State-space approach to three-dimensional generalized thermoelasticity with fractional order strain

Abstract

ABSTRACTIn this work, a three-dimensional (3D) model of the generalized thermoelasticity with fractional order strain is constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transform techniques have been applied to a 3D half-space subjected to thermal shock 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 results for the strain, thermal stress, displacement, and temperature are represented graphically based on various values of the strain fractional order parameter to stand on its effect on the thermo-mechanical waves. The fractional order parameter of the strain has significant effects on the mechanical waves while it has a limited effect on the thermal waves.