For an inhomogeneous material under a thermal shock, the dynamic behavior of a one-dimensional generalized thermoelastic heat conduction problem is examined. In order to justify finite thermal wave propagation, the governing coupled equations of motion and heat conduction are developed within the framework of Lord and Shulman's generalized thermoelasticity theory. The system of partial differential equations is transformed into a set of ordinary differential equations by removing the time variable using the Laplace transform technique, which facilitates an analytical transform domain solution. A direct method appropriate for inhomogeneous situations is utilized to solve these equations analytically. The inhomogeneous physical fields are recovered using numerical inversion techniques once the solutions in the Laplace domain have been gained. The resulting distributions of temperature, displacement, dilatation, and stress are recorded and visually depicted. The results highlight the differences between the coupled and different generalized thermoelastic models, demonstrating the significant influence of relaxation effects on wave propagation, stress development, and thermal response within the inhomogeneous material. The temperature , displacement , dilatation , and stress of the inhomogeneous material for different classical and LS theories ( , , ).
El-Mekawy et al. (Fri,) studied this question.