基于Hamilton变分原理，建立了考虑时滞作用下的MR阻尼器-斜拉索控制系统的非线性运动方程。采用Galerkin方法和多尺度法，从理论上推导出时滞动力系统的分岔响应，得到了该系统主共振的一阶近似解及响应峰值关于时滞的解析式。进而，分析了时滞、控制增益、外激励幅值等参数对系统主共振幅值响应的影响。结果表明，受控系统的主共振幅值存在跳跃和滞后现象，并随着时滞量、控制反馈增益和外激励幅值的增大而增大，且系统可能出现失稳；主共振响应的峰值与时滞正相关，当时滞达到一定值后，峰值显著增大。
Abstract
Based on Hamilton principle, the nonlinear motion equations of MR damper-stay cable systems with time delay is obtained. The bifurcation responses of the delay system are derived by Galerkin method and the method of multiple scale; the approximate expressions of the primary resonance and the peak of the response amplitude with time delay are obtained. To illustrate the characteristics of the primary resonance, the effects of major parameters on the response of the system are studied, such as, the time delay, feedback gains and external excitation. The numerical results show that the frequency-response curves of the controlled system have jump and hysteresis, and the response amplitude increases along with the time delay, feedback gain and external excitation amplitude; Observed a positive correlation between The peak amplitude of the primary resonance response and time delay, and the time delay reaches a certain value, the peak was significantly increased.
关键词
MR阻尼器 /
斜拉索 /
时滞 /
主共振
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Key words
MR damper /
stay cable /
time delay /
primary resonance
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参考文献
[1] 王修勇, 陈政清, 倪一清, 高赞明. 斜拉桥拉索磁流变阻尼器减振技术研究 [J]. 中国公路学报, 2003, 16(2): 52-56.
WANG Xiu-yong, CHEN Zheng-qing, NI Yi-qing, GAO Zan- ming. Study of mitigating cables vibration on the cable-stayed bridges using magnetorheological (MR) dampers [J]. China Journal of Highway and Transport, 2003, 16(2): 52-56.
[2] Zhou Q, Nielsen S R K, Qu W L. Stochastic response of an inclined shallow cable with linear viscous dampers under stochastic excitation [J]. Journal of Engineering Mechanics, ASCE, 2010, 136(11):1411-1421.
[3] Cha Y J, Agrawal A K, Dyke S J. Time delay effects on large-scale MR damper based semi-active control strategies [J]. Smart Materials and Structures, 2013, 22(1): 015011.
[4] Hu H Y, Dowell E H, Virgin L N. Stability estimation of linear dynamical systems under state delay feedback control [J]. Journal of Sound and Vibration, 1998,214(3): 497-511.
[5] Ying Z G, Ni Y Q, Ko J M. Parametrically excited instability analysis of a semi-actively controlled cable [J]. Engineering Structures, 2007, 29(4): 567-575.
[6] Abdel-Rohman M, John M J, Hassan M F. Compensation of time delay effect in semi-active controlled suspension bridges [J]. Journal of Vibration and Control, 2010,16(10): 1527-1558.
[7] 彭剑, 赵珧冰, 孙测世, 王连华. 磁流变阻尼器—斜拉索控制系统中的时滞效应 [J]. 工程力学, 2014, 31(4): 155-159.
PENG Jian, ZHAO Yao-bing, SUN Ce-shi, WANG Lian-hua. Time delay effects in MR damper-stay cable control systems [J]. Engineering Mechanics, 2014, 31(4): 155-159.
[8] 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, 31:57-61.
SONG Pan, DONG Xing-jian, MENG Guang. Dynamic reduction modeling and time delay for an active vibration isolation system with flexible base [J]. Journal of Vibration and Shock, 2012, 31:57-61.
[9] 申永军, 祁玉玲, 杨绍普, 邢海军. 含时滞的单自由度半主动悬架系统的动力学分析 [J]. 振动与冲击. 2012, 31:38-40
SHEN Yong-jun, QI Yu-ling, YANG Shao-pu, XING Hai-jun. Dynamic analysis of a SDOF semi-active suspension system with time-delay [J]. Journal of Vibration and Shock, 2012, 31:38-40.
[10] Irvine H M. Cable structures [M]. MIT Press, Cambridge, 1981.
[11] Wang L H, Zhao Y Y. Large amplitude motion mechanism and non-planar vibration character of stay cables subject to the support motions [J]. Journal of Sound and Vibration, 2009, 327(1-2):121-133.
[12] 胡建华, 王修勇, 陈政清, 倪一清. 斜拉桥拉索磁流变阻尼器减振技术的参数优化研究 [J]. 土木工程学报, 2006, 39(3): 91-97.
HU Jian-hua, WANG Xiu-yong, CHEN Zheng-qing, NI Yi- qing. Parametric optimization for mitigating cable vibration by using MR dampers on cable-stayed bridges [J]. China Civil Engineering Journal, 2006, 39(3): 91-97.
[13] Pacheco B M, Fujino Y, Sulekh A. Estimation curve for modal damping in stay cables with viscous damper [J]. Journal of Structural Engineering, 1993; 119(6): 1961-1979.
[14] Zhou H J, Xu Y L. Wind-rain-induced vibration and control of stay cables in a cable-stayed bridge [J]. Structural Control and Health Monitoring, 2007, 14(7): 1013-1033.
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