Stroh Formalism and Rayleigh Waves by Kazumi TanumaStroh Formalism and Rayleigh Waves by Kazumi Tanuma

Stroh Formalism and Rayleigh Waves

byKazumi Tanuma

Paperback | October 19, 2010

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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 these equations.This exposition is divided into three chapters. Chapter 1 gives a succinct introduction to the Stroh formalism so that the reader can grasp the essentials as quickly as possible. In Chapter 2 several important topics in static elasticity, which include fundamental solutions, piezoelectricity, and inverse boundary value problems, are studied on the basis of the Stroh formalism.Chapter 3 is devoted to Rayleigh waves, for long a topic of utmost importance in nondestructive evaluation, seismology, and materials science. There we discuss existence, uniqueness, phase velocity, polarization, and perturbation of Rayleigh waves through the Stroh formalism.This work will appeal to students and researchers in applied mathematics, mechanics, and engineering science.
Title:Stroh Formalism and Rayleigh WavesFormat:PaperbackDimensions:164 pages, 9.25 × 6.1 × 0 inPublished:October 19, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048176220

ISBN - 13:9789048176229

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Table of Contents

PrefaceChapter 1: The Stroh Formalism for Static ElasticitySection 1.1: Basic ElasticitySection 1.2: Stroh's Eigenvalue ProblemSection 1.3: Rotational Invariance of Stroh Eigenvector in Reference PlaneSection 1.4: Forms of Basic Solutions When Stroh's Eigenvalue Problem is DegenerateSection 1.5: Rotational Dependence When Stroh's Eigenvalue Problem is DegenerateSection 1.6: Angular Average of Stroh's Eigenvalue Problem: Integral FormalismSection 1.7: Surface Impedance TensorSection 1.8: ExamplesSubsection 1.8.1: Isotropic MediaSubsection 1.8.2: Transversely Isotropic MediaSection 1.9: Justification of the Solutions in the Stroh FormalismSection 1.10: Comments and ReferencesSection 1.11: ExercisesChapter 2: Applications in Static ElasticitySection 2.1: Fundamental SolutionsSubsection 2.1.1: Fundamental Solution in the Stroh FormalismSubsection 2.1.2: Formulas for Fundamental Solutions: ExamplesSection 2.2: PiezoelectricitySubsection 2.2.1: Basic TheorySubsection 2.2.2: Extension of the Stroh FormalismSubsection 2.2.3: Surface Impedance Tensor of PiezoelectricitySubsection 2.2.4: Formula for Surface Impedance Tensor of Piezoelectricity: ExampleSection 2.3: Inverse Boundary Value ProblemSubsection 2.3.1: Dirichlet to Neumann mapSubsection 2.3.2: Reconstruction of Elasticity TensorSubsubsection 2.3.2.1: Reconstruction of Surface Impedance Tensor from Localized Dirichlet to Neumann MapSubsubsection 2.3.2.2: Reconstruction of Elasticity Tensor from Surface Impedance TensorSection 2.4: Comments and ReferencesSection 2.5: ExercisesChapter 3:  Rayleigh waves in the Stroh formalismSection 3.1: The Stroh Formalism for Dynamic ElasticitySection 3.2: Basic Theorems and Integral FormalismSection 3.3: Rayleigh Waves in Elastic Half-spaceSection 3.4: Rayleigh Waves in Isotropic ElasticitySection 3.5: Rayleigh Waves in Weakly Anisotropic Elastic MediaSection 3.6: Rayleigh Waves in Anisotropic ElasticitySubsection 3.6.1: Limiting Wave SolutionSubsection 3.6.2: Existence Criterion Based on S_3Subsection 3.6.3: Existence Criterion Based on ZSubsection 3.6.4: Existence Criterion Based on Slowness SectionsSection 3.7: Comments and ReferencesSection 3.8: Exercises