Behavior of poroelastic isotropic beam derivation by asymptotic expansion method

This paper deals with the dynamic behavior of poroelastic beams, i.e. rod made of a biphasic medium described by the Biot model. The study mostly focuses on situations where the inner flow is dominated by viscosity, but also investigate the case of visco-inertial inner flow. Using the inverse of the slenderness as a small parameter, one establishes through asymptotic expansions the 1D beam description in harmonic regime: the Euler–Bernoulli kinematic still applies, however the equilibrium of the section induces a poroelastic problem with pressure diffusion. The beam parameters are rigorously derived from this problem and can be computed numerically. They are complex and frequency dependent which implies creep/relaxation mechanisms. This theoretical formulation is discussed according to the level of permeability, the flow conditions on the section periphery, the gas or liquid nature of the fluid, the frequency range of the oscillations. Analytical and numerical results are provided for circular and flat beam sections.