Study of Dynamic Response in a Functionally Graded Spherically Isotropic Hollow Sphere with Temperature Dependent Elastic Parameters

Abstract

This paper is concerned with the investigation of thermoelastic interactions in a functionally graded spherically isotropic hollow sphere in which the thermophysical properties are temperature dependent in the context of the linear theory of generalized thermoelasticity (Green and Lindsay theory). Both the boundaries are stress free and are subjected to prescribed temperatures. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by eigenvalue approach. The numerical inversion of the transforms is carried out using a method of Bellman et al. The thermoelastic dynamic displacements, stresses and temperatures are computed numerically and presented graphically in a number of figures. The results, corresponding to the cases when the material properties are temperature independent and the outer radius of the sphere tends to infinity, agree with those of the existing literature.