Three-Phase-Lag Effect on Rayleigh Waves in a Generalized Thermoelastic Diffusion Medium with Modified Couple Stress

This study examines the behavior of Rayleigh waves propagating through a homogeneous, isotropic material, analyzed using a three-phase-lag thermoelastic diffusion framework enhanced by modified couple stress theory. The mathematical model integrates coupled thermoelastic and diffusive effects, incorporating phase-lags associated with (1) temperature gradients, (2) heat flux, and (3) thermal displacement gradients. By solving the derived governing equations analytically subject to stress-free, thermally insulated, and impermeable boundary conditions, we obtain the characteristic secular equation for Rayleigh wave propagation. Numerical simulations conducted on a copper medium evaluate how the secular equation’s determinant, wave velocity, and attenuation coefficient vary with angular frequency. The analysis focuses particularly on the influence of phase-lag parameters, including thermal and diffusion gradients and relaxation times. Results demonstrated that increasing the displacement gradient phase-lag elevated the secular determinant but reduced wave velocity and attenuation, while temperature gradient phase-lags exhibited the opposite trend. The study highlights the sensitivity of Rayleigh wave propagation to thermo-diffusive coupling and microstructural effects, offering insights applicable to seismic wave analysis, geophysical exploration, and material processing. Comparisons with prior theories underscore the model’s advancement in capturing size-dependent and memory-dependent phenomena.