Analytical Porothermoelastodynamic Modeling of Stress Wave Through a Fluid‐Saturated Porous Cylinder

Abstract

Analytical porothermoelastodynamic (PTED) solutions are rare in the literature. The responses of fluid‐saturated porous materials subject to coupled mechanisms of loading frequency, fluid flow, stress, and temperature are unclear. In this paper, we use the PTED theory and derive the analytical solutions of pore pressure, temperature, stress, force, and displacement for an isotropic fluid‐saturated porous cylinder subject to a harmonic vibration. The coupled partial differential equations among pore pressure, displacement, and temperature are decoupled by matrix diagonalization and solved by further introducing a potential function and separation of variables. The PTED solution reproduces the poroelastodynamic (PED) one by easing the thermal effect. A demonstration example shows that the coupled mechanisms among pore pressure, stress, and displacement are highly frequency dependent. The thermal effect is more pronounced at low frequencies than at high frequencies when the inertial impact is more significant. Pore pressure is almost uniform in the ‐direction at low frequencies and becomes nonuniform at high frequencies for both PTED and PED cases. Displacements exhibit linear behavior at low frequencies and become nonlinear at high frequencies. Thermal stress and expansion significantly impact the pore pressure and displacement. A brief sensitivity analysis shows that pore pressure responds linearly and monotonically with the increase of the volumetric thermal expansion coefficient of the solid matrix at low frequencies and becomes nonlinear and nonmonotonic at high frequencies. The volumetric thermal expansion coefficient of the solid matrix has a minor effect on the vertical displacement and significantly influences the radial displacement.