Radial vibrations of functionally graded spheres due to thermal load

Abstract

A study on radial vibrations of functionally graded, isotropic, thermoelastic, thick-walled hollow sphere due to a thermal load has been carried out in the context of non-Fourier law of heat conduction (LS model). The material and thermal parameters have been assumed to vary according as simple power-law function of the radial coordinate. Closed-form solution to the problem has been derived with the aid of Laplace transform and elimination procedure. The inverse Laplace transforms of radial displacement and temperature have been obtained by employing the theory of residues. The solution in case of uncoupled and classical coupled thermoelasticity has been obtained directly by deducing the results of present analysis. The deduced results have been validated with the benchmark results available in the literature. Also the radial stress, hoop stress, temperature gradient for various grading parameters at different radial distances have been computed and presented graphically for validating and giving more emphasis on these field quantities. A significant effect of grading parameter on the stress and temperature gradient produced in the sphere has been noticed. A comparative analysis has been done for homogeneous and functionally graded spheres.