Stroh Formalism and Rayleigh Waves

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.

Introduces a powerful and elegant mathematical method for the analysis of anisotropic elasticity equations The reader can grasp the essentials as quickly as possible Can be used as a textbook, which presents compactly introduction and applications of the Stroh formalism Appeals to the people not only in mathematics but also in mechanics and engineering science Prerequisites are only basic linear algebra, calculus and fundamentals of differential equations

Klappentext

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.

Inhalt

From the contents

Chapter 1: Stroh's Formalism for Static Elasticity. Chapter 2: Applications in Static Elasticity. Chapter 3: Rayleigh waves in Stroh's formalism.