含分数阶Bingham模型的阻尼减振系统时滞半主动控制

针对基于磁流变液阻尼器的半主动控制系统中存在的时滞问题, 采用了一种将可控的时滞变量引入半主动控制切换条件的控制策略, 研究了考虑时滞的天棚阻尼控制切换条件对半主动阻尼减振系统的影响, 分析了含有分数阶Bingham模型的线性刚度系统在基础激励下的振动特性. 利用平均法得到了系统在含时滞半主动控制策略下主共振响应的近似解析解, 根据Lyapunov理论分析了系统的稳定性. 通过数值解验证了近似解析解的准确性, 二者具有较好的一致性. 利用近似解析解分析了固定激励频率下时滞对系统幅频响应特性的影响, 以及主共振峰值响应和共振频率随时滞变化的特性规律. 结果表明, 含时滞的半主动控制系统存在一个小时滞区间, 使得系统的振幅在主共振峰对应的频率附近低于不考虑时滞时系统的振幅, 且存在最优时滞使得系统的振幅大幅度降低; 而大时滞的引入会加剧系统的振动, 导致系统的颤振. 确定了基于分数阶Bingham模型的线性刚度系统在天棚阻尼半主动控制下的时滞选取原则, 为振动系统半主动阻尼控制中的时滞选取提供了参考. 

TIME-DELAYED SEMI-ACTIVE CONTROL OF DAMPING SYSTEM WITH FRACTIONAL-ORDER BINGHAM MODEL

On the issues of time delay in the semi-active control system with magnetorheological fluid damper, the controllable time-delay variable is introduced into the switching conditions of semi-active control strategy. The influences of time delay in the switching conditions of sky-hook damping control system are studied. The vibration characteristics of a linear stiffness system under foundation excitation, with magnetorheological fluid damper based on fractional-order Bingham model, are analyzed by the approximate analytical method. The analytical solutions of the primary resonance of the semi-active control system with time delay are obtained through the averaging method, and the stability conditions of the steady-state solution of the system are demonstrated according to Lyapunov theory. The amplitude-frequency responses of analytical solutions show a good correlation with the numerical solutions close-by the resonance frequency, which validates the accuracy and efficiency of the analytical solutions. Furthermore, the influences of time delay on the amplitude-frequency responses of the system at fixed excitation frequency, the primary resonance amplitude responses and the corresponding resonance frequencies changed with different time-delay values are investigated by using the approximate analytical solution. The results suggest that the amplitude responses of the semiactive control system in a small time-delay range is lower than the control system without time delay near the excitation frequency corresponding to the resonance peak, and there is an optimal time delay making a significant reduction of the amplitude of the primary resonance peak. However, the vibration of the control system would be worsened with larger time delays, leading to the flutter of the control system at high frequencies. The principles of time delay introducing to linear stiffness system with fractional-order Bingham model under semi-active control of sky-hook damping are determined. It provides a reference of selecting a feasible time delay in semi-active damping control vibration system.