GENERALIZED THERMOELASTIC PROBLEM OF A THICK PLATE UNDER AXISYMMETRIC TEMPERATURE DISTRIBUTION

Abstract

The two-dimensional problem of a thick plate whose lower and upper surfaces are traction free and subjected to a given axisymmetric temperature distribution is considered within the context of the theory of generalized thermoelasticity with one relaxation time. Potential functions together with Laplace and Hankel transform techniques are used to derive the solution in the transformed domain. The Hankel transforms are inverted analytically. The inversion of the Laplace transforms are carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series and to evaluate the improper integrals involved to obtain the temperature and stress distributions in the physical domain. Analysis of wave propagation in the medium is presented. Numerical results are represented graphically and discussed. A comparison is made with the solution of the corresponding coupled problem.