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Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 3, Pages 225-240
http://dx.doi.org/10.1155/S1048953391000187
On generalized thermoelastic disturbances in an elastic solid with a spherical cavity
1Department of Mathematics, Bengal Engineering College, Howarh 711103, West Bengal, India
2Department of Mathematics, Presidency College, Calcutta 700 073, India
3Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA
Received 1 October 1990; Revised 1 April 1991
Copyright © 1991 Hindawi Publishing Corporation. 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
In this paper, a generalized dynamical theory of thermoelasticity is employed to study disturbances in an infinite elastic solid containing a spherical cavity which is subjected to step rise in temperature in its inner boundary and an impulsive dynamic pressure on its surface. The problem is solved by the use of the Laplace transform on time. The short time approximations for the stress, displacement and temperature are obtained to examine their discontinuities at the respective wavefronts. It is shown that the instantaneous change in pressure and temperature at the cavity wall gives rise to elastic and thermal disturbances which travel with finite velocities