An investigation on responses of thermoelastic interactions in a generalized thermoelasticity with memory-dependent derivatives inside a thick plate

Abstract

The present work is carried out under generalized thermoelasticity theory with memory-dependent derivatives. The main purpose of this work is to analyze the thermoelastic interactions inside an infinitely extended thick plate due to axis-symmetric temperature distribution applied at the lower and upper surfaces of the plate under memory-dependent generalized thermoelasticity. The formulation of the problem is done in the context of the theory of thermoelasticity under memory-dependent derivatives with inclusion of time delay parameter $\tau$ and kernel functions that are defined in a slipping interval $\left[t-\tau ,t\right)$ . The potential function concept along with Laplace and Hankel transform techniques is used to solve the problem. Furthermore, inversion of the Hankel transform technique is used to find the solution in the Laplace transform domain. The final solution in the space–time domain is obtained by employing a numerical method of Laplace inversion. We have also compared the present findings with work which has been done earlier. An analysis and the comparison of all the physical fields inherent to the generalized thermoelasticity with one relaxation parameter are given in a detailed way. The special findings and differences of using different kernel functions are highlighted.