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.

中文翻译：

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沿边界的穿孔墙吸收声音

摘要

我们分析复数域中的亥姆霍兹方程。边界部分的吸声结构由具有周期性的周期性几何建模$\epsilon >0$. 厚度为ε的谐振器体积与细通道（开口${\epsilon }^3$) 与宏观域的主要部分。对于这个具有三个不同尺度的问题，我们在极限中分析解决方案$\epsilon \to 0$并发现有效系统可以描述吸声。