Sound absorption by perforated walls along boundaries

ABSTRACT

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

Keywords:

• Helmholtz equation
• sound absorbers
• homogenization
• complex domain

MSC:

• 35B27
• 78M40

Acknowledgments

This work was initiated when the three authors attended in summer 2019 workshop 1931 ‘Computational Multiscale Methods’ in Oberwolfach. The invitation and the hospitality of the institute are gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author(s).