Wave propagation in anisotropic poroelastic beam with axial–flexural coupling

Abstract

The exact solution of the governing partial differential equations describing the motion of an anisotropic porous beam with axial-flexural coupling is presented. The motion of the beam is described by the classical Euler–Bernoulli theory. The pore-fluid pressure is governed by the generalized Darcy’s law with relaxation and retardation time parameters to account for the inertia and viscosity of the fluid. Solutions are sought in the frequency domain where the governing equations are converted into a polynomial eigenvalue structure and solved exactly. The wavenumbers and group speeds of propagating waves in the beam are studied in detail. It is found that the presence of fluid-filled porous micro-structure introduces three additional propagating modes, other than the axial and bending modes predicted by the classical beam theory. The effect of diffusion boundary conditions on the transverse motion of a porous beam is investigated in detail. It is also found that the material parameters have considerable influence on the magnitude of the transverse velocity, the group speed of propagation and the behavior of the pressure resultants.