1 Axisymmetric Torsional Waves