最优二维固/固声子晶体带隙特性研究

声子晶体是一种具有弹性波带隙特性的周期性复合材料，其带隙特性受单胞拓扑形状的影响。通过拓扑优化技术，能够突破传统设计方法的局限，实现对声子晶体的主动设计。本文基于遗传算法和改进的平面波展开法，通过两阶段的优化过程，得到具有最大相对带隙的二维铜/环氧树脂声子晶体结构，并进一步研究不同带隙最优声子晶体单胞拓扑形状及其带隙特性。结果表明，利用所开发的带隙优化程序，能够得到满足带隙要求的具有全局最优的声子晶体结构；声子晶体最低带隙所对应的单胞是简单晶格结构，其散射体形状简单，而且对应的带隙频率最低，相对带隙最大，对于隔音减振最有实用价值。

THE CHARACTERISTICS OF OPTIMAL TWO-DIMENSIONAL SOLID/SOLID PHONONIC CRYSTALS

Phononic crystals (PnCs) is a kind of periodic composite with elastic band-gap characteristics, the distribution of elastic materials within a unit cell has significant effect on the band-gaps. In this paper, the topology optimization (TOP) techniques are utilized to obtain two-dimensional (2D) square lattice Cu/Epoxy PnCs with maximized relative band-gaps between multiple consecutive bands. The optimization follows two-stage design process which adopts genetic algorithms (GAs) and plane wave expansion method (PWE). The results show that the optimal PnCs with different band-gaps, which can easily be found by the developed method, have different material layout, and the PnCs with the lowest band-gap are simple lattice and have the highest value of application.