Level set-based topology optimization for the design of labyrinthine acoustic metamaterials

Abstract

We present a topology optimization method for the design of labyrinthine metamaterials with a large path length for acoustic wave propagation. An objective function maximizes the pressure gradient in an air-filled region at a low frequency, and a level set-based optimization method enables the optimal design of the labyrinthine structure with high computational efficiency owing to the concept of topological derivative. First, we explain the design settings of labyrinthine metamaterials. Next, the objective functions to obtain labyrinthine structures are introduced, and the corresponding topological derivatives are obtained. The optimization problem is formulated in the framework of the level set topology optimization method, and two-dimensional numerical examples are provided to demonstrate the validity of the proposed method. Based on the frequency responses of the effective parameters and dispersion analysis, the optimized designs are characterized by a negative refractive index over a wide frequency interval, which can be controlled by a parameter introduced in the objective function.