An Analytical Investigation Into Novel Poroelastic Boundary Conditions for Noise-Reducing Metamaterials

Howe’s poroelastic boundary condition has been used extensively in aeroacoustics to study the scattering properties of elastic surfaces with small perforations. In this paper, we revisit Howe’s methodology and demonstrate how altering either the governing bending wave equation or the pores’ edge conditions leads to amended homogenized boundary conditions. We amend Howe’s poroelastic boundary condition for several diverse materials to account for pre-tension in the material. This amendment is driven by inconsistencies in descriptions of some noisereducing materials like Kevlar as either a bending plate (using Howe’s theory) or an impermeable tensioned membrane. Our results show that the new model balances the effects of bending stiffness and tension in a rigorous manner whilst also including effects from porosity. We also derive the poroelastic equation with clamped pores to demonstrate the influence of changing edge conditions. These boundary conditions also influence the wall-pressure spectrum. We show that adapting the pressure Poisson equation to poroelastic boundary conditions requires careful attention to ensure well-posedness.