# Homogenization of the vibro-acoustic transmission on perforated plates

## TL;DR

This paper develops a homogenized model for vibro-acoustic transmission through perforated elastic plates, using asymptotic analysis and finite element validation, to simplify complex fluid-structure interactions in perforated layers.

## Contribution

It introduces a novel homogenized interface model for vibro-acoustic transmission in perforated plates based on two-scale asymptotic analysis.

## Key findings

- The homogenized model accurately predicts vibroacoustic transmission.
- Finite element implementation validates the model against direct numerical simulations.
- The approach simplifies complex fluid-structure interaction analysis.

## Abstract

The paper deals with modelling of acoustic waves which propagate in inviscid fluids interacting with perforated elastic plates. The plate can be replaced by an interface on which transmission conditions are derived by homogenization of a problem describing vibroacoustic fluid-structure interactions in a transmission layer in which the plate is embedded. The Reissner-Mindlin theory of plates is adopted for periodic perforations designed by arbitrary cylindrical holes with axes orthogonal to the plate midplane. The homogenized model of the vibroacoustic transmission is obtained using the two-scale asymptotic analysis with respect to the layer thickness which is proportional to the plate thickness and to the perforation period. The nonlocal, implicit transmission conditions involve a jump in the acoustic potential and its normal one-side derivatives across the interface which represents the plate with a given thickness. The homogenized model was implemented using the finite element method and validated using direct numerical simulations of the non-homogenized problem. Numerical illustrations of the vibroacoustic transmission are presented.