The bandgap,an important characteristic of the periodic structure,is dispersionrelated,which can be designed by tailoring the layout of materials within the periodic microstructures.A typical example of a periodic structure is phononic crystals (PnCs),which are traditionally fabricated from two-phase materials.Herein,we investigate the topologies of periodic three-phase PnCs.The microstructures of the three-phase PnCs are optimized using a two-stage genetic algorithm,and three case studies are proposed to obtain the following:(1)the maximum relative bandgap width,(2)the maximum absolute bandgap width,and (3)the max- imum bandgap at a specified frequency.More importantly,the three-phase material provides significant advantages compared to the typical two-phase materials,such as a low-frequency bandgap.This research is expected to contribute highly to vibration and noise isolation,elastic wave filters,and acoustic devices.
WeiKai XuJinying NingMeng ZhangWei WangTianzhi Yang
