Stroh Formalism and Rayleigh Waves |
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Authors: | Kazumi Tanuma |
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Institution: | (1) Department of Mathematics, Graduate School of Engineering, Gunma University, Kiryu 376-8515, Japan |
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Abstract: | 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 could 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.
The Table of Contents and Index are also provided as Electronic Supplementary Material for online readers at doi:
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Keywords: | Anisotropic elasticity Rayleigh waves The Stroh formalism Equations of elasticity Inverse problems |
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