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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 8, Pages 555-562

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 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.


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.