Band-gap optimization of two-dimensional phononic crystals based on genetic algorithm and FPWE

Phononic crystals (PnCs) with band-gaps can confine the propagation of elastic waves. In many applications, it is desired to have a unit cell with favored band-gaps. Topological distribution of elastic materials within a unit cell has a significant effect on the band-gap properties, which are extremely difficult to determine without an optimization-based systematic synthesis procedure. In this paper, the two-stage design method, based on genetic algorithm conjunction with fast plane wave expansion method, is adopted to carry out the topology optimization of the two-dimensional (2D) PnCs in square lattices configuration with the maximized relative band-gap between two prescribed dispersion branches. Three numerical examples are given to the optimization of 2D steel-epoxy PnCs in one-eighth symmetry for coupled mode, acoustic mode, and mixed mode, respectively. The results show that the developed method provides an effective tool for the design of the 2D PnCs with favorable band-gaps' properties.