Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2011, Article ID 763429, 47 pages doi:10.1155/2011/763429 Research Article Rayleigh Waves in Generalized Magneto-Thermo-Viscoelastic Granular Medium under the Influence of Rotation, Gravity Field, and Initial Stress A. M. Abd-Alla, 1 S. M. Abo-Dahab, 1, 2 and F. S. Bayones 3 1 Mathematics Department, Faculty of Science, Taif University, Taif 21974, Saudi Arabia 2 Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt 3 Mathematics Department, Faculty of Science, Umm Al-Qura University, P.O. Box 10109, Makkah 13401, Saudi Arabia Correspondence should be addressed to S. M. Abo-Dahab, sdahb@yahoo.com Received 4 December 2010; Revised 14 January 2011; Accepted 25 February 2011 Academic Editor: Ezzat G. Bakhoum Copyright q 2011 A. M. Abd-Alla et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The surface waves propagation in generalized magneto-thermo-viscoelastic granular medium subjected to continuous boundary conditions has been investigated. In addition, it is also subjected to thermal boundary conditions. The solution of the more general equations are obtained for thermoelastic coupling. The frequency equation of Rayleigh waves is obtained in the form of a determinant containing a term involving the coefficient of friction of a granular media which determines Rayleigh waves velocity as a real part and the attenuation coefficient as an imaginary part, and the effects of rotation, magnetic field, initial stress, viscosity, and gravity field on Rayleigh waves velocity and attenuation coefficient of surface waves have been studied in detail. Dispersion curves are computed numerically for a specific model and presented graphically. Some special cases have also been deduced. The results indicate that the effect of rotation, magnetic field, initial stress, and gravity field is very pronounced. 1. Introduction The dynamical problem in granular media of generalized magneto-thermoelastic waves has been studied in recent times, necessitated by its possible applications in soil mechanics, earthquake science, geophysics, mining engineering, and plasma physics, and so forth. The granular medium under consideration is a discontinuous one and is composed of numerous large or small grains. Unlike a continuous body each element or grain cannot only translate