Phononic crystal bandgap optimization based on a multistage grid-pixel refinement method

Abstract

Phononic crystal (PnC) is a kind of periodic distribution structure with elastic constants and densities, which prevents the propagation of waves in the bandgap by the interaction of internal microstructures. A slow convergence process and topological ill-conditioned structure cannot fail to have noticed during the fine grid optimization process of PnC. In this paper, a multistage grid-pixel refinement method (MGPRM) is proposed to quickly obtain the high-quality PnC topology based on the fast plane wave expansion method. Combined with the MGPRM and genetic algorithm, the bandgap of PnC is used to optimize. Results show that the MGPRM combined with the optimization algorithm can provide high-quality original configurations for the tunable parameterized microstructures. Compared with invariant grids of different densities and traditional refinement methods, the MGPRM has higher quality and a faster convergence rate for the process of optimization. Using the MGPRM for multi-objective optimization, the highly nonlinear correspondence between the characteristic bandgap and the topological morphology is obtained. In addition, the dynamic response of the finite PnC microstructure plate composed of the optimized topology and the calculated transmission spectrum are in perfect agreement with the bandgap of PnC. The MGPRM is further applied to the structure design and performance optimization of PnC.