时滞影响下MR阻尼器—斜拉索控制系统主共振分析

Primary resonance of MR damper-stay cable control systems with time delay

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。

Based on Hamilton principle,nonlinear motion equations of MR damper-stay cable systems with time delay were obtained.The bifurcation responses of this type system were derived with Galerkin method and the method of multiple scale.The approximate expressions of the primary resonance and the peak of the response amplitude versus time delay were deduced.To illustrate the characteristics of the primary resonance,the effects of major parameters,such as,time delay,control gains and external excitation on the system response were studied.The numerical results showed that the frequency-response curves of the controlled system have jump and hysteresis phenomena,and the response amplitude increases with increase in time delay,control feedback gain and external excitation amplitude;a positive correlation between the peak amplitude of the primary resonance response and time delay is observed,and when time delay reaches a certain value,the peak significantly increases.