Propagation of Rayleigh waves in various elastic half spaces

Abstract

The research work presented in this thesis deals with Propagation of Rayleigh waves in various elastic half-spaces . Chapter 1 contains a basic introduction about continuum mechanics, stress and strain, Generalized Hooke s law and equations of small motion in rotating elastic media along with the literature review. In chapter 2, the propagation of Rayleigh waves in an incompressible rotating orthotropic material is studied by using impedance boundary conditions. The governing equations of the medium are specialized in a plane and solved for Rayleigh surface wave solutions. A secular equation for Rayleigh surface wave is obtained and solved numerically to show the dependence of non-dimensional wave speed on non-dimensional material constant, rotation parameter and impedance boundary parameters. In chapter 3 Rayleigh wave in a rotating compressible elastic half-space of orthotropic type with impedance boundary conditions is explored. An explicit secular equation of Rayleigh wave is derived and numerically solved to illustrate graphically the non-dimensional speed of Rayleigh wave against rotation, material and impedance boundary parameters. In chapter 4, the propagation of Rayleigh wave on impedance boundary of rotating incompressible monoclinic elastic half-space is investigated. In chapter 5, the Rayleigh wave propagation is explored in context of linear elasticity for rotating half-space of compressible monoclinic elastic materials with impedance boundary conditions. The governing equations of the medium are solved to obtain a secular equation with the help of impedance boundary conditions. In chapter 6, Rayleigh-type surface wave is explored in context of theory of nonlocal elasticity for an isotropic diffusive material. The specialized governing equations in a plane are solved to deduce a Rayleigh characteristic equation with the help of traction free boundary conditions. newline