旨在为减振设计提供理论基础,研究约束阻尼结构拓扑动力学优化。以阻尼材料用量、振动特征方程、模态频率为约束,以多模态损耗因子倒数加权和最小为目标,建立了约束阻尼结构拓扑优化模型,并引入MAC因子控制结构的振型跃阶。在引入质量阵惩罚因子基础上推导出优化目标灵敏度。考虑到目标函数的非凸性,采用常规准则法(OC)寻优可能会使拓扑变量出现负值或陷入局部优化,故引入数学规划移动渐近技术对OC法进行改进,从而将全体拓扑变量纳入改进算法的优化迭代全过程。编程实现了约束阻尼板改进OC法拓扑动力学优化并对改进法性能进行了仿真,结果显示:改进算法可得到更合理的约束阻尼层构形,可使结构取得更佳减振效果。研究表明:改进算法迭代稳定性更好、寻优效率更高、更具全域最优性。
Abstract
A dynamic topology optimization for plates with constrained damping was conducted to provide a theoretical basis for vibration reduction design.Taking maximizing plate’s multi-modal loss factor as an objective,and taking amount of damping material,frequency equation and frequency region,and MAC factor as constraints,a topology optimization model was developed.The penalty factors for mass matrix were introduced,and the multi-modal loss factor sensitivity was deduced.Considering optimal objective function being non-convex,using a common optimal criterion might lead to the topological variables to be negative,or the optimization calculation to fall into a local optimization.So a moving asymptotic technique of mathematical programming was adopted to improve the common optimal criterion.With the improved criterion,all topological variables were brought into the optimization process so as to avoid the occurrence of local optimization.Dynamic optimization for the plates based on improved optimal criterion method were simulated.The results showed that a more reasonable constrained damping layer’s configuration is obtained with the improved method and algorithm,the plates with constrained damping achieve a better vibration reduction effect; the improved method has a better iteration stability and a faster optimization speed,and can more effectively provide a global optimal solution.
关键词
约束阻尼板 /
多模态损耗因子 /
改进优化准则法 /
减振特性 /
动力学拓扑优化
{{custom_keyword}} /
Key words
plate with constrained damping /
multi-modal loss factor /
improved optimal criteria method /
vibration reduction characteristics /
dynamic topology optimization
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1]Mary Baker. Analysis method to support design for damp -ing[J].Engineering with Computer, 2007, 23 (1):1-10.
[2] 王明旭,陈国平. 基于变密度方法约束阻尼层动力学性能优化[J]. 南京航空航天大学学报,,2010,42(03):83-86.
WANG Ming-xu, Cheng Guo-ping. Dynamics performance optimization of constrained damping layer using variable density method [J].Journal of Nanjing University of Aeronautic -s & Astronautics, 2010,42(3):283-287.
[3] 蒋亚礼,吕林华,杨德庆. 提高船用阻尼材料应用效果的优化设计方法[J]. 中国舰船研究,2012,7(4):48-53.
JIANG Ya-li, LV Lin-hua, YANG De-qing. Design methods for damping materials applied to ships [J]. Chinese Journal of Ship Research, 2012,7(4):48-53.
[4] 杨德庆. 动响应约束下阻尼材料配置优化的拓扑敏度法[J]. 上海交通大学学报,2003,37(8): 1209-1 225.
YANG De-qing. Topological sensitivity method for the optimal plancement of unconstrained damping materials under dynamic response constraints [J]. Journal of Shanghai Jiaotong Universit -y, 2003,37(8):1109-1212,1225.
[5] 韦 勇,陈国平. 一般阻尼结构的模态阻尼比优化设计[J]. 振动工程学报,2006, 19(4): 433-437.
WEI Yong, CHEN Guo-ping. Modal damping optimization for general damped structure [J]. Joural of Vibration Engineering, 2006, 19(4): 433-437.
[6]李 攀,郑 玲,房占鹏. SIMP插值的约束层阻尼结构拓扑优化.机械科学与技术,2014,33(8):1122-1126.
LI Pan, ZHENG Ling, FANG Zhanpeng. Topology optimization of constrained layer damping structue based on SIMP interpol -ation method [J]. Mechanical Science and Technology for Aeropace Engineering, 2014,33(8):1122-1126.
[7]Bendsoe M P, Sigmund O. Topology optimization: theory, method and application[M].2nd ed. Berlin:Springer Verlag.2003.
[8] 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(06): 2387-2391.
GUO Zhong-ze, CHEN Yu-ze. Topology Optimization of the Damping Structurewith Optimal Criteria [J]. Journal of Astronautics, 2009, 30(06): 2387-2391.
[9] 郑 玲,谢熔炉,王 宜. 基于优化准则的约束阻尼材料优化配置[J]. 振动与冲击,2010,29(11):156-159,259.
ZHENG Ling, XIE Rong-lu, WANG Yi, et al. Optimal placement constrained damping material in structures based on optimality criteria [J]. Journal of Vibration and Shock, 2010,29(11):156-159,259.
[10]JOHNSON C D, KIENHOLZ D A. Finite element prediction of damping in structures with constrained viscoelastic layers[J], AIAA Journal, 1982, 20(9):1284-1290.
[11] Z.-D.Ma, N.Kikuchi, I.Hagiwara. Structural topology and shape optimization for a frequency response problem[J]. Computation -al Mechanics, 1993,13:157-174.
[12] 王慧彩,赵德有. 粘弹性阻尼夹层板动力特性分析及其试验研究[J]. 船舶力学,2005, 9(4) :109-118.
WANG Hui-cai, ZHAO De-you. Dynamic analysis and experiment of viscoelastic damped sandwich plate [J]. Journal of Ship Mechanics, 2005, 9(4) :109-1
[13] Amichi, K. et Atalla, N. A new 3D finite element for sandwich structures with a viscoelastic core. Canadian Acoustics Associ- ation Conference / CAA, 2007, Montreal, Canada, Canadian Acoustics Vol. 35(3):197-198.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}