Topology optimization for hyperbolic acoustic metamaterials using a high-frequency homogenization method
Topology optimization for hyperbolic acoustic metamaterials using a high-frequency homogenization method
复制标题
DOI：
10.1016/j.cma.2018.02.031
复制
发表时间：
2018-06
影响因子：
7.2
通讯作者：
Y. Noguchi;T. Yamada;K. Izui;S. Nishiwaki
中科院分区：
文献类型：
--
作者：
Y. Noguchi;T. Yamada;K. Izui;S. Nishiwaki
本文提出了一种基于水平集的双曲声学超材料的高频均匀化拓扑优化设计方法。为了估计声学超材料的性质，我们首先介绍了前人提出的高频均匀化方法，通过这种方法，即使入射声波的波长与单胞的大小相当，也可以得到周期性结构的宏观波动行为。本文在高频均匀化方法的基础上，提出了一种新的基于水平集的拓扑优化方法，可以提供具有双曲离散特性的单胞设计。我们使用一个表示拓扑导数和形状导数之间关系的方程来计算拓扑导数。数值算例验证了该优化方法的有效性。得到的优化单胞设计，空气和铝的构型，通过利用单胞中诱导的共振表现出双曲型色散。
In this paper, we propose a level set-based topology optimization method for the design of hyperbolic acoustic metamaterials using a high-frequency homogenization method. To estimate the properties of acoustic metamaterials, we first introduce the high-frequency homogenization method proposed in previous work, through which the macroscopic wave behavior of periodic structures can be obtained even if the wavelength of impinging acoustic waves is comparable to the size of the unit cell. We propose a new level set-based topology optimization method based on the high-frequency homogenization method that can provide unit cell designs that exhibit hyperbolic dispersion. We compute the topological derivatives using an equation that expresses the relationship between the topological and shape derivatives. Numerical examples are provided to confirm the utility of the newly proposed optimization method. The obtained optimized unit cell designs, configurations of air and aluminum, exhibit hyperbolic dispersion by exploiting resonances induced in the unit cell.