The boundary value problem of a three-dimensional generalized thermoelastic half-space subjected to moving rectangular heat source

Abstract

This paper deals with a new mathematical model of three-dimensional generalized thermoelasticity which has been improved using Lord-Shulman theory. The governing equations on non-dimensional forms have been applied to a three-dimensional half-space subjected to a rectangular moving heat source and traction-free surface by using the Laplace and double Fourier transform techniques. The inverses of the double Fourier and Laplace transforms have been calculated numerically by applying the complex formula of inversion of the transform by of the Fourier expansion method. The numerical results of the temperature increment, strain, stress, and displacement distributions have been represented in graphs for various values of the heat source speed parameter to show its effect on the thermo-mechanical waves. The heat source speed parameter leads to significant effects on both the thermal and mechanical waves.

The Thermoelastic Dynamic Response of a Rod Due to a Moving Heat Source under the Fractional-Order Thermoelasticity Theory

“…This provides a theoretical basis for the design and application of materials. In conjunction with the generalized thermoelasticity theory, Youssef et al [28][29][30] examined the thermoelastic behavior of several mathematical models with the existence of a mobile source of heat and examined the heat source's impact on the physical field's distribution. Mondal [31] incorporated memory-related derivatives into the L-S thermoelasticity model to develop a novel theoretical framework for the investigation of the transient responses of thermoelastic rods subjected to the influence of magnetic induction fields and moving heat sources.…”