Poroelastic and Viscoelastic Hallmarks in the Response of Porous and Transversely Isotropic Beams to Harmonic Excitation

Abstract

A general solution to harmonic excitation of beam-shaped specimens made from porous, fluid-saturated, transversely isotropic, and viscoelastic materials is developed and presented. The solution draws from Biot's theory of dynamic poroviscoelasticity and adopts a modification of Timoshenko beam model to account for the moment due to pore fluid pressure. Closed-form expressions for transverse displacement and rotation angle of the beam are obtained for the case of three-point bending experiments. Solutions for Rayleigh and Euler–Bernoulli beam models are recovered as special cases. Implications for possible characterization through relevant dynamic mechanical analysis testing are discussed for materials which exhibit certain anisotropy in both the mechanical and flow properties. Three timescale groups shape the dynamic response of the vibrating beam. These timescales pertain to energy dissipation rate within the solid phase, viscous flow of the pore fluid, as well as the natural frequencies of the test specimen. The interplay of a varying excitation frequency with the described timescales is shown to enable simultaneous characterization of the viscoelastic and poroelastic parameters of the specimen constitutive behavior through the obtained dynamic moduli and loss angles of beam vibrations.