Topology Optimization and Wave Propagation of Three-Dimensional Phononic Crystals

Phononic crystals are periodically engineered structures with special acoustic properties that natural materials cannot have. One typical feature of phononic crystals is the emergence of band gaps wherein the wave propagation is prohibited due to the spatial periodicity of constituents. This article presents a generalized plane wave expansion method (GPWEM) and a voxel-based discretization technique to calculate the band structures of given three-dimensional phononic crystals. Integrated with the adaptive genetic algorithm (AGA), the proposed method is used to perform topological optimization of constituent distribution to achieve maximized band gap width. Numerical results yielded from the optimization of a three-dimensional cubic phononic crystal verify the effectiveness of the proposed method. Eigenmodes of the phononic crystal with the optimized topology are investigated for a better understanding of the mechanism of band gap broadening.

Automated summary

Phononic crystals are engineered structures with unique acoustic properties that cannot be found in natural materials. These crystals exhibit band gaps where wave propagation is prohibited due to their periodic structure. This article presents a method using a generalized plane wave expansion and voxel-based discretization to calculate the band structures of three-dimensional phononic crystals. The proposed method, integrated with an adaptive genetic algorithm, is used for topological optimization of constituent distribution to maximize the width of the band gap. Numerical results validate the effectiveness of the method for optimizing a cubic phononic crystal, and the eigenmodes of the optimized crystal are investigated to better understand the mechanism of band gap broadening.