Abstract
A three-dimensional model of the generalized thermo-viscoelasticity is established. The formulation is applied to the generalized thermo-viscoelasticity theories: Lord-Shulman and Green-Lindsay as well as to the dynamic coupled theory. The resulting nondimensional coupled equations together with the Laplace and double Fourier transforms techniques are applied to a specific problem of a half space subjected to thermal shock and traction-free surface. The inverses of Fourier transforms and Laplace transforms are obtained numerically by using the complex inversion formula of the transform together with Fourier expansion techniques. Numerical results for the temperature, thermal stress, strain, and displacement distributions are represented graphically.