Level Set-based Topology Optimization of Acoustic Metamaterials

1. Abstract This paper discusses a topology optimization method for the design of acoustic metamaterials that exhibit negative bulk modulus, using level set-based boundary expression. The purpose of the optimization problem here is to find optimal configurations of acoustic metamaterial unit cells composed of rubber and epoxy that achieve a negative effective bulk modulus. The presence of grayscale areas in an optimal configuration significantly affects the performance of acoustic metamaterials, therefore, in this study, we use a level set-based approach to avoid this problem. The effective bulk modulus of the acoustic metamaterials is computed based on reflection and transmission coefficients. The optimization problem is formulated to minimize the effective bulk modulus at a target frequency. The optimization algorithm uses the adjoint variable method (AVM) to obtain design sensitivities and the finite element method (FEM) to solve the acoustic wave propagation problem, the adjoint problem, and the reaction diffusion equation used to update the level set function. Finally, several numerical examples including twoand three-dimensional problems are provided to confirm the utility and validity of the proposed method.