Acoustic scattering by multi-layered gratings

Abstract

Acoustic scattering by layered array gratings and diverse boundary conditions is considered by adapting the semi-analytic Fokas method to periodic geometries. The generalised Dirichlet-to-Neumann (DtN) map is solved numerically and the scattering solution is recovered through a Green’s integral representation. The boundary conditions on the array gratings include sound-hard, sound-soft and elastic. Acoustic scattering by layered array gratings with different periods is also discussed. Engineering applications include the use of layered perforated structures as anti-reflection coatings and anti-transmission coatings. The method is also presented as a baseline upon which to build a theoretical homogenisation model for effective impedance parameters for perforated structures.