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International Journal of Mathematics and Mathematical Sciences
Volume 21, Issue 3, Pages 595-602

Transient disturbances in a relaxing thermoelastic half space due to moving internal heat source

Department of Mathematics, Jadavpur University, Calcutta, 700 032, India

Received 5 April 1995; Revised 14 November 1996

Copyright © 1998 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.


This paper is concerned with the transient waves created by a line heat source that suddenly starts moving with a uniform velocity inside a thermoelastic semi-infinite medium with thermal relaxation of the type of Lord and Shulman. The source moves parallel to the boundary surface which is traction-free. The problem is reduced to the solution of three differential equations, one involving the elastic vector potential, and the other two coupled, involving the thermoelastic scalar potential and the temperature. Using Fourier and Laplace transforms, the solution for the displacements have been obtained in the transform domain. The displacements have been calculated on the boundary surface for small time.