基于变密度法的薄壁复合壳结构阻尼减振优化  

The Damping Optimization of Thin-walled Composite Shell Structures Based on Variable Density Method

作　　者：余志豪 贺红林[1] 李冀 鄢殷期 YU Zhi-hao;HE Hong-lin;LI Ji;YAN Yin-qi(School of Aeronautical Manufacturing,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学航空制造工程学院,南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2021年第4期9-15,共7页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(52165008);江西省自然科学基金重点项目(20202ACB202003)。

摘　　要：旨在降低薄壁壳的结构振动并实现其轻量化,研究阻尼壳拓扑优化问题。首先,构建以模态损耗因子为优化目标,阻尼单元相对密度为拓扑变量,阻尼材料用量及薄壁壳固有频率为约束的阻尼壳优化模型;然后,基于变密度法思路且采用拉格朗日乘子法求解该模型,并引入SIMP插值模型对拓扑变量进行惩罚而使其向0、1汇聚;进而,推导出优化目标对于拓扑变量的灵敏度计算式以及拓扑变量优化迭代式;最后,编程实现了阻尼壳的拓扑动力学优化。当阻尼材料用量分别为40%、50%、60%时,薄壁壳阻尼层优化构型及其敷设位置大体相一致。研究表明,该优化法能在保证阻尼壳固有频率基本不变的前提下,使其模态损耗因子显著增加并使其模态振幅发生明显下降。In order to reduce the vibration of the thin shell structure and make it lightweight,topology dynamics optimization of the damping shells was studied.Firstly,an optimization model for the constrained damping shell was established,which took modal loss factor as optimization objective,the relative density of damping element as topological variable,the amount of damping material and the natural frequency of the structure as constraints.Then,the variable density optimization method and the Lagrange multiplier method were adopted to solve the model,while a SIMP material interpolation model was employed to punish the topological variables so as to make them converge to 0 and 1.Moreover,both the sensitivity calculation formula of the optimization objective to the topology variable and the optimization iteration formula of the topology variable were derived.Finally,the dynamic optimization of constrained thin-walled shell was realized by programming.When the amount of damping material was controlled to 40%,50%or 60%,the optimized shape and laying position of damping layer of thin-walled shell was roughly the same.The results showed that the optimization method could not only significantly increase the modal loss factor,but also significantly reduced the modal amplitude of the damping shell on the premise of keeping the natural frequency of the damping shell unchanged.

关 键 词：SIMP插值 模态损耗因子 拓扑敏度 响应峰值 

分 类 号：U458[建筑科学—桥梁与隧道工程]