SPHERICALLY SYMMETRIC THERMO-ELASTIC WAVE PROPAGATION WITHOUT ENERGY DISSIPATION IN AN UNBOUNDED MEDIUM WITH A SPHERICAL CAVITY

摘要

The present paper is concerned with spherically symmetric thermo-elastic wave propagation without energy dissipation in an unbounded elastic medium with a spherical cavity. The inner boundary of the cavity is subjected to a unit step in stress and a zero temperature change. Short-time approximations of the solutions for displacement, temperature and stresses are given. The Laplace Transform is applied as a mathematical tool. It is observed that the solutions consist of two types of waves-modified thermal wave, traveling with speed v_1, and modified elastic wave, traveling with speed v_2. Waves propagate without attenuation which is not the case in the Lord-Shulman theory (LST), Green-Lindsay theory (GLT) and Conventional Coupled theory (CCT). It is observed that the displacement is continuous at both the wave fronts while the temperature and stresses suffer jump discontinuities at these locations and that the jumps vary inversely with the radial distance from the center of the cavity in contrast to the case of LST, GLT, CCT where the jumps decay exponentially with distance from the centre of the cavity. The radial displacement, temperature, radial and circumferential stresses are numerically computed for different values of the radial distance' from the centre of the cavity and their graphical representation is made.