论文标题
沿边界的穿孔壁吸收声音
Sound absorption by perforated walls along boundaries
论文作者
论文摘要
我们分析复杂域中的Helmholtz方程。边界一部分处的声音吸收结构由具有周期性$ \ varepsilon> 0 $的周期性几何形状建模。厚度$ \ varepsilon $的谐振器体积与宏观域的主要部分相连（打开$ \ varepsilon^3 $）。对于三个不同量表的这个问题，我们在限制$ \ varepsilon \ to 0 $中分析解决方案，并发现有效的系统可以描述吸收声音。
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.
