Multi-scale topology optimization method of anisotropic acoustic metamaterials based on high-frequency homogenization method

Abstract

In this research, we propose a multi-scale design method of anisotropic acoustic metamaterials using level set-based topology optimization, based on a high-frequency homogenization method. Anisotropic acoustic metamaterials exhibit highly unique properties, generally based on the local resonance induced by their unit cells of its periodic structure. In previous work, metamaterials which are only composed of a single type of unit cell were in interest, leading to a limit in the macroscopic wave propagation properties that could be obtained. Therefore, in the present work, we focus on metamaterials that is combined of several types of unit cells, in order to achieve complex wave propagation. First, we introduce the high frequency homogenization method, which is capable of evaluating the macroscopic material property of periodic media based on local resonance. We then formulate the optimization problem for the micro-scale unit cell structures using the level-set based topology optimization method, designing unit cells which possess different wave propagation property at the same resonance frequency. Furthermore, we arrange the optimized unit cell structures in the macro-scale, in order to achieve complex dynamic properties. Finally, we present numerical examples to demonstrate the validity of the proposed multi-scale design method.