Free vibrations of a generalized thermoelastic sphere

Abstract

The problem of the free vibrations of a sphere whose surface is kept at a constant temperature is studied. The sphere is assumed to be made of a temperature-rate-dependent thermoelastic material. The frequency equations of the torsional and the spheroidal vibrations are obtained. Because of the difficulty of solving these equations analytically, numerical solutions are given for some values of parameters. Some modes for displacements and temperature changes are plotted.