基于移动可变形组件法的格栅平板隔振结构自振频率拓扑优化

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (11) : 149-156.

振动理论与交叉研究

基于移动可变形组件法的格栅平板隔振结构自振频率拓扑优化

周锦航1，商超2，王强勇2，代成名2，李刚*1,3

作者信息 +

Topology optimization of natural frequency of grid plate vibration isolation structure based on MMC method

ZHOU Jinhang1, SHANG Chao2, WANG Qiangyong2, DAI Chengming2, LI Gang*1,3

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文章历史 +

摘要

隔振结构在工程结构中主要用于设备与主体结构的连接，其动力学特性对隔振效果有着显著影响。通过移动可变形组件方法，针对典型的格栅平板隔振结构，解决其基频拓扑优化问题。首先，使用梁单元对格栅平板隔振结构进行模型简化。其次基于简化后的优化对象的梁单元结构进行移动可变形组件框架的改进，加入基于改进框架的冗余梁单元自适应修剪，提升计算效率。最后计算不同工况下设备布局以及以单频和多频作为优化目标的拓扑优化结果并进行比对。该方法对隔振结构设计中如何提升结构基频并兼顾结构轻量化，避免在工作频率范围上共振现象的产生有实际意义。

Abstract

Isolation structures are essential in engineering as they connect equipment to the main structure, and their dynamic characteristics significantly influence the isolation effect. The Moving Morphable Components (MMC) method is applied to solve the fundamental frequency topology optimization problem for typical grid plate vibration isolation structures. Initially, beam elements are used to simplify the vibration isolation structure. The MMC method based on beam elements is then enhanced by adaptively pruning redundant elements to improve computational efficiency. Finally, topology optimization results under various objectives and working conditions are compared. This method has practical significance for improving the fundamental frequency in lightweight isolation structure design, thereby helping to prevent resonance phenomena.

导出引用

周锦航1, 商超2, 王强勇2, 代成名2, 李刚1, 3. 基于移动可变形组件法的格栅平板隔振结构自振频率拓扑优化[J]. 振动与冲击, 2025, 44(11): 149-156

ZHOU Jinhang1, SHANG Chao2, WANG Qiangyong2, DAI Chengming2, LI Gang1, 3. Topology optimization of natural frequency of grid plate vibration isolation structure based on MMC method[J]. Journal of Vibration and Shock, 2025, 44(11): 149-156

参考文献

[1] Cha S I, Chun H H.Insertion loss prediction of floating floors used in ship cabins [J].Applied Acoustics, 2008, 69(10):913-917.
[2] 马永涛,周炎.舰船浮筏隔振技术综述[J].舰船科学技术,2008(04):22-26+32.
Ma Y T, Zhou Y Summary of floating raft system [J]. Ship Science and Technology, 2008(04): 22-26+32.
[3] Bondaryk J E, Dyer I, Chiasson L, et al. Experimental measurements of vibrational energy and acoustic radiation for a 3-D truss[J]. The Journal of the Acoustical Society of America,1995, 98(5):2889.
[4] Keane A J, Bright A P. Passive vibration control via unusual geometries: experiments on model aerospace structures[J]. Journal of Sound and Vibration, 1996, 190(4):602-608
[5] C.K. Hui,C.F. Ng. New floating floor design with optimum isolator location [J]. Journal of Sound and Vibration, 2007, 303(1): 221-238.
[6] McMillan A J, Keane A J. Vibration isolation in a thin rectangular plate using a large number of optimally positioned point masses[J]. Journal of Sound and Vibration, 1997, 202(2): 219–234.
[7] 胡泽超,何琳,李彦.隔振器分布对浮筏隔振系统隔振性能的影响[J].舰船科学技术, 2016, 38(21):48-52.
Zhang W Y, Feng Y R, Liu Z X, et al. Optimization design study on vibration isolation charateristics of floating raft system [J]. Ship Engineering, 2012, 34(05): 20-23.
[8] 张维英, 冯燕茹, 刘梓顼等. 浮筏隔振系统隔振性能优化设计研究[J]. 船舶工程,2012,34(05):20-23.
Zhang W Y, Feng Y R, Liu Z X, et al. Optimization design study on vibration isolation charateristics of floating raft system [J]. Ship Engineering, 2012,34(05):20-23.
[9] 赵楠,王禹,陈林等.分布式声学黑洞浮筏系统隔振性能研究[J].振动与冲击,2022,41(13):75-80.
Zhao N, Wang Y, Chen L, et al. Vibration isolation performance of distributed acoustic black hole floating raft system [J]. Journal of Vibration and Shock, 2022, 41(13): 75-80.
[10] Diaz A R, Kikuchi N. Solutions to shape and topology eigenvalue optimization problems using a homogenization method [J]. International Journal for Numerical Methods in Engineering， 1992, 35(7): 1487-1502.
[11] Xie Y M, Steven G P. Evolutionary structural optimization for dynamic problems [J]. Computers & Structures, 1996, 58(6): 1067-1073.
[12] Huang X, Zuo Z H, Xie Y M. Evolutionary topological optimization of vibrating continuum structures for natural frequencies [J]. Computers & Structures, 2010, 88(5): 357-364.
[13] Pedersen N L. Maximization of eigenvalues using topology optimization [J]. Structural and Multidisciplinary Optimization, 2000, 20(1): 2-11.
[14] Allaire G, Jouve F. A level-set method for vibration and multiple loads structural optimization [J]. Computer Methods in Applied Mechanics & Engineering, 2005, 194(30–33): 3269-3290.
[15] Li J, Zhang Y, Du Z, et al. Topology Optimization Considering Steady-State Structural Dynamic Responses via Moving Morphable Component (MMC) Approach [J]. Acta Mechanica Solida Sinica, 2022, 35(6): 949-960.
[16] Cowper G R. The shear coefficient in Timoshenko’s beam theory[J]. Journal of applied mechanics, 1966, 33(2): 335-340.
[17] 王勖成, 邵敏. 有限单元法基本原理和数值方法[M]. 清华大学出版社有限公司, 1997.
Wang X C, Shao M. Basic Principles and Numerical Methods of Finite Element Method [M] Tsinghua University Press , 1997
[18] Guo X, Zhang W, Zhong W. Doing topology optimization explicitly and geometrically—a new moving morphable components based framework[J]. Journal of Applied Mechanics, 2014, 81(8): 081009.
[19] Zhou J, Zhao G, Zeng Y, et al. A novel topology optimization method of plate structure based on moving morphable components and grid structure[J]. Structural and Multidisciplinary Optimization, 2024, 67(1): 8.
[20] K. Svanberg, The method of moving asymptotes—a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering 24 (1987) 359–373.