Effect of impedance boundary on reflection of thermoelastic plane waves in a nonlocal elastic solid with thermal relaxation

The impedance boundary condition represents the resistance of a medium's surface to wave motion, linking stress and displacement components to account for energy dissipation. This study investigates the reflection behavior of thermoelastic plane waves at a rigid, thermally insulated or isothermal boundary within the framework of the Lord-Shulman generalized thermoelasticity model incorporating nonlocal elasticity. By applying appropriate boundary conditions and solving the coupled field equations, analytical expressions for amplitude ratios of reflected waves are derived. A sensitivity analysis is conducted to assess the influence of thermal relaxation time and nonlocality parameters. Numerical simulations demonstrate that both parameters significantly affect the amplitude and phase of reflected waves, especially at higher incidence angles. The results provide physical insights into wave propagation in microstructured and functionally graded materials, with implications for the design of thermoelastic devices and nondestructive evaluation techniques.