基于形状记忆合金声子晶体的带隙优化设计

BANDGAP OPTIMIZATION DESIGN OF PHONONIC CRYSTALS BASED ON SHAPE MEMORY ALLOY

声子晶体是一种具有声子带隙的周期性结构,通过对其带隙的动态调控设计,进而满足航空航天领域中重大装备对减振降噪性能的特定需求.文章在声子晶体的带隙设计中,引入智能材料,采用拓扑优化方法,开展多功能声子晶体带隙动态调控设计.首先采用有限元方法分析声子晶体的带隙性能,并建立形状记忆合金的温度本构关系模型;其次基于变密度法的拓扑优化方法,在满足特定体分比及强度约束、保证声子晶体单胞之间的连接性约束条件下,以相对带隙最大化为目标函数建立声子晶体带隙设计优化模型;最后根据改进的材料插值模型,分析求解设计灵敏度,采用移动渐进法开展多功能声子晶体带隙结构的拓扑优化设计.优化结果表明:在XY模式下形状记忆合金从马氏体转换到奥氏体带隙拓宽了103.9%,在Z模式下带宽增大了3.75倍.研究结果为声子晶体在复杂环境下实现更为主动带隙调控提供了一种有效的设计方法.

Phononic crystal is a kind of periodic structures with the phononic band gap.The dynamically controllable design of its band gap could improve the vibration and noise reduction performance of major equipment in the aerospace field.In the work,smart materials are introduced for band gap design of phononic crystals.And the topological optimization method is used to design the multifunctional phononic crystal with the dynamically controllable band gaps.Firstly,the band gap of phononic crystals are computed by finite element analysis.Simultaneously,the temperature constitutive model of shape memory alloy is established.Secondly,based on variable density method,topology optimization model is established with maximizing the relative band gap under the specific volume ratio and strength constraints.At the same time,the connectivity constraints among phononic crystal unit cells must be ensured.Lastly,the band gaps of multifunctional phononic crystals are optimized by using the moving asymptotic method.During the optimization process,the design sensitivities are calculated with the improved material interpolation model.The optimization results show that the band gap is widened by 103.9%in XY mode with the transformation of shape memory alloy from martensite to austenite.And the bandwidth is increased by 3.75 times in Z mode.This research provides an effective design way for more actively control the phononic crystals band gaps in the complex application environments.And the novel phononic crystals have a wider application prospect.