圆柱壳振动控制中约束阻尼拓扑优化研究

窦松然，桂洪斌，李承豪，乔永亮

(哈尔滨工业大学(威海) 船舶与海洋工程学院，山东威海264209)

摘要：基于RAMP(Rational Approximation of Material Properties)插值模型密度法，以结构模态损耗因子倒数最小化为优化目标、阻尼结构体积为约束条件、约束阻尼单元相对密度为设计变量，建立约束阻尼结构拓扑优化模型。基于优化准则法推导设计变量更新准则，结合有限元法编写约束阻尼材料拓扑优化程序，对圆柱壳在振动控制中约束阻尼结构进行拓扑优化分析。结果表明，基于优化准则的振动拓扑优化方法所需迭代次数少，能有效减少结构的振动响应。从而验证设计方法的有效性。

关键词：拓扑优化；RAMP插值；密度法；优化准则法；约束阻尼；有限元

中图分类号:O328；TB535文献标志码：A

基金项目：国家自然科学基金资助项目(51208471)；高等学校博士学科点专项科研基金(20114101120008)；河南省科技攻关计划项目(142102210486)；郑州大学优秀青年教师发展基金(1421322059)

收稿日期：2014-05-19修改稿收到日期：2014-10-17

Topological optimization for constrained damping in vibration control of cylindrical shell

DOUSong-ran,GUIHong-bin,LICheng-hao,QIAOYong-liang(School of Naval Architecture and Ocean Engineering, Harbin Institute of Technology at Weihai, Weihai 264209, China)

Abstract:Structures with damping have a better performance in reducing vibration. Based on the density approach with RAMP interpolation model, a topologic model of constrained damping structure was established with the minimum of reciprocal of modal loss factors as a target function, the volume of damping structure as a constraint condition, and the relative density of constrained damping element as a design variable. The updating criterion of design variable was derived based on an optimal criteria method. And the topologic optimization program was developed based on the finite element method. The topological optimization for constrained damping structure in vibration control of cylindrical shell was carried out. The analysis shows that the topologic optimization method combined with the optimal criteria method needs less number of iterations and can reduce the vibration response of structure effectively, which indicates the validity of the design approach.

Key words:topologic optimization; RAMP interpolation; density approach; optimal criteria method; constrained damping; finite element

圆柱壳结构在潜艇、飞机等工程领域中应用较广，其振动普遍存在。为抑制结构振动，常在表面敷设约束阻尼[1]。在船舶、航空、汽车、土木等工程振动、噪声控制中，若将阻尼敷设于整个结构表面，并不能有效利用阻尼，会造成材料浪费；而实际中为减轻结构重量会减少阻尼敷设面积。因此如何正确敷设阻尼、提高结构减振效果成为研究解决的重要问题。

对约束阻尼圆柱壳振动已有诸多研究。Bieniek[2]提出约束阻尼圆柱壳受迫振动研究方法，并对载荷垂直壳体中性面情形进行分析。……