基于MO-RAMP插值模型的阻尼板GCMOC法拓扑减振优化

贺红林,李洪坤,李冀,赵伟鹏,余志豪

振动与冲击 ›› 2021, Vol. 40 ›› Issue (23) : 223-231.

PDF(2468 KB)
PDF(2468 KB)
振动与冲击 ›› 2021, Vol. 40 ›› Issue (23) : 223-231.
论文

基于MO-RAMP插值模型的阻尼板GCMOC法拓扑减振优化

  • 贺红林,李洪坤,李冀,赵伟鹏,余志豪
作者信息 +

Topology dynamic optimization of damping plates using GCMOC method based on MO-RAMP

  • HE Honglin, LI Hongkun, LI Ji, ZHAO Weipeng, YU Zhihao
Author information +
文章历史 +

摘要

为了有效实现板件的抗振性动力学设计,研究约束阻尼板拓扑动力学优化方法。建立约束阻尼板有限元动力学分析模型,推导出模态损耗因子计算公式;建立了基于模态损耗因子最大化目标,以阻尼层单元相对密度为拓扑变量,以阻尼材料使用量及结构频率作为控制的阻尼板优化数学模型;利用序列凸规划理论而对传统优化准则法进行改进,采用改进准则法GCMOC解算优化模型以求取全域性优化解,推导出面向GCMOC的拓扑变量迭代式;考虑到多阶次RAMP函数的形状具有较理想的可控下凹几何特征,提出在优化迭代中采用多阶次RAMP材料插值模型(MO-RAMP)对拓扑变量集合进行惩罚以实现其快速的0、1二值化,并尽量减少处于0.3~0.7的中间拓扑变量值出现;编制了面向约束阻尼板的拓扑动力学优化程序,实现了基于MO-RAMP的约束阻尼板GCMOC法变密度式减振拓扑动力学优化过程。算例分析表明,MO-RAMP与GCMOC复合的算法用于阻尼板拓扑迭代时,可将阻尼单元密度值快速地推向逼近0或1的值。它能得到清晰的阻尼单元优化密度云并有利于优化构型的实现;能在大幅减少阻尼材料用量条件下充分发挥其黏弹耗能效应,能在保证阻尼板动力学特性基本稳定的前提下使结构获得更好的减振效果。

Abstract

Aiming at effective implementation of anti-vibration dynamic design of engineering structural plates, the topological dynamic optimization method of damping plates was studied. A dynamical finite element method for constrained damping plates was built with which a formula for calculation the modal loss factors of the plates could be derived. Based on the objective of maximizing modal loss factor, an optimization mathematical model for the damping plates was presented, which took the relative density of damping layer elements as topological variables, and the amount of damping materials and structural frequency as optimal control. Using the theory of sequential convex programming, and by improving the traditional optimization criterion method, an optimal method called GCMOC was proposed to solve the optimization model, so as to obtain a global solution of topology dynamics optimization problem, and an iteration formula of topological variables for GCMOC was achieved. Considering that the shape of multi-order RAMP function had ideal controllable concave geometric feature, a multi-order RAMP material interpolation(MO-RAMP) model was introduced into the optimization iteration, so as to punish topological variables effectively and realize its 0 and 1 binarization quickly, and minimize the occurrence of intermediate topological variable values of 0.3 ~ 0.7 as well. A topological dynamic optimization program for the plates was developed, and the variable density vibration reduction topology dynamic optimization process of GCMOC method based on MO-RAMP was implemented. The results showed that GCMOC combined with MO-RAMP can push the damping element density to the value close to 0 or 1 quickly. It obtained clear optimized density cloud for the damping layer, which was very conducive to the process realization. It exerted its viscoelastic energy dissipation effect under the condition of greatly reducing damping materials. It can keep the dynamic characteristics of the plate basically stable, and made it get better vibration reduction effect.

关键词

约束阻尼板 / 拓扑动力学优化 / MO-RAMP材料插值模型 / GCMOC优化 / 减振特性

Key words

constrained damping plates / topology dynamic optimization / multi-order RAMP / GCMOC optimization method / vibration reduction characteristics

引用本文

导出引用
贺红林,李洪坤,李冀,赵伟鹏,余志豪. 基于MO-RAMP插值模型的阻尼板GCMOC法拓扑减振优化[J]. 振动与冲击, 2021, 40(23): 223-231
HE Honglin, LI Hongkun, LI Ji, ZHAO Weipeng, YU Zhihao. Topology dynamic optimization of damping plates using GCMOC method based on MO-RAMP[J]. Journal of Vibration and Shock, 2021, 40(23): 223-231

参考文献

[1] 刘文光. 含裂纹构件振动疲劳损伤预测理论与方法[M]. 北京: 机械工业出版社, 2019
    Liu W G. Theory and method of vibration fatigue damage prediction for cracked components [M]. Beijing: China Machine Press, 2019  (In Chinese)
[2] Xiao P., Zhang, Z K. Topology optimization of damping layers for minimizing sound radiation of shell structures[J]. Journal of Sound and Vibration 2013, 332:2500-2519
[3] Zainab Abdul Malik,Naveed Akmal Din. Passive vibration control of plate using nodal patterns of mode shape[J]. Vibroengineering Procedia,2019,207(06):16-23
[4] Zhao J., Wang C. Dynamic response topology optimization in  the time domain using model reduction method[J]. Structural and Multidisciplinary Optimization, 2016, 53(1): 101-114
[5] 房占鹏,张孟珂,李宏伟.平稳随机激励下约束阻尼结构布局优化设计[J]. 郑州大学学报(工学版),2020,41(5):87-91.
FANG Z P, ZHANG M G, Li H W. Layout optimization of constrained layer damping structure under stationary random excitation[J]. Journal of Zhengzhou University (Engineering Science) ,2020,41(5):87-91.
[6] 贺红林,陶结. 约束阻尼板增材式拓扑渐进法减振动力学优化[J]. 机械科学与技术. 2017,36(06):971-975
    HE H L,TAO J. Vibration reduction and optimization for constrained damping plates based on adding material evolutionary method [J]. Mechanical Science and Technology for Aerospace Engineering, 2017,36(06): 971-975  (In Chinese)
[7] 徐伟,张志飞,庾鲁思,等. 附加自由阻尼板阻尼材料降噪拓扑优化[J]. 振动与冲击,2017,36(08):192-198
XU W, ZHANG Z F, YU L S. Topology optimization for noise reduction of damping materials with additional free damping plate [J]. Journal of Vibration and Shock, 2017,36(08):192-198  (In Chinese)
[8] 张志飞,倪新帅,徐中明,等. 基于优化准则法的自由阻尼材料拓扑优化[J]. 振动与冲击, 2013,32(14):98-102.
Zhang Z F., Ni X S, Xu Z M,et al. Topologic optimization of a free damping material based on optimal criteria method[J]. Journal of Vibration and Shock, 2013,32(14):98-102  (In Chinese)
[9] 胡卫强,叶文,曲晓燕. 谐和激励下阻尼材料的配置优化[J]. 噪声与振动控制, 2013, 33(4): 40-43.
Hu W G., Ye W, Qu X Y. Topology optimization for free-damping treatment under harmonic excitation [J]. Noise and Vibration Ccontrol,2013, 33(4): 40-43. (In Chinese)
[10] 郑玲,谢熔炉. 基于优化准则的约束阻尼材料优化配置[J]. 振动与冲击,2010,11,29(11):156-159
Zheng L., Xie R L Optimal placement of constrained damping material in structures based on optimality criteria[J]. Jounal of Vibration and Shock,2010, 29(11):156-159  (In Chinese)
[11] 郭中泽,陈裕泽. 基于准则法的阻尼结构拓扑优化[J]. 宇航学报, 2009, 30(6): 2387-2391.
Guo Z Z., Chen Y Z. Topology optimization of the damping structure with optimal criteria[J]. Journal of Astronautics, 2009,30(6):2337-2391  (In Chinese)
[12] 李攀,郑玲. SIMP插值的约束层阻尼结构拓扑优化[J]. 机械科学与技术, 2014, 33(8): 1122-1126.
Li P., Zheng L.Topology pptimization of constrained layer damping structure based on SIMP interpolation method[J]. Mechanical Science and Technology for Aerospace Engineering,2014,33(8): 1122-1126. (In Chinese)
[13] Kim S Y, Mechefske C K, Kim I Y.Optimal damping layout in a shell structure using topology optimization [J].Journal of Sound and Vibration,2013,332:2873-2883.
[14] Sigmund O., Maute K.. Topology optimization approaches [J]. Structural and Multidisciplinary Optimization, 2013, 48(6): 1031-1055.
[15] Rao D.K. Frequency and loss factors of sandwich beams under various boundary condition[J]. Journal of Mechanical Engineering Science,1978,20(5): 270-282

PDF(2468 KB)

Accesses

Citation

Detail

段落导航
相关文章

/