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时滞耦合质量摆动力吸振器减振系统的等峰优化理论与实验

THEORY AND EXPERIMENT OF EQUAL-PEAK OPTIMIZATION OF TIME DELAY COUPLED PENDULUM TUNED MASS DAMPER VIBRATING SYSTEM

  • 摘要: 摆式调谐质量阻尼器因其便于安装、维修、更换, 且经济实用, 广泛应用于结构减振. 它通过将摆的自振频率调谐到接近主系统的控制频率, 使摆产生与主系统相反的振动, 从而抑制或消除主系统的振动. 本文通过对主系统无阻尼的被动减振系统和主系统有阻尼的时滞反馈主动减振系统进行多目标优化设计, 实现了对主系统幅频响应曲线的等峰控制和共振峰与反共振峰差值的有效控制. 首先, 建立了时滞耦合质量摆动力吸振器减振系统的力学模型和振动微分方程, 通过对主系统无阻尼的被动减振系统进行等峰优化, 获得了减振系统的最优频率比和质量摆的最优阻尼比. 对于主系统存在阻尼的被动减振系统, 在该优化参数下主系统的幅频响应曲线等峰优化失效. 其次, 对于主系统存在阻尼的时滞反馈优化控制系统, 采用CTCR方法得到了反馈增益系数和时滞的稳定区域. 在保证系统稳定的前提下, 通过调节反馈增益系数和时滞量两个控制参数能够实现对主系统幅频响应曲线的等峰控制. 再次, 对共振点处主系统振幅放大因子时滞敏感度和反馈增益系数敏感度进行分析, 表明共振点幅值对反馈增益系数比对时滞更为敏感. 最后, 通过实验分别在频域和时域内对理论结果进行了验证. 研究表明, 通过采用时滞反馈对摆式调谐质量阻尼减振系统进行等峰优化控制, 在较宽的频率区间内抑制了主系统的振幅; 通过控制共振峰和反共振峰的差值, 保证了幅频响应曲线的平坦性.

     

    Abstract: Pendulum tuned mass damper is widely used in structural vibration suppression because it is easy to install, maintain, replace economically and practically. The vibration of the primary system could be suppressed by tuning the natural frequency of the pendulum. The vibration of the pendulum is opposite to primary system by tuning the natural frequency of the pendulum to or close to the control frequency of the primary system. The multi-objective optimization designs are analyzed for both passive system when primary system without damping and time delay feedback active system when primary system with damping. It is realized equal-peak control of the amplitude-frequency response curve of the primary system and difference control between the resonance peak and the anti-resonance point. First, the mechanical model and vibration differential equation of the time-delay coupled pendulum tuned mass damper are established. The optimal frequency ratio of system and the optimal damping ratio of the pendulum tuned mass damper are obtained by equal-peak optimization for the passive system when primary system without damping. For the passive system when primary system with damping, equal-peak phenomenon of the amplitude-frequency response curve for the primary system is destroyed under these optimization parameters. Secondly, for the time delay feedback active optimal control system when primary system with damping, the stability region of feedback gain coefficient and time delay are obtained by using the CTCR method. The equal-peak control of the amplitude frequency response curve for primary system could be realized by adjusting the two control parameters of the feedback gain coefficient and time delay under the conditions of system is stable. Thirdly, the time delay sensitivity and feedback gain sensitivity of the primary system amplitude amplification factor at the resonance point are analyzed. It is shown that the resonance point amplitude is more sensitive to the feedback gain coefficient than to the time delay. Finally, the theoretical results are verified by experiments in frequency domain and time domain. The research shows that the amplitude of the primary system is suppressed in a wide frequency range by using the time delay feedback equal-peak optimization. The flatness of the amplitude-frequency response curve is ensured by controlling the difference between the resonance peak and the anti-resonance point.

     

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