Level set-based topology optimization for the design of acoustic metamaterial using two-phase material model

Abstract

Acoustic metamaterials are artificial materials composed of periodic structures made of elastic and fluid material. They could be used for noise reduction problems and efficient sound propagation control by their unusual properties, such as negative bulk modulus, mass density, and refractive index. The performance of acoustic metamaterial is strongly affected by its designs rather than its material properties. Therefore, topology optimization method could be used to obtain a desired property of acoustic metamaterial. To model acoustic-elastic coupled system, we introduce a two-phase material model where the solid and fluid phases are mixed. While coupling boundary conditions are required in a usual acoustic-elastic coupled analysis, this model allows us to analyze the system without imposing such boundary conditions since their conditions are satisfied naturally. In this research, we propose a level set-based topology optimization method for the design of acoustic metamaterial. First, we introduce the two-phase material model and level set-based topology optimization method. An optimization problem for an acoustic metamaterial that has negative mass density is formulated and sensitivity analysis is performed based on the concept of topological derivative. After verifying the topological derivative by comparing it to numerical differences, we present two-dimensional numerical examples for negative mass acoustic metamaterial.