Topology Optimization of 3D Acoustic Diodes in Waveguides

Abstract

An acoustic diode is a structure that exhibits opposing functions, allowing sound waves of a specific frequency to propagate in one direction while blocking them in the opposite direction. This paper proposes a topology optimization method for the design of high-performance acoustic diodes. In such an acoustic diode design scheme, a coupled acoustic-structural status should be analyzed. Sound propagation is governed by the Helmholtz equation in air and the elastic equation in a structure, and the interaction at the boundary between air and the structure must also be considered during the analysis. However, it is cumbersome to switch the governing equations during optimization according to the shape and topological changes of the design domain. To mitigate this problem, a topology optimization method using a two-phase material model, which represents the ratio of the air phase to the solid phase (elastic body) as a normalized density, has been proposed. However, the conventional density approach using such a two-phase material model tends to generate grayscale regions to achieve the high diode performance. Furthermore, even when the binarization from the obtained grayscales is performed using a filtering scheme, the binarized structure does not yield the desired diode performance. Therefore, this paper formulates a two-phase material model based on a new physical property interpolation, in which the power of the design variable is applied to the RAMP method, and develops an optimization algorithm based on this formulation. The proposed method is then applied to the structural design of an acoustic diode, confirming the obtained structures with clear boundaries and desired performance.