Topology optimization for the design of acoustic metamaterial that exhibits a desired dispersion relation based on high-frequency homogenization method

Abstract

We propose a topology optimization method based on a high-frequency homogenization method for the design of acoustic metamaterial that exhibits a desired dispersion relation. Negative refraction, which is one of the most typical phenomena in acoustic metamaterials, is achieved by obtaining the desired dispersion relation of metamaterial via topology optimization. First, the high-frequency homogenization method to express the dispersion relation of metamaterials is briefly explained. Next, optimization problem based on the high-frequency homogenization method is formulated so that the optimized design has a desired dispersion relation which satisfies conditions for negative refraction. A level set-based topology optimization is introduced to solve the optimization problem, and two-dimensional numerical example is provided to show the validity of our proposed method.