International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 20, Pages 3303-3318
Magneto-thermoelastic waves in a perfectly conducting elastic half-space in thermoelasticity III
Department of Mathematics, University of Burdwan, Bardhaman 713104, West Bengal, India
Received 21 April 2005
Copyright © 2005 S. K. Roychoudhuri and Nupur Bandyopadhyay. 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 propagation of magneto-thermoelastic disturbances in an elastic half-space caused by the application of a thermal shock on the stress-free bounding surface in contact with vacuum is investigated. The theory of thermoelasticity III proposed by Green and Naghdi is used to study the interaction between elastic, thermal, and magnetic fields. Small-time approximations of solutions for displacement, temperature, stress, perturbed magnetic fields both in the vacuum and in the half-space are derived. The solutions for displacement, temperature, stress, perturbed magnetic field in the solid consist of a dilatational wave front with attenuation depending on magneto-thermoelastic coupling and also consists of a part diffusive in nature due to the damping term present in the heat transport equation, while the perturbed field in vacuum represents a wave front without attenuation traveling with Alfv'en acoustic wave speed. Displacement and temperatures are continuous at the elastic wave front, while both the stress and the perturbed magnetic field in the half-space suffer finite jumps at this location. Numerical results for a copper-like material are presented.