Sound absorption by perforated walls along boundaries

TL;DR

This paper investigates how perforated walls along boundaries can absorb sound by analyzing the Helmholtz equation in a complex, multi-scale domain, deriving an effective model as the perforation scale diminishes.

Contribution

It introduces a multi-scale analysis of sound absorption through perforated boundary structures, deriving an effective system for the Helmholtz equation as the perforation size approaches zero.

Findings

Effective system models sound absorption in perforated walls.

Multi-scale analysis captures the influence of thin channels and resonator volume.

Asymptotic analysis provides insights into boundary sound absorption mechanisms.

Abstract

We analyze the Helmholtz equation in a complex domain. A sound absorbing structure at a part of the boundary is modelled by a periodic geometry with periodicity $\varepsilon>0$. A resonator volume of thickness $\varepsilon$ is connected with thin channels (opening $\varepsilon^3$) with the main part of the macroscopic domain. For this problem with three different scales we analyze solutions in the limit $\varepsilon\to 0$ and find that the effective system can describe sound absorption.