International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 8, Pages 555-562
doi:10.1155/S0161171200001514
Thermoelastic waves without energy dissipation in an unbounded body with a spherical cavity
1Department of Mathematics, Bangalore University, Central College Campus, Bangalore 560 001, India
2Department of Mathematics, Islamia Institute of Technology, National Park Road, Bangalore 560 076, India
Received 20 March 1998
Copyright © 2000 D. S. Chandrasekharaiah and K. S. Srinath. 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
The linear theory of thermoelasticity without energy dissipation
is employed to study waves emanating from the boundary of a
spherical cavity in a homogeneous and isotropic unbounded
thermoelastic body. The waves are supposed to be spherically
symmetric and caused by a constant step in temperature applied to
the stress-free boundary of the cavity. Small-time solutions for
the displacement, temperature, and stress fields are obtained by
using the Laplace transform technique. It is found that there
exist two coupled waves, of which one is predominantly elastic and
the other is predominantly thermal, both propagating with finite
speeds but with no exponential attenuation. Exact expressions for
discontinuities in the field functions that occur at the
wavefronts are computed and analysed. The results are compared
with those obtained earlier in the contexts of some other models
of thermoelasticity.