Acoustic scattering by a finite rigid plate with a poroelastic extension

Abstract

The scattering of sound by a finite rigid plate with a finite poroelastic extension interacting with an unsteady acoustic source is investigated to determine the effects of porosity, elasticity and the length of the extension when compared to a purely rigid plate. The problem is solved using the Wiener-Hopf technique, and an approximate Wiener-Hopf factorisation process is implemented to yield reliable far-field results quickly. Importantly, finite chord-length effects are taken into account, principally the interaction of a rigid leading-edge acoustic field with a poroelastic trailing-edge acoustic field. The model presented discusses how the poroelastic trailing-edge property of owls' wings could inspire quieter aeroacoustic designs in bladed systems such as wind turbines, and provides a framework for analysing the potential noise reduction of these designs.

Aerodynamic noise from rigid trailing edges with finite porous extensions

“…The far-field acoustics are obtained by employing rational approximations, however this approach cannot be used to determine mid-or near-field results accurately since the functions involved are not meromorphic and cannot be accurately represented by rational functions everywhere. Additionally, the results were most accurate in Ayton (2016) when considering high frequency interactions. In this paper we propose a different extension to the pole removal technique for functions that have arbitrary singularities.…”

“…The results are heavily dominated by the Fresnel zone at the angle of reflection of the incident sound wave, θ = 3π/4 and uniformly valid expansions for the far-field directivity are required to deal with the pole singularity at this angle. Note that the pole removal method of Ayton (2016) was seen only to be accurate at high frequencies and does not have a formal error bound to an exact solution, whilst our new iterative method is proved to converge to the exact solution (Kisil 2017) thus is able to present results to within a specified error bound. Further, the pole removal method can only recover the far-field acoustic field and not the mid or near field.…”

“…Here we compare results for our semi-infinite partially porous plate to the sound scattering results for a finite partially porous plate given by Ayton (2016). Ayton (2016) uses a pole removal technique to obtain the far-field acoustic directivity due to a sound wave scattering off a flat plate that consists of a finite impermeable rigid section and a finite poroelastic section (which for the purposes of this section we consider to be only porous).…”

“…Ayton (2016) uses a pole removal technique to obtain the far-field acoustic directivity due to a sound wave scattering off a flat plate that consists of a finite impermeable rigid section and a finite poroelastic section (which for the purposes of this section we consider to be only porous). For our new iterative method we require a multiplicative factorisation of (γP − 1), equivalently, µ + γ, where the constant porosity parameter, µ, is small.…”

“…However, even with this extension the class of functions which can be solved is rather limited. In Ayton (2016) scattering by a finite flat plate with poroelastic extension is considered yielding a 3 x 3 Wiener-Hopf matrix system. The far-field acoustics are obtained by employing rational approximations, however this approach cannot be used to determine mid-or near-field results accurately since the functions involved are not meromorphic and cannot be accurately represented by rational functions everywhere.…”