Wave propagation in thermoporoelastic plate

Abstract

Governing equations for wave propagation of a thermoporoelastic plate are derived. The material obeys the theory of Pecker and Dersiewicz [C. Pecker and H. Dersiewicz, Acta Mech. 16, 45–64 (1973)]. The temperatures of solid and liquid phases are assumed to be different. Due to temperature difference in both phases at every point in the medium, there is a coupling parameter in heat conduction equations. The frequency equation is obtained for stress-free and thermally insulated boundary conditions. Numerical results are calculated for isothermal and adiabatic wave propagation corresponding to kerosene filled sandstone. Phase velocities and the attenuation factor are plotted against frequencies for symmetric and antisymmetric mode. In an isothermal case, the phase velocity oscillates sharply for the symmetric mode but it is not so sharp for the antisymmetric mode. But the behavior of the attenuation factor is reverse. In the adiabatic case, the phase velocity oscillates very less, up to frequency of 2 Hz; afterwards, it oscillates for both modes. In the attenuation factor, there is rapid oscillation throughout for the antisymmetric mode but it is less in the symmetric mode. Oscillation is almost absent between 2.5 and 4.5 Hz in the symmetric mode. The phase velocity is higher for the isothermal case than the adiabatic case whereas it is opposite for the attenuation factor.