A fast numerical framework to compute acoustic scattering by poroelastic plates of arbitrary geometry

We present a fast numerical framework for the computation of acoustic scattering by poroelastic plates of arbitrary geometries. A boundary element method, BEM, is applied to solve the Helmholtz equation subjected to boundary conditions related to structural vibrations. This analysis is performed by rewriting the BEM boundary conditions in terms of a modal basis of the poroelastic plate which is computed by the finite element method, FEM. The current formulation allows a direct solution of the fully coupled fluid-structure interaction problem. In order to accelerate the solution of the large dense linear systems from the BEM formulation in three-dimensional problems, a wideband adaptive multi-level fast multipole method, FMM, is employed. A parametric study is carried out for the trailing-edge scattering of sample acoustic sources, representative of either uncorrelated turbulent eddies or a non-compact turbulent jet. Firstly, the noise scattering by a compact quadrupole source is analyzed for low and high frequencies for square and trapezoidal plates. Results show that geometric features such as trailing-edge sweep and serrations are very effective in the reduction of noise scattering. Moreover, it is shown that finite elastic plates are more effective in reducing the scattered noise at higher frequencies. On the other hand, porosity is more effective in reducing the radiated sound for lower frequencies. Results demonstrate that elasticity and porosity can be combined with trailing-edge sweep and serrations to reduce the scattered noise at a broader range of frequencies for poroelastic plates.