International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 8, Pages 529-546
doi:10.1155/S0161171200004221
The reflection phenomena
of SV-waves in a generalized thermoelastic
medium
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.
Abstract
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.