Initial Stress and Viscosity on Propagation of Rayleigh Waves in Modified Couple Stress Thermoelastic Diffusion Medium

This research examines how Rayleigh surface waves propagate in a visco-thermoelastic medium modeled using modified couple stress theory (MCST), while accounting for the effects of initial stress, viscosity, and thermo-diffusion coupling. The study is conducted within the frameworks of the Lord–Shulman (L-S) and Green–Lindsay (G-L) generalized thermoelastic theories. The fundamental governing equations and secular equations are derived under conditions of a stress-free surface, thermal insulation, and impermeable boundaries. A numerical algorithm is developed to analyze the impact of hydrostatic initial stress, viscosity, and diffusion on wave parameters such as phase velocity and attenuation. Compared to earlier models that neglected viscosity or initial stress, the present results show that these factors significantly modify the secular determinant and dispersion characteristics of Rayleigh waves. Notably, the inclusion of initial stress leads to increased stiffness in the medium, reducing wave speed and enhancing attenuation. Viscosity introduces stronger damping effects, while diffusion coupling alters the thermal-mechanical interaction, especially at higher frequencies. The study also provides graphical comparisons between the L-S and G-L models, highlighting how the dual relaxation times in G-L lead to more pronounced attenuation. These findings extend previous work by offering a more comprehensive model that captures microstructural and pre-stress effects, which are vital in applications related to geophysics, seismology, and advanced material characterization.