Spherically symmetric thermoelastic waves in a temperature-rate dependent medium with a spherical cavity

Abstract

The temperature-rate dependent thermoelasticity theory is employed to study spherically symmetric thermoelastic waves in an infinite medium with a spherical cavity whose inner boundary is subjected to (i) unit-step in temperature change and zero stress and (ii) unit-step in stress and zero temperature change. The effect of thermal relaxation times on the thermoelastic disturbances being short-lived, short-time approximations of the solutions for deformation, temperature and stresses have been considered. It is observed that the temperature and deformation are discontinuous at both the wave fronts while the stresses suffer delta-function singularities in case (i) and in case (ii), the deformation and temperature are continuous at both the wave fronts, while the stresses are discontinuous at these locations.