Stroh Formalism and Rayleigh Waves

Softcover Nachdruck of hardcover 1. Auflage 2007
ISBN: 978-90-481-7622-9
Verlag: Springer Netherlands

Buch, Englisch, 159 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 260 g

Stroh formalism is a powerful mathematical method developed for the analysis of equations of anisotropic elasticity. This exposition introduces the essence of this formalism and demonstrates its effectiveness in both static and dynamic elasticity. The book gives a succinct introduction to Stroh formalism, discusses several important topics in static elasticity, and examines Rayleigh waves, a key topic in nondestructive evaluation, seismology, and materials science.

Zielgruppe

Research

Autoren/Hrsg.

Tanuma, Kazumi

Fachgebiete

• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Mechanik Akustik, Schwingungsanalyse
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik

Inhaltsverzeichnis

Preface

Chapter 1: The Stroh Formalism for Static Elasticity

Section 1.1: Basic Elasticity

Section 1.2: Stroh's Eigenvalue Problem

Section 1.3: Rotational Invariance of Stroh Eigenvector in Reference Plane

Section 1.4: Forms of Basic Solutions When Stroh's Eigenvalue Problem is Degenerate

Section 1.5: Rotational Dependence When Stroh's Eigenvalue Problem is Degenerate

Section 1.6: Angular Average of Stroh's 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