多频激励作用下悬索时滞减振控制研究

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摘要悬索作为一类典型的柔性结构，因其本身质量轻，柔性大，阻尼小等特点，在多频激励的作用下容易产生大幅振动，易造成结构疲劳破坏，从而导致工程灾害的发生。因此，悬索的振动控制是工程实际应用中亟须解决的问题。该研究采用时滞速度反馈控制策略对多频激励下的悬索进行减振控制。基于Hamilton变分原理，建立多频激励下受控悬索的非线性振动控制模型。利用Galerkin法得到离散后的时滞微分方程，通过多尺度法求解受控悬索发生超谐波与亚谐波联合共振时的幅频响应方程，并判断稳态解的稳定性，分析了受控悬索的非线性动力学行为，以及控制系统参数对共振响应的影响。研究结果表明：多频激励时悬索系统同时出现超谐共振和亚谐共振响应的特性，随着时滞值的增大不同分枝之间距离减小，随着控制增益减小分枝的稳定和不稳定解的相位趋于接近。通过调节控制增益和时滞值的大小可以改变共振范围、响应幅值及其相位，达到最优控制效果。

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	夏慧1
	彭剑1
	2
	李禄欣1
	孙洪鑫1
	2
	禹见达1
	2
	邵宏利1

关键词 ：时滞反馈, 共振响应, 悬索, 多频激励

Abstract：Suspension cable is a typical flexible structure. It has the characteristics of light weight, large flexibility and small damping. Under the action of multi-frequency excitation, it is easy to produce large vibration, which is easy to cause the fatigue failure of structure and the occurrence of engineering disaster. Therefore, the vibration control of suspension cable is an urgent problem to be solved in practical engineering applications. The time-delay velocity feedback control strategy is used to reduce the vibration of the suspension cable under multi-frequency excitation. Based on Hamilton variational principle, a nonlinear vibration control model of a controlled suspension cable under multi-frequency excitation is established. The delay differential equation is obtained by Galerkin method. The multiscale method is used to solve the amplitude-frequency response equations when the superharmonic and subharmonic resonance occurs in the controlled suspension structure, and the stability of the steady-state solution is determined. The nonlinear dynamic behavior of the controlled cable and the influence of the parameters of the control system on the resonance response are analyzed. The results show that the response of superharmonic resonance and subharmonic resonance occurs simultaneously in the multi-frequency excitation system. The distance between different branches decreases with the increase of time delay. As the control gain decreases, the phases of stable and unstable solutions of the branches tend to approach. By adjusting the control gain and time delay, the resonance range, response amplitude and phase can be changed, so as to achieve the optimal control effect.

Key words： delay feedback the resonant response suspension cable multi-frequency excitation

收稿日期: 2022-11-28 出版日期: 2023-09-15

引用本文:

夏慧1，彭剑1,2，李禄欣1，孙洪鑫1,2，禹见达1,2，邵宏利1. 多频激励作用下悬索时滞减振控制研究[J]. 振动与冲击, 2023, 42(17): 182-187.
XIA Hui1, PENG Jian1,2, LI Luxin1, SUN Hongxin1,2, YU Jianda1,2, SHAO Hongli1. Time delay vibration reduction control for suspension cable under multi-frequency excitation. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(17): 182-187.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I17/182

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