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工程设计学报
工程设计学报  2015, Vol. 22 Issue (4): 351-358    DOI: 10.3785/j.issn. 1006-754X.2015.04.008
建模、分析、优化和决策     
基于复合模态阻尼比的阻尼板渐进法减振优化
贺红林，周楠兰，袁维东
南昌航空大学 航空制造工程学院，江西 南昌 330063
Evolutionary topology optimization of damped plates based on multiple modes damping ratio
HE Hong-lin， ZHOU Nan-lan， YUAN Wei-dong
School of Aeronautical Manufacturing， Nanchang Hangkong University， Nanchang 330063， China
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摘要： 研究阻尼板黏弹减振优化方法，为阻尼板设计奠定一定基础.建立了阻尼板运动方程及其求解模型，推导出模态阻尼比敏度算式；构建了以多模态复合模态阻尼比最大、黏弹材料用量及频率变动最小为约束的阻尼板优化模型，采用拓扑渐进法求解优化模型；引入绕单元敏度均化技术解决优化迭代中的棋盘格问题；在引入虚拟单元及逻辑删除技术基础上，编程实现了渐进优化算法；对任意四边形板进行了优化仿真，实现了该板复合阻尼比最大化设计；引入阻尼比体积密度评析拓扑优化效能.研究表明，在阻尼板设计时若实现其多模态阻尼比最大化，则能使板获得良好减振效果.
关键词： 阻尼板;  多模态阻尼比;  渐进法优化;  减振控制    
Abstract: To develop theoretical instructions for vibration suppression design of damped plates, a topology optimization method for the plates was presented. Firstly, a dynamic equation for a plate was proposed and a FEM solution to the equation was given, so that the plate's modal ratio model could be derived. Then, oriented to maximizing multiple modes' damping ratios, and aimed to make use of damping materials as less as possible and to remain the plate's modal frequency basically unchanged as well, a topology optimization model was built for the plate. Moreover, the modal damping ratio sensitivity was derived, and evolutionary method was employed to solve the optimization model, which used weighted mean of modal ratio sensitivity to determine the elements' deletion, so as to avoid checkerboard layout of damping materials in optimization. Finally, a program was accomplished for optimization, so that simulations could be executed on a quadrilateral plate, which validated the optimization method proposed well. Simulations show that a damping plate can obtain better vibration suppression effects, as long as the damping materials distribution on the plate can make multi-mode damping ratio maximize.
Key words: damped plate    multi-mode damping ratio    evolutionary optimization    vibration suppression
收稿日期: 2015-02-25 出版日期: 2015-08-28
基金资助:

国家自然科学基金资助项目（51265040）
作者简介: 贺红林（1967—），男，江西永新人，教授，博士，从事复杂结构动力学优化、精密驱动技术等研究，E-mail: Hehonglin1967@163.com.
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引用本文:

贺红林，周楠兰，袁维东. 基于复合模态阻尼比的阻尼板渐进法减振优化[J]. 工程设计学报, 2015, 22(4): 351-358.

HE Hong-lin， ZHOU Nan-lan， YUAN Wei-dong. Evolutionary topology optimization of damped plates based on multiple modes damping ratio. Chinese Journal of Engineering Design, 2015, 22(4): 351-358.

链接本文:

https://www.zjujournals.com/gcsjxb/CN/10.3785/j.issn. 1006-754X.2015.04.008    或    https://www.zjujournals.com/gcsjxb/CN/Y2015/V22/I4/351

[1] 贺红林，周楠兰，袁维东. 基于复合模态阻尼比的阻尼板渐进法减振优化[J]. 工程设计学报, 2015, 22(5): 351-358.