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Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 763429, 47 pages
http://dx.doi.org/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

1Mathematics Department, Faculty of Science, Taif University, Taif 21974, Saudi Arabia
2Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
3Mathematics Department, Faculty of Science, Umm Al-Qura University, P.O. Box 10109, Makkah 13401, Saudi Arabia

Received 4 December 2010; Revised 14 January 2011; Accepted 25 February 2011

Academic Editor: Ezzat G. Bakhoum

Copyright © 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.

Abstract

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.