Stroh Formalism and Rayleigh Waves

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.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.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 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, 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.§This work will appeal to students and researchers in applied mathematics, mechanics, and engineering science.