Dynamic problem of fractional order thermoelasticity for a thick circular plate with finite wave speeds

Abstract

This article is aimed at determining the thermoelastic displacement, stress, and temperature in a thick circular plate of finite thickness and infinite extent whose lower and upper surfaces are traction free, subjected to a given axisymmetric temperature distribution. The problem is formulated in the context of fractional order thermoelasticity theory with finite wave speeds. Integral transform technique is used to obtain the general solution in Laplace transform domain. Inversion of the Laplace transforms is done using a numerical scheme. A mathematical model is prepared for a copper material plate. Thermoelastic stresses, temperature and displacement are shown graphically and the effects of fractional-order parameters are discussed.