The present research is on the propagation of Rayleigh waves in a homogenous thermoelastic solid half-space by considering the compact form of six different theories of thermoelasticity. The medium is subjected to an insulated boundary surface that is free from normal stress, tangential stress, and a temperature gradient normal to the surface. After developing a mathematical model, a dispersion equation is obtained with irrational terms. To apply the algebraic method, this equation must be converted into a rational polynomial equation. From this, only those roots are filtered out, which has satisfied both of the above equations for the propagation of waves decaying with depth. With the help of these roots, different characteristics are computed numerically, like phase velocity, attenuation coefficient, and path of particles. Various particular cases are compared graphically by using phase velocity and attenuation coefficient. The elliptic path of surface particles in Rayleigh wave propagation is also presented for the different theories using physical constants of copper material for different depths and thermal conductivity.

The study examines the impact of various theories on the reflection and transmission phenomena caused by obliquely incident longitudinal and transverse waves at the interface between a continuously elastic solid half-space and a thermoelastic half-space, using multiple thermoelastic models. Numerical calculations reveal that the thermoelastic medium supports one transmitted transverse wave and two transmitted longitudinal waves. The modulus of amplitude proportions is analyzed as a function of the angle of incidence, showing distinct variations across the studied models. Energy ratios, derived from wave amplitudes under consistent surface boundary conditions for copper, are computed and compared across angles of incidence. The results demonstrate that the total energy ratio consistently sums to one, validating energy conservation principles. Graphical comparisons of amplitude proportions and energy ratios for SV and P waves across different models illustrate significant differences in wave behavior, emphasizing the influence of thermoelastic properties on wave transmission and reflection.