Scattering by composite poroelastic–rigid plates in flow using the unified transform method

Abstract

The Unified Transform Method (UTM) is applied for the first time to acoustic scattering by poroelastic plates in uniform grazing flow. We extend the UTM framework to incorporate low-Mach-number flow over either a finite poroelastic plate or a composite plate composed of alternating impermeable rigid and poroelastic sections. The method captures edge singularities through tailored basis functions and avoids the kernel factorization difficulties of Wiener–Hopf approaches, while remaining computationally efficient. A flow-dependent Rayleigh conductivity is introduced to quantify how porosity effects are modified by grazing flow under both plane-wave and point quadrupole excitation. Results reveal a Strouhal-controlled regime in which flow can modulate the noise-reducing properties of pores, but beyond this limit the effects of pores are nullified completely. For composite plates, the placement and length of poroelastic inserts and their rigid supports relative to the trailing edge are critical: downstream inserts, when sufficiently long, provide the most effective suppression of trailing-edge noise and elastic insert displacement. These findings demonstrate the UTM as a versatile semi-analytical framework for analyzing noise-control strategies with poroelastic surfaces in flow.