Stroh Formalism and Rayleigh Waves [electronic resource] /
Tanuma, Kazumi.author.
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 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, which has long been a topic of the utmost importance in nondestructive evaluation, seismology, and materials science. Here existence, uniqueness, phase velocity, polarization, and perturbation of Rayleigh waves are discussed through the Stroh formalism. This work will appeal to students and researchers in applied mathematics, mechanics, and engineering science. Reprinted from the Journal of Elasticity, Vol. 89:1-3, 2007. .
Description based upon print version of record.
CONTENTS; Foreword / Roger Fosdick; Preface / Kazumi Tanuma; Stroh Formalism and Rayleigh Waves; Abstract; 1 The Stroh Formalism for Static Elasticity; 1.1 Basic Elasticity; 1.2 Stroh's Eigenvalue Problem; 1.3 Rotational Invariance of Stroh Eigenvector in Reference Plane; 1.4 Forms of Basic Solutions When Stroh's Eigenvalue Problemis Degenerate; 1.5 Rotational Dependence When Stroh's Eigenvalue Problemis Degenerate; 1.6 Angular Average of Stroh's 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 Formalism1.10 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
2.3.2.1 Reconstruction of Surface Impedance Tensor fromLocalized Dirichlet to Neumann Map2.3.2.2 Reconstruction of Elasticity Tensor from SurfaceImpedance 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
3.6.3 Existence Criterion Based on Z3.6.4 Existence Criterion Based on Slowness Sections; 3.7 Comments and References; 3.8 Exercises; References; Index
Includes bibliographical references and index.
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 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, which has long been a topic of the utmost importance in nondestructive evaluation, seismology, and materials science. Here existence, uniqueness, phase velocity, polarization, and perturbation of Rayleigh waves are discussed through the Stroh formalism. This work will appeal to students and researchers in applied mathematics, mechanics, and engineering science. Reprinted from the Journal of Elasticity, Vol. 89:1-3, 2007. .
Applied mathematics.
Engineering mathematics.
Partial differential equations.
Physics.
Mechanics.
Acoustics.
Mathematical and Computational Engineering.
Partial Differential Equations.
Mathematical Methods in Physics.
Classical Mechanics.
Acoustics.