Axisymmetric Generalized Thermoelasticity Problems Using Cylindrical Coordinates

Overview

In 1967, the theory of generalized thermoelasticity with one relaxation time was introduced by Lord and Shulman [1]. The motivation behind the introduction of this theory was to deal with the apparent paradox of infinite speeds of propagation predicted by the coupled theory of thermoelasticity introduced by Biot [2] in 1956. The generalized equation of heat conduction is hyperbolic and hence automatically ensures finite speeds of wave propagation. This theory was extended by Dhaliwal and Sherief [3] to include the effects of anisotropy.

Among the contributions to this theory are the proofs of uniqueness theorems by Ignaczak [4] and by Sherief [5]. Anwar and Sherief [6] and Sherief [7] completed the state-space formulation for one-dimensional problems. Sherief and Anwar [8] conducted the state-space formulation for two-dimensional problems. The fundamental solutions for the cylindrically symmetric spaces were obtained by Sherief and Anwar [9].

The importance of axisymmetric...