Abstract
The aim of the present investigation is to examine the memory-dependent derivatives (MDD) in 2D transversely isotropic homogeneous magneto thermoelastic medium with two temperatures. The problem is solved using Laplace transforms and Fourier transform technique. In order to estimate the nature of the displacements, stresses and temperature distributions in the physical domain, an efficient approximate numerical inverse Fourier and Laplace transform technique is adopted. The distribution of displacements, temperature and stresses in the homogeneous medium in the context of generalized thermoelasticity using LS (Lord-Shulman) theory is discussed and obtained in analytical form. The effect of memory-dependent derivatives is represented graphically.
Highlights
Magneto-thermoelasticity deals with the relations of the magnetic field, strain and temperature
In recent years, inspired by the successful applications of fractional calculus in diverse areas of engineering and physics, generalized thermoelasticity (GTE) models have been further comprehensive into temporal fractional ones to express memory dependence in heat conductive sense
The memory-dependent derivatives (MDD) theory is revisited and it is adopted to analyse the effect of MDD in a homogeneous transversely isotropic magneto-thermoelastic solid
Summary
Magneto-thermoelasticity deals with the relations of the magnetic field, strain and temperature. Ezzat et al (2016) discussed a generalized model of two-temperature thermoelasticity theory with time delay and Kernel function and Taylor theorem with memorydependent derivatives involving two temperatures. Not much work has been carried out in memory-dependent derivative approach for transversely isotropic magneto-thermoelastic medium with two temperatures. The memory-dependent derivatives (MDD) theory is revisited and it is adopted to analyse the effect of MDD in a homogeneous transversely isotropic magneto-thermoelastic solid. The kernel function K(t − ξ) is differentiable with respect to the variables t and ξ The motivation for such a new definition is that it provides more insight into the memory effect (the instantaneous change rate depends on the past state) and better physical meaning, which might be superior to the fractional models. The comma is further used to indicate the derivative with respect to the space variable, and the superimposed dot represents the time derivative
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