Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 245965, 22 pages
http://dx.doi.org/10.1155/2012/245965
Research Article

Influence of Initial Stress and Gravity Field on Propagation of Rayleigh and Stoneley Waves in a Thermoelastic Orthotropic Granular Medium

S. M. Ahmed1 and S. M. Abo-Dahab2,3

1Department of Mathematics, Faculty of Education, Suez Canal University, EL-Arish 45111, Egypt
2Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi Arabia
3Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt

Received 9 May 2011; Revised 11 October 2011; Accepted 26 October 2011

Academic Editor: Moran Wang

Copyright © 2012 S. M. Ahmed and S. M. Abo-Dahab. 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 propagation of Rayleigh and Stoneley waves in a thermoelastic orthotropic granular half-space supporting a different layer under the influence of initial stress and gravity field is studied. The frequency equation of Rayleigh waves in the form of twelfth-order determinantal expression and the frequency equation of Stoneley waves in the form of eighth-order determinantal expression are obtained. The standard equation of dispersion is discussed to obtain Rayleigh and Stoneley waves that have complex roots; the real part gives the velocity of Rayleigh or Stoneley waves but the imaginary part gives the attenuation coefficient. Finally, the numerical results have been given and illustrated graphically, and their physical meaning has been explained.