Title Stroh Formalism and Rayleigh Waves / Kazumi Tanuma

Published Dordrecht : Springer, ©2007

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Description 1 online resource Contents 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 Summary The Stroh formalism is a powerful and elegant mathematical method developed for the analysis of the equations of anisotropic elasticity. The purpose of this exposition is to introduce the essence of this formalism and demonstrate its effectiveness in both static and dynamic elasticity. The equations of elasticity are complicated, because they constitute a system and, particularly for the anisotropic cases, inherit many parameters from the elasticity tensor. The Stroh formalism reveals simple structures hidden in the equations of anisotropic elasticity and provides a systematic approach to thes Bibliography Includes bibliographical references and index Notes Print version record Subject Seismic waves -- Mathematical models Differential equations. Ingénierie. Differential equations Seismic waves -- Mathematical models Form Electronic book ISBN 9781402063893 140206389X 1281875902 9781281875907 1402063881 9781402063886

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