Analytical Solution for a Free Vibration of a Thermoelastic Hollow Sphere

For a free vibration problem of a thermoelastic hollow sphere into the context of the generalized thermoelasticity theory with one relaxation time, exact analytic solutions are obtained with the use of eigenvalue approach. Both the inner and outer curved surfaces of the sphere are considered stress-free and isothermal surfaces. The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollow sphere are derived. The numerical results have been presented graphically in respect of natural frequencies, thermoelastic damping, and frequency shift.