Homogenized Perforated Interface in Acoustic Wave Propagation – Modeling and Optimization

Abstract

We consider acoustic wave propagation described by Helmholtz equation and involving homogenized transmission conditions imposed along a thin perforated interface which separates two halfspaces occupied by the acoustic medium. On this interface homogenized transmission conditions are imposed; they were obtained by the two-scale homogenization of a layer with an immersed perforated slab designed as a periodic structure. Design of the perforation can modify significantly acoustic wave propagation, therefore, optimization of the perforation can contribute to development of noise-isolation devices and to other practical acoustic applications. We developed the sensitivity of coefficients involved in the homogenized transmission conditions with respect to the design of the “holes” in the slab. Using the two-scale approach we treat the acoustic waves propagating in a duct which is equipped with the perforated interface. Using numerical examples we illustrate, how the perforation geometry influences the acoustic transmission. The optimization problem is solved with a few parameters describing shape of the perforation.