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