%0 Journal Article
%T Rayleigh Waves in a Rotating Orthotropic Micropolar Elastic Solid Half-Space
%A Baljeet Singh
%A Ritu Sindhu
%A Jagdish Singh
%J International Journal of Geophysics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/690249
%X A problem on Rayleigh wave in a rotating half-space of an orthotropic micropolar material is considered. The governing equations are solved for surface wave solutions in the half space of the material. These solutions satisfy the boundary conditions at free surface of the half-space to obtain the frequency equation of the Rayleigh wave. For numerical purpose, the frequency equation is approximated. The nondimensional speed of Rayleigh wave is computed and shown graphically versus nondimensional frequency and rotation-frequency ratio for both orthotropic micropolar elastic and isotropic micropolar elastic cases. The numerical results show the effects of rotation, orthotropy, and nondimensional frequency on the nondimensional speed of the Rayleigh wave. 1. Introduction Material response to external stimuli depends heavily on the motions of its inner structures. Classical elasticity does not include this effect, where only translation degrees of freedom of material point of body are considered. Eringen [1] developed the linear micropolar theory of elasticity, which included the intrinsic rotations of the microstructure. It provides a model which can support body and surface couples and display high frequency optical branch of the wave spectrum. For engineering applications, it can model composites with rigid chopped fibres, elastic solid with rigid granular inclusions, and other industrial materials such as liquid crystals. The assumptions of isotropy in a solid medium may not capture some of significant features of the continuum responses of soils, geological materials, and composites. Iesan [2¨C4] studied some static problems in orthotropic micropolar elasticity. Kumar and Choudhary [5, 6] studied the mechanical sources and dynamic behaviour of orthotropic micropolar elastic medium. Kumar and Chaudhary [7] studied the plane strain problem in a homogeneous orthotropic micropolar elastic solid. Kumar and Ailawalia [8] studied the response of a micropolar cubic crystal due to various sources. Kumar and Gupta [9] studied the propagation of waves in transversely isotropic micropolar generalized thermoelastic half-space. Singh [10] investigated the two-dimensional plane wave propagation in an orthotropic micropolar elastic solid. Surface waves in elastic solids were first studied by Rayleigh [11] for an isotropic elastic solid. The extension of surface wave analysis and other wave propagation problems to anisotropic elastic materials has been the subject of many studies; see, for example, [12¨C21]. The aim of the present paper is to study the propagation of
%U http://www.hindawi.com/journals/ijge/2013/690249/