基于分析与设计序列迭代方法的三维声子晶体拓扑优化及参数分析  

Three⁃dimensional phononic crystals topology optimization via successive iteration of analysis and design,and parameter exploration

作　　者：王燕[1,2] 朱奕筱 吴圣川 亢战[3] WANG Yan;ZHU Yixiao;WU Shengchuan;KANG Zhan(State Key Laboratory of Rail Transit Vehicle System,Southwest Jiaotong University,Chengdu 610031,China;CRRC Qingdao Sifang Co.,Ltd.,Qingdao 266111,China;State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]西南交通大学轨道交通运载系统全国重点实验室,成都610031 [2]中车青岛四方机车车辆股份有限公司,山东青岛266111 [3]大连理工大学工业装备结构分析优化与CAE软件全国重点实验室,辽宁大连116024

出　　处：《振动与冲击》2025年第4期97-104,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金重点项目(12332007)。

摘　　要：在常规的声子晶体拓扑优化中,内层的多波矢特征值分析和外层的单胞布局设计变量寻优构成双层嵌套问题,两个层次嵌套式迭代求解导致三维拓扑优化设计面临计算量剧增的难题。为提高优化设计的效率,将用于结构固有频率优化问题的分析与设计序列迭代的思想拓展至三维声波声子晶体的拓扑优化,通过将内层特征值问题转化为单次逆迭代获得拓扑优化中间结果对应的逐次近似能带结构,并根据优化结果进行参数化建模以研究三维声子晶体拓扑优化解的带隙特性。通过参数化扫掠,给出了不同参数下的相对带隙和带隙上下界。进一步总结了不同参数对声子晶体带隙的影响,为三维声波声子晶体构型设计提供指导。Conventional topology optimization of PnCs needs to perform an inner eigenvalue analysis corresponding to many wave vectors,and an outer design optimization to find the optimal unit cell configuration.Such a double⁃loop nested problem becomes extremely computationally demanding for three⁃dimensional cases.In this study,based on the successive iteration of analysis and design method,topology optimization of three⁃dimensional acoustic PnCs was performed to improve the efficiency of design optimization.Therein,the inner loop problem was converted into a single⁃step inverse iteration to provide sequentially approximated band structures of the intermediate designs.According to the optimization results,several parametric models were built to study the bandgap properties of the optimized three⁃dimensional PnCs designs.The results of the relative bandgaps and their upper/lower bounds of the unit cells were given through parameter scanning.The influences of different parameters on the bandgap property were analyzed,which may provide useful guidance to the design of three⁃dimensional acoustic PnCs.

关 键 词：三维声波声子晶体 拓扑优化 分析与设计序列迭代方法 参数化建模 相对带隙 

分 类 号：O429[理学—声学]