Stroh Formalism and Rayleigh Waves

Preface

Chapter 1: The Stroh Formalism for Static Elasticity

Section 1.1: Basic Elasticity

Section 1.2: Strohs Eigenvalue Problem

Section 1.3: Rotational Invariance of Stroh Eigenvector in Reference Plane

Section 1.4: Forms of Basic Solutions When Strohs Eigenvalue Problem is Degenerate

Section 1.5: Rotational Dependence When Strohs Eigenvalue Problem is Degenerate

Section 1.6: Angular Average of Strohs Eigenvalue Problem: Integral Formalism

Section 1.7: Surface Impedance Tensor

Section 1.8: Examples

Subsection 1.8.1: Isotropic Media

Subsection 1.8.2: Transversely Isotropic Media

Section 1.9: Justification of the Solutions in the Stroh Formalism

Section 1.10: Comments and References

Section 1.11: Exercises

Chapter 2: Applications in Static Elasticity

Section 2.1: Fundamental Solutions

Subsection 2.1.1: Fundamental Solution in the Stroh Formalism

Subsection 2.1.2: Formulas for Fundamental Solutions: Examples

Section 2.2: Piezoelectricity

Subsection 2.2.1: Basic Theory

Subsection 2.2.2: Extension of the Stroh Formalism

Subsection 2.2.3: Surface Impedance Tensor of Piezoelectricity

Subsection 2.2.4: Formula for Surface Impedance Tensor of Piezoelectricity: Example

Section 2.3: Inverse Boundary Value Problem

Subsection 2.3.1: Dirichlet to Neumann map

Subsection 2.3.2: Reconstruction of Elasticity Tensor

Subsubsection 2.3.2.1: Reconstruction of Surface Impedance Tensor from Localized Dirichlet to Neumann Map

Subsubsection 2.3.2.2: Reconstruction of Elasticity Tensor from Surface Impedance Tensor

Section 2.4: Comments and References

Section 2.5: Exercises

Chapter 3: Rayleigh waves in the Stroh formalism

Section 3.1: The Stroh Formalism for Dynamic Elasticity

Section 3.2: Basic Theorems and Integral Formalism

Section 3.3: Rayleigh Waves in Elastic Half-space

Section 3.4: Rayleigh Waves in Isotropic Elasticity

Section 3.5: Rayleigh Waves in Weakly Anisotropic Elastic Media

Section 3.6: Rayleigh Waves in Anisotropic Elasticity

Subsection 3.6.1: Limiting Wave Solution

Subsection 3.6.2: Existence Criterion Based on S_3

Subsection 3.6.3: Existence Criterion Based on Z

Subsection 3.6.4: Existence Criterion Based on Slowness Sections

Section 3.7: Comments and References

Section 3.8: Exercises