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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010184932 | TA418 T36 2007 | Open Access Book | Book | Searching... |
Searching... | 30000003490368 | TA418 T36 2007 | Open Access Book | Book | Searching... |
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Summary
Summary
Roger Fosdick The Journal of Elasticity: The Physical and Mathematical Science of Solids invites expository articles from time-to-time in order to collect results in areas of research that have made significant impact on the field of solid mechanics and that show continued interest in present-day research and thinking. The Stroh formalism is one such area, especially as it impacts upon the analysis of anisotropic media, that has been generalized from linear elastostatics to cover linear theories of piezoelectro-elasticity and megneto-elasticity as well as elastic wave phenomena. In this work, Kazumi Tanuma presents the essential elements of the Stroh formalism, its major theorems with proofs and applications, in a research-level textbook form. The presentation is self-contained and the development is clear and concise. Professor Tanuma's efforts to produce a straightforward, accurate and readable account of this subject are clearly evident. He has organized the subject with a common logical thread throughout and he has given basis for not only the importance of this area of research, but, most importantly, for understanding its meaning and significance.
Table of Contents
| Foreword | p. 1 |
| Preface | p. 3 |
| Stroh Formalism and Rayleigh Waves | p. 5 |
| Abstract | p. 5 |
| 1 The Stroh Formalism for Static Elasticity | p. 6 |
| 1.1 Basic Elasticity | p. 6 |
| 1.2 Stroh's Eigenvalue Problem | p. 10 |
| 1.3 Rotational Invariance of Stroh Eigenvector in Reference Plane | p. 14 |
| 1.4 Forms of Basic Solutions When Stroh's Eigenvalue Problem is Degenerate | p. 17 |
| 1.5 Rotational Dependence When Stroh's Eigenvalue Problem is Degenerate | p. 22 |
| 1.6 Angular Average of Stroh's Eigenvalue Problem: Integral Formalism | p. 25 |
| 1.7 Surface Impedance Tensor | p. 28 |
| 1.8 Examples | p. 31 |
| 1.8.1 Isotropic Media | p. 31 |
| 1.8.2 Transversely Isotropic Media | p. 35 |
| 1.9 Justification of the Solutions in the Stroh Formalism | p. 44 |
| 1.10 Comments and References | p. 53 |
| 1.11 Exercises | p. 55 |
| 2 Applications in Static Elasticity | p. 59 |
| 2.1 Fundamental Solutions | p. 59 |
| 2.1.1 Fundamental Solution in the Stroh Formalism | p. 59 |
| 2.1.2 Formulas for Fundamental Solutions: Examples | p. 60 |
| 2.2 Piezoelectricity | p. 63 |
| 2.2.1 Basic Theory | p. 63 |
| 2.2.2 Extension of the Stroh Formalism | p. 65 |
| 2.2.3 Surface Impedance Tensor of Piezoelectricity | p. 70 |
| 2.2.4 Formula for Surface Impedance Tensor of Piezoelectricity: Example | p. 71 |
| 2.3 Inverse Boundary Value Problem | p. 74 |
| 2.3.1 Dirichlet to Neumann map | p. 74 |
| 2.3.2 Reconstruction of Elasticity Tensor | p. 76 |
| 2.3.2.1 Reconstruction of Surface Impedance Tensor from Localized Dirichlet to Neumann Map | p. 76 |
| 2.3.2.2 Reconstruction of Elasticity Tensor from Surface Impedance Tensor | p. 87 |
| 2.4 Comments and References | p. 90 |
| 2.5 Exercises | p. 92 |
| 3 Rayleigh Waves in the Stroh Formalism | p. 95 |
| 3.1 The Stroh Formalism for Dynamic Elasticity | p. 95 |
| 3.2 Basic Theorems and Integral Formalism | p. 100 |
| 3.3 Rayleigh Waves in Elastic Half-space | p. 105 |
| 3.4 Rayleigh Waves in Isotropic Elasticity | p. 111 |
| 3.5 Rayleigh Waves in Weakly Anisotropic Elastic Media | p. 117 |
| 3.6 Rayleigh Waves in Anisotropic Elasticity | p. 127 |
| 3.6.1 Limiting Wave Solution | p. 128 |
| 3.6.2 Existence Criterion Based on S[subscript 3] | p. 134 |
| 3.6.3 Existence Criterion Based on Z | p. 141 |
| 3.6.4 Existence Criterion Based on Slowness Sections | p. 145 |
| 3.7 Comments and References | p. 147 |
| 3.8 Exercises | p. 148 |
| References | p. 151 |
| Index | p. 155 |
