Analytical Treatment of Dynamic Coupled Thermal Shock in an Inhomogeneous One-Dimensional Lamina Within the Exponential Thermoelastic Theory

Within the context of generalized thermoelasticity, this paper examines the transient thermoelastic response of an inhomogeneous lamina under coupled mechanical and thermal shock loading. The spatial and temporal distributions of temperature, displacement, dilatation, and stress are obtained analytically by means of the Laplace transform technique and its numerical inversion. To investigate the impacts of relaxation time and higher-order approximations, the analysis is conducted inside various thermoelastic Lord and Shulman models. The impact of geographical position and the inhomogeneity parameter on the propagation of thermoelastic waves is demonstrated numerically. It is found that raising the inhomogeneity parameter considerably lessens the amplitude of the thermoelastic fields and moderates the spatial variation of material properties. In addition, compared to the classical model, generalized theories anticipate smoother field distributions and finite-speed wave propagation.