Acoustic scattering by a finite plate with a poroelastic extension using the unified transform method

This paper investigates sound scattering by a finite rigid plate with various extensions using the unified transform method. Different boundary conditions, including rigid, elastic, perforated, and poroelastic conditions are addressed thanks to this efficient method. Parametric studies for the elasticity, the porosity, and the extension length are also conducted over a wide frequency range to explore the combined effects of these variables. Results show that the observed noise reduction can be attributed to the attenuation of pressure difference across the plate. For the case of a finite plate with a poroelastic extension, at a low frequency (k(0) <= 0.1, where k(0) is the non-dimensional wavenumber), porosity can achieve more noise reduction than elasticity. Elasticity generally enhances noise reductions, especially when combined with low porosities. At a high frequency (k(0) >= 10), the maximum noise reduction can be achieved through either high elasticity or large porosity, which is, however, still smaller than that at low frequencies. The extension length is more effective in noise reduction when applied with large porosity at a low frequency or high elasticity at a medium or high frequency. This study reveals the potential noise reduction by a poroelastic extension attached to a finite rigid plate, and helps shed more light on the noise reduction mechanisms as well as an optimal design of realistic poroelastic extensions.