Three-Dimensional Generalized Thermoelasticity with Fractional Order Heat Conduction of a Half-Space Subjected to Rectangular Thermal Pulse: State-Space Approach

摘要

In this paper, a mathematical model of three-dimensional generalized thermoelasticity with fractional order heat conduction has been improvement. The non-dimensional governing equations together with the Laplace and double Fourier transform techniques have been applied to a three-dimensionalhalf-space subjected to rectangular thermal pulse and traction free surface. The inverses of double Fourier transforms and Laplace transforms have been obtained numerically by using a complex inversion formula of the transform with the techniques of the Fourier expansion. Numerical resultsfor the strain, thermal stress, displacement, and temperature are represented graphically based on various values of the heat conduction fractional order parameter to stand on its effect on the thermo-mechanical waves. The fractional order parameter of the heat conduction has significant effectson the thermal and the mechanical waves.