Relaxation effects on thermally induced vibrations in a generalized thermoviscoelastic medium with a spherical cavity

Thermally induced vibrations of an infinite isotropic viscoelastic solid containing a spherical cavity are investigated. The stress-free boundary of the cavity is subjected to a temperature that varies harmonically with time. The classical dynamical coupled theory of thermoelasticity and the generalized theories of thermoelasticity proposed by Lord and Shulman and Green and Lindsay are applied to consider the thermoelastic coupling. The analytical expressions for the solutions of displacement, temperature, and stresses are determined. The relaxation effects on the vibrations are studied to compare the three theories. Numerical values of displacement temperature, and stresses are computed for a particular material; and the results are presented graphically to illustrate the solution.