Abstract
This paper discusses a level set-based topology optimization method for the design of negative bulk modulus acoustic metamaterials. Acoustic metamaterials are engineered materials that are designed to have extraordinary acoustic properties, such as a negative effective bulk modulus and effective density. Novel applications such as sound isolation devices, acoustic cloaking, acoustic superlenses, and others have been proposed using such acoustic metamaterials. Most metamaterials consist of periodic structures of unit cells that are adequately small compared to the wavelength of target frequency. The overall structure of such periodic structures can be considered as an effectively homogeneous acoustic structure, and behaves as a material having negative effective properties exhibited globally. The purpose of the optimization problem here is to find optimized configurations of acoustic metamaterials composed of rubber and epoxy that achieve a negative effective bulk modulus. In the design of acoustic metamaterials, the presence of grayscale areas in an optimal configuration significantly affects its performance, so we use a level set-based approach that inherently avoids the grayscale problem. The effective bulk modulus of the acoustic metamaterials is computed based on the reflection and transmission coefficients and the optimization problem is formulated to minimize the effective bulk modulus. Optimization algorithm uses the adjoint variable method (AVM) for sensitivity analysis and the finite element method (FEM) for solving the acoustic wave propagation problem, the adjoint problem, and the reaction diffusion equation to update the level set function. Finally, several numerical examples are provided to confirm the utility and validity of the proposed method.
