多频激励作用下悬索时滞减振控制研究  

Time delay vibration reduction control for suspension cable under multi-frequency excitation

作　　者：夏慧 彭剑[1,2] 李禄欣 孙洪鑫[1,2] 禹见达[1,2] 邵宏利 XIA Hui;PENG Jian;LI Luxin;SUN Hongxin;YU Jianda;SHAO Hongli(School of Civil Engineering,Hunan University of Science and Technology,Xiangtan 411201,China;Hunan Provincial Key Lab for Structures’Wind Resistance and Vibration Control,Hunan University of Science and Technology,Xiangtan 411201,China)

机构地区：[1]湖南科技大学土木工程学院,湖南湘潭411201 [2]湖南科技大学结构抗风与振动控制湖南省重点实验室,湖南湘潭411201

出　　处：《振动与冲击》2023年第17期182-187,274,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(52078210,52278307);湖南省自然科学基金资助项目(2021JJ10003,2023JJ60527);湖南省大学生创新创业训练计划项目(S202110534003)。

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。Suspension cable is typical flexible structure,it is easy to have large amplitude vibration under multi-frequency excitation,and cause structural fatigue damage and occurrence of engineering disasters due to their lightweight,large flexibility and low damping characteristics.Therefore,vibration control of suspension cable is an urgent problem to be solved in practical engineering applications.Here,a time delay velocity feedback control strategy was adopted to perform vibration reduction control of suspension cable under multi-frequency excitation.Based on Hamilton variational principle,a nonlinear vibration control model for a controlled suspension cable under multi-frequency excitation was established.Galerkin method was used to discretize this model,and then obtain time delay differential equation.The multi-scale method was used to solve the amplitude-frequency response equation of the controlled suspension cable when it having super-harmonic and sub-harmonic joint resonance,and the stability of the obtained steady-state solution was judged.With this steady state solution,the nonlinear dynamic behavior of the controlled suspension cable and effects of control system parameters on its resonance response were analyzed.The study results showed that the controlled suspension cable system can have response characteristics of both super-harmonic resonance and sub-harmonic resonance under multi-frequency excitation;with increase in time delay value,distance between different response branches decreases;with decrease in control gain,phases of stable and unstable solutions of branches tend to approach each other;adjusting control gain and time delay values can change resonance range,response amplitude and phase to reach the optimal control effect.

关 键 词：时滞反馈 共振响应 悬索 多频激励 

分 类 号：TH113[机械工程—机械设计及理论]