International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 8, Pages 529-546

The reflection phenomena of SV-waves in a generalized thermoelastic medium

Abo-El-Nour N. Abd-Alla1 and Amira A. S. Al-Dawy2

1Department of Mathematics, Faculty of Science, Sohag 82526, Egypt
2Girls College of Science, Dammam, Saudi Arabia

Received 20 December 1998

Copyright © 2000 Abo-El-Nour N. Abd-Alla and Amira A. S. Al-Dawy. 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.


We discuss the reflection of thermoelastic plane waves at a solid half-space nearby a vacuum. We use the generalized thermoelastic waves to study the effects of one or two thermal relaxation times on the reflection plane harmonic waves. The study considered the thermal and the elastic waves of small amplitudes in a homogeneous, isotropic, and thermally conducting elastic solid. The expressions for the reflection coefficients, which are the ratio of the amplitudes of the reflected waves to the amplitude of the incident waves are obtained. It has been shown, analytically, that the elastic waves are modified due to the thermal effect. The reflection coefficients of a shear wave that incident from within the solid on its boundary, which depend on the thermoelastic coupling factor and included the thermal relaxation times, have been found in the general case. The numerical values of reflection coefficients against the angle of incidence for different values of thermal relaxation times have been calculated and the results are given in the form of graphs. Some special cases of reflection have also been discussed, for example, in the absence of thermal effect our results reduce to the ordinary pure elastic case.