Stroh Formalism and Rayleigh Waves

Cover -- Contents -- Foreword -- Preface -- Stroh Formalism and Rayleigh Waves -- Abstract -- 1 The Stroh Formalism for Static Elasticity -- 1.1 Basic Elasticity -- 1.2 Strohs Eigenvalue Problem -- 1.3 Rotational Invariance of Stroh Eigenvector in Reference Plane -- 1.4 Forms of Basic Solutions When Strohs Eigenvalue Problem is Degenerate -- 1.5 Rotational Dependence When Strohs Eigenvalue Problem is Degenerate -- 1.6 Angular Average of Strohs Eigenvalue Problem: Integral Formalism -- 1.7 Surface Impedance Tensor -- 1.8 Examples -- 1.8.1 Isotropic Media -- 1.8.2 Transversely Isotropic Media -- 1.9 Justification of the Solutions in the Stroh Formalism -- 1.10 Comments and References -- 1.11 Exercises -- 2 Applications in Static Elasticity -- 2.1 Fundamental Solutions -- 2.1.1 Fundamental Solution in the Stroh Formalism -- 2.1.2 Formulas for Fundamental Solutions: Examples -- 2.2 Piezoelectricity -- 2.2.1 Basic Theory -- 2.2.2 Extension of the Stroh Formalism -- 2.2.3 Surface Impedance Tensor of Piezoelectricity -- 2.2.4 Formula for Surface Impedance Tensor of Piezoelectricity: Example -- 2.3 Inverse Boundary Value Problem -- 2.3.1 Dirichlet to Neumann map -- 2.3.2 Reconstruction of Elasticity Tensor -- 2.4 Comments and References -- 2.5 Exercises -- 3 Rayleigh Waves in the Stroh Formalism -- 3.1 The Stroh Formalism for Dynamic Elasticity -- 3.2 Basic Theorems and Integral Formalism -- 3.3 Rayleigh Waves in Elastic Half-space -- 3.4 Rayleigh Waves in Isotropic Elasticity -- 3.5 Rayleigh Waves in Weakly Anisotropic Elastic Media -- 3.6 Rayleigh Waves in Anisotropic Elasticity -- 3.6.1 Limiting Wave Solution -- 3.6.2 Existence Criterion Based on S -- 3.6.3 Existence Criterion Based on Z -- 3.6.4 Existence Criterion Based on Slowness Sections -- 3.7 Comments and References -- 3.8 Exercises -- References -- Index.