Abstract
The theory of two-temperature generalized thermoelasticity based on the theory of Youssef is used to solve boundary value problems of two dimensional half-space with heating its boundary with different types of heating. The governing equations are solved using new mathematical methods under the purview of the Lord-Shulman (LS) and the classical dynamical coupled theory (CD). The general solution obtained is applied to a specific problem of a half-space subjected to one types of heating the thermal shock type. The normal mode method is used to obtain the exact expressions for the displacement components, force stresses and temperature distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results between the two theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The conductive temperature, the dynamical temperature, the stress and the strain distributions are shown graphically with some comparisons.