Acoustic scattering by finite poroelastic plates

Resumo

We present a numerical method to compute acoustic scattering by finite poroelastic plates. A boundary element method is applied to solve the Helmholtz equation subjected to boundary conditions related to the vibration of the plate. This analysis is performed by rewriting the boundary conditions in terms of the vibration modes of the plate, which allows an iterative solution of the problem. A parametric study is carried out for a two-dimensional acoustic problem of scattering by a point quadrupole by poroelastic plates with infinite span but finite chord, with a clamped leading edge and a free trailing edge. It is shown that both elasticity and porosity tend to decrease the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce the strength of acoustic scattering when excited near resonance by an acoustic source. However, finite- plate effects become significant for low Helmholtz numbers, where elasticity is shown to produce lower sound reductions compared to the rigid case, and in some cases an increase of the scattered sound. Porosity, on the other hand, is shown to become more effective in reducing the radiated sound for low Helmholtz numbers. Poroelastic plates have the combined beneficial effects of elasticity and porosity, and are shown to be effective in reducing the scattered sound for a broader range of Helmholtz numbers.