Theory of Generalized Thermoelasticity with Memory-Dependent Derivatives

Abstract

This paper theoretically demonstrates two aspects of a generalized heat conduction model with memory-dependent derivatives. The characteristics of transient effects in an isotropic, thermoelastic medium were analyzed in terms of memory-dependent thermoelasticity theory. The Lord–Shulman (LS) model gives an upper bound of thermal disturbances in a memory-dependent generalized thermoelasticity model. For numerical implementation, a one-dimensional semi-infinite medium with one end subjected to a transient load was considered. An integral transform method and, while in inverse transformation, an efficient and pragmatic numerical inverse Laplace transform (NILT) were adopted. Parameter studies were performed to evaluate the effect of the kernel function and time delay. An appropriate Lyapunov function, which is a significant scheme to study numerous qualitative properties, is proposed.