Oscillatory Singularities in a Saturated Poroelastic Medium

摘要

The fundamental oscillatory singularities of the mass source and the point force for a linearly elastic porous medium, saturated with a compressible fluid, are derived in the present report. Integrations of these singular solutions yield the corresponding line and plane singularities. Due to the linearity of the governing equations multipoles are readily constructed. The solution to the general time-periodic boundary-value problem is represented through the displacement integral equations. These equations give the solid and fluid displacement vectors in terms of boundary integrations of the known singular solutions and the boundary conditions. The oscillatory mass source and force singularities and higher-order poles are directly applied to solve the sphere, cylinder, and plane problems involving various modes of vibration.