Homogenization of the vibro-acoustic transmission on periodically perforated elastic plates with arrays of resonators

TL;DR

This paper develops a homogenized model for acoustic wave transmission through perforated elastic plates with embedded resonators, enabling efficient simulation and control of sound transmission in complex structures.

Contribution

It introduces a novel homogenization approach for vibro-acoustic metasurfaces with resonators, simplifying complex geometries into effective transmission conditions.

Findings

Homogenized model accurately predicts acoustic transmission suppression.

Effective parameters can change sign, affecting impedance and mass.

Model reduces computational complexity significantly.

Abstract

Based on our previous work, we propose a homogenized model of acoustic waves propagating through periodically perforated elastic plates with metamaterial properties due to embedded arrays of soft elastic inclusions serving for resonators. Such structures enable to suppress the acoustic transmission for selected frequency bands. Homogenization of the vibro-acoustic fluid-structure interaction problem in a 3D complex geometry of the transmission layer leads to effective transmission conditions prescribed on the acoustic meta-surface associated with the mid-plane of the Reissner-Mindlin plate. Asymptotic analysis with respect to the layer thickness, proportional to the plate thickness and to the perforation period, yields an implicit Dirichlet-to-Neumann operator defined on the homogenized metasurface. An efficient method is proposed for computing frequency-dependent effective parameters involved in the homogenized model of the layer. These can change their signs, thus modifying the acoustic impedance and the effective mass of the metasurface. The global problem of the acoustic wave propagation in a waveguide fitted with the plate is solved using the finite element method. The homogenized interface allows for a significant reduction of the computational model. Numerical illustrations are presented.