主动约束层阻尼薄板有限元建模及振动控制

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (24) : 101-108.

论文

主动约束层阻尼薄板有限元建模及振动控制

黄志诚1，彭焕有1，王兴国1，褚福磊2

作者信息 +

Finite element modeling and vibration control of an active confinement layer damping thin plate

HUANG Zhicheng1，PENG Huanyou1，WANG Xingguo1，CHU Fulei2

Author information +

文章历史 +

摘要

为了解决薄板结构在应用于各个工程领域所产生的振动过大问题，以主动约束层阻尼（ACLD）薄板结构作为研究对象，进行振动控制研究。首先，构造4节点28自由度单元对该结构进行离散，其中粘弹性层采用复常数剪切模量本构模型，引入等效Rayleigh阻尼表示基层的阻尼，通过Hamilton原理推出了ACLD薄板结构的动力学模型；其次，针对建立的动力学模型自由度过大的问题，采用物理空间下动力缩聚和状态空间内平衡联合降阶保证模型具有良好可控性和可观性；最后使用最优二次型（LQR）控制对系统进行振动控制。研究结果表明：本文建立的有限元模型在不同边界条件、覆盖方式不同情况下仍然具有有效性，使用联合降阶法后模型依旧能够准确、可靠的表述原系统动态特性。在脉冲激励和带限白噪声下依旧能够抑制系统振动。

Abstract

In order to solve the problem of excessive vibration caused by thin plate structure applied in various engineering fields, vibration control of active constrained damping (ACLD) thin plate structure is carried out in this paper. Firstly, the structure was divide into 4-node, 28-DOF elements by finite element modeling method. equivalent Rayleigh damping was introduced to represent the damping of the base layer. The dynamic model of ACLD thin plate structure was derived by Hamilton principle. Secondly, the established dynamic model has too many degrees of freedom. The dynamic model obtained by using dynamic iteration in physical space and equilibrium in state space combined reduction method has good control effect. Finally, the optimal quadratic (LQR) control is used to control the vibration of the system. The results show that the finite element model established in this paper is still effective under different boundary conditions and different coverage modes, and the model can accurately and reliably describe the dynamic characteristics of the original system after using the joint reduced order method. Finally, the vibration of the structure can be suppressed by using LQR control under pulse excitation.

导出引用

黄志诚1，彭焕有1，王兴国1，褚福磊2. 主动约束层阻尼薄板有限元建模及振动控制[J]. 振动与冲击, 2023, 42(24): 101-108

HUANG Zhicheng1，PENG Huanyou1，WANG Xingguo1，CHU Fulei2. Finite element modeling and vibration control of an active confinement layer damping thin plate[J]. Journal of Vibration and Shock, 2023, 42(24): 101-108

参考文献

[1] 宋玉宝,温激鸿,郁殿龙,沈惠杰.板结构振动与噪声抑制研究综述[J].机械工程学报,2018,54(15): 60-77.
SONG Yubao,WEN Jihong,YU Dianlong,SHEN Huijie.Review of vibration and noise control of the plate structures[J].Journal of Mechanical Engineering,2018,54(15): 60-77.
[2] 黄志诚,王兴国,吴南星,褚福磊,罗经.黏弹夹芯板的有限元建模及实验研究[J].计算力学学报,2020,37(06): 715-721.
HUANG Zhicheng,WANG Xingguo,WU Nanxing,CHU Fulei,LUO Jing.Finite element modeling and experimental study ofviscoelastic sandwich plate[J].Chinese Journal of Computational Mechanics,2020,37(06): 715-721.
[3] Zhu, R.Z., Zhang, X.N., Zhang, S.G., Dai, Q.Y., Qin, Z.Y., Chu, F.L. Modeling and topology optimization of cylindrical shells with partial CLD treatment. International Journal of Mechanical Sciences, 2022, 220(15): 107145.
[4] 黄志诚,王兴国,吴南星,褚福磊,罗经.基于层合理论的被动约束层阻尼板有限元建模及动力学分析[J].振动与冲击,2020,39(23): 148-153+201.
HUANG Zhicheng,WANG Xingguo,WU Nanxing,CHU Fulei,LUO Jing.Finite element modeling and dynamic analysis of passive constrained layer damping plate based on laminated theory[J].Journal of Vibration And Shock,2020,39(23): 148-153+201.
[5] BAZA,Robustcontrol of active constrained layer damping[J].journal of Sound and Vibration,1998, 211(3): 467-480.
[6] Zhang, L.F., Zhang, F.B., Qin, Z.Y., Han, Q.K., Wang, T.Y., Chu, F.L. Piezoelectric energy harvester for rolling bearings with capability of self-powered condition monitoring. Energy, 2022, 238: 121770.
[7] Sahoo S. R., Ray M. C. .Active Control of Nonlinear Transient Vibration of Laminated Composite Beams Using Triangular SCLD Treatment With Fractional Order Derivative Viscoelastic Model[J].Journal of Dynamic Systems, Measurement, and Control,2019,141(11): 111014.
[8] Gao Y.S.,Zhang S.Q.,Zhao G.Z.,Schmidt R. Numerical modeling for cantilever sandwich smart structures with partially covered constrained viscoelastic layer[J].Composite Structures,2022,281(281): 114981.
[9] Li Ming, Sun Wei,Liu Yue,Ma Hongwei. Influence analysis of control signal phase on the vibration reduction effect of active constrained layer damping[J]. Applied Acoustics,2022,190: 108658.
[10] Ambesh Kumar, Satyajit Panda,Ashish Kumar,Vivek Narsaria. Performance of a graphite wafer-reinforced viscoelastic composite layer for active-passive damping of plate vibration[J].Composite Structures,2018,186(186): 303-314.
[11] 杨鑫,吴军,卢秋铸,王亮.基于ARX模型的船舶航向保持LQR控制[J].控制工程,2020,27(06): 984-991.
YANG Xin,WU Jun,LU Qiuzhu,WANG Liang.Ship Course Keeping LQR Control Based on ARX Model[J].Control Engineering of China,2020,27(06): 984-991.
[12] S.R. Sahoo,M.C. Ray.Active control of laminated composite plates using elliptical smart constrained layer damping treatment[J].Composite Structures,2018,211(211): 376-389.
[13] Panping Lu,Pan Wang,Jun Lu. Decentralized vibration control of smart constrained layer damping plate[J].Journal of Vibration and Control,2020,27(5-6): 529-542.
[14] Jun Lu,Pan Wang,Zhenfei Zhan. Active vibration control of thin-plate structures with partial SCLD treatment[J].Mechanical Systems and Signal Processing,2017,84: 531-550.
[15] Reza Soheilifard. A hierarchical non-iterative extension of the Guyan condensation method for damped structures[J]. Journal of Sound and Vibration,2015,344: 434-446.
[16] Yang Chen,Xia Yuanqing. Optimal sensor placement based on dynamic condensation using multi-objective optimization algorithm[J]. Structural and Multidisciplinary Optimization,2022,65(7): 210.
[17] 郑玲,王宜,谢熔炉.主动约束层阻尼结构的振动控制[J].重庆大学学报,2010,33(02): 1-7.
ZHENG Ling,WANG Yi,XIE Ronglu.Vibration control of active constrained layer damping structure[j].Journal of Chongqing University,2010,33(02): 1-7.
[18] 张东东.主动约束层阻尼结构多目标优化及自适应控制研究[D].重庆大学,2015.
ZHANG Dongdong.Study on multi-objective opimization and adaptive control of active constrained layer damping structure[D].Chongqing University,2015.
[19] Liu T X, Hua H X, Chen Z N, et al. Study on the model of finite element of constrained layer damping plate[J]. Chinese Journal of Mechanical Engineering, 2002, 38(4): 108-114.
[20] Y.M.Shi,Z.F.Li,H.X.HUA AND Z.F.FU.The modelling and vibration control of beams with active constrained layer damping[J]Journal of Sound And Vibration,(2001),245(5): 785-800.
[21] 宋攀,董兴建,孟光.柔性基础主动隔振系统的缩聚建模和时滞问题研究[J].振动与冲击,2012,31(23): 57-61.
SONG Pan,DONG Xingjian,MENG Guang.Dynamic reduction modeling and time delay for an active vibration isolation system with flexible base[J].Journal of Vibration And Shock,2012,31(23): 57-61.
[22] 王攀,王正亚,孔德飞,阳小光,邓兆祥.机敏约束层阻尼薄板的μ综合鲁棒控制研究[J].振动工程学报,2017,30(05): 781-789
WANG Pan,WANG Zhengya,KONG Defei,YANG Xiaoguang,DENG Zhaoxiang.Study on μ-synthesis control of the thin plate with smart constrained layer damping[J].Journal of Vibration Engineering,2017,30(05): 781-789
[23] 王攀,鲁俊,邓兆祥,阳小光,王正亚,廖海辰.SCLD板模态控制模型及振动控制[J].西南交通大学学报,2015,50(04): 717-724.WANG Pan,LU Jun,DENG Zhaoxiang,YANG xiaoguang,WANG Zhenegya,LIAO Haichen.Modal control model and vibration control of scld plate[J].Journal of southwest jiaotong university,2015,50(04): 717-724.