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Journal of Applied Mathematics
Volume 2013, Article ID 562369, 20 pages
http://dx.doi.org/10.1155/2013/562369
Research Article

Effects of Rotation and Gravity Field on Surface Waves in Fibre-Reinforced Thermoelastic Media under Four Theories

1Mathematics Department, Faculty of Science, Taif University 888, Saudi Arabia
2Mathematics Department, Faculty of Science, Sohag University, Egypt
3Mathematics Department, Faculty of Science, Qena 83523, Egypt

Received 4 August 2013; Accepted 22 October 2013

Academic Editor: Morteza Rafei

Copyright © 2013 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

Estimation is done to investigate the gravitational and rotational parameters effects on surface waves in fibre-reinforced thermoelastic media. The theory of generalized surface waves has been firstly developed and then it has been employed to investigate particular cases of waves, namely, Stoneley waves, Rayleigh waves, and Love waves. The analytical expressions for surface waves velocity and attenuation coefficient are obtained in the physical domain by using the harmonic vibrations and four thermoelastic theories. The wave velocity equations have been obtained in different cases. The numerical results are given for equation of coupled thermoelastic theory (C-T), Lord-Shulman theory (L-S), Green-Lindsay theory (G-L), and the linearized (G-N) theory of type II. Comparison was made with the results obtained in the presence and absence of gravity, rotation, and parameters for fibre-reinforced of the material media. The results obtained are displayed by graphs to clear the phenomena physical meaning. The results indicate that the effect of gravity, rotation, relaxation times, and parameters of fibre-reinforced of the material medium is very pronounced.