Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 3, Pages 225-240

On generalized thermoelastic disturbances in an elastic solid with a spherical cavity

Basudeb Mukhopadhyay,1 Rasajit Bera,2 and Lokenath Debnath3

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 Basudeb Mukhopadhyay 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.


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 v1 and v2(>v1) respectively. The stress, displacement and temperature are found to experience discontinuities at the respective wavefronts. One of the significant findings of the present analysis is that there is no diffusive nature of the waves as found in classical theory.