Based on the fluctuation theory of elastic medium

the fluctuation equation of thermoviscoelastic medium is established by using the Kelvin-Voigt viscoelastic model

the equation of motion of viscoelastic medium and the generalized thermoelasticity theory. This approach considers soil viscosity and thermal effects. Then the dispersive characteristic equation of the body wave in the thermoviscoelastic medium is derived by introducing the displacement potential function of the solid-phase medium. Numerical calculations were performed to analyze the influence of thermophysical parameters

such as thermal expansion coefficient

medium temperature and relaxation time on the wave velocity and attenuation coefficient of thermoelastic waves. The results indicate significant differences in the wave velocity and attenuation coefficient of thermal elastomer waves under the three theoretical models: elastic theory

thermoelastic theory

and thermoviscoelastic theory. For each 0.5×10 s increase in relaxation time

the P-wave speed and attenuation coefficient increased by up to 5.18% and 34.67%

respectively; the S-wave speed and attenuation coefficient increased by up to 9.27% and 34.6%

respectively; and the T-wave speed and attenuation coefficient decreased by up to 2.18% and 2.24%

respectively. As frequency increases

the wave velocity and attenuation coefficient of each thermoelastic wave gradually increase. An increase in medium temperature results in higher P-wave and T-wave speeds and a higher P-wave attenuation coefficient. Specifically

for every 20 K increase in temperature

the P-wave speed and attenuation coefficient increase by approximately 3% and 2%

respectively. However

temperature changes do not affect the S-wave propagation characteristics and the T-wave attenuation coefficient. An increase in the thermal expansion coefficient leads to an increase in P-wave velocity and a decrease in T-wave velocity

significantly affecting the attenuation coefficients of both P-wave and T-wave. Additionally

heat flux and the phase delay time of the temperature gradient significantly influence the wave velocity and attenuation coefficient of the T-wave.