Homogenization of the vibro-acoustic transmission on periodically perforated elastic plates interacting with flow

TL;DR

This paper develops a homogenized model for vibro-acoustic wave transmission through perforated elastic plates interacting with flow, enabling efficient analysis of flow effects on acoustic transmission in complex geometries.

Contribution

It introduces a flow-dependent homogenized model for vibro-acoustic transmission on perforated plates, incorporating flow effects into the interface coefficients for improved analysis.

Findings

Flow speed significantly influences acoustic transmission.

The homogenized model accurately predicts wave behavior in flow conditions.

Geometrical features affect transmission characteristics.

Abstract

We consider acoustic waves propagating in an inviscid fluid interacting with a rigid periodically perforated plate in the presence of permanent flows. The paper presents a model of an acoustic interface obtained by the asymptotic homogenization of a thin transmission layer in which the plate is embedded. To account for the flow, a decomposition of the fluid pressure and velocity in the steady and fluctuating parts is employed. This enables for a linearization and an efficient use of the homogenization method which leads to a model order reduction effect. The dependence of an extended Helmholtz equation on the permanent flow introduces a locally periodic velocity field in the perforated plate vicinity, so that the coefficients of the homogenized interface depend on the flow. The derived model extended by natural coupling conditions provides an implicit Dirichlet-to-Neumann operator. Numerical simulations of wave propagation in a waveguide illustrate the flow speed influence on the acoustic transmission. Also some geometrical aspects are explored.