Level set-based topology optimization for programmable acoustic structures

Abstract

Controlling acoustic waves is essential in noise-reduction applications. Acoustic structures, which can efficiently manipulate acoustic waves based on their structural design, have been used to achieve the desired wave propagation behaviors. To meet various demands on sound propagation, it is crucial to design acoustic structures with multiple functionalities. In this research, we propose a level set-based topology optimization method for acoustic structures with desired acoustic performances that depend on their deformation. Firstly, we introduce a mathematical model that represents acoustic wave propagation based on the Helmholtz equation and the coordinate transformation. Next, we formulate the optimization problem based on the framework of a level set-based topology optimization method. A two-dimensional numerical example is provided to demonstrate the validity of the proposed method. As an example, we optimize a sound reflective structure with the desired acoustic responses that are dependent on the deformation of the optimized structure.