负刚度时滞反馈控制动力吸振器的等峰优化

相比于传统动力吸振器, 负刚度动力吸振器同时具有更好的减振能力和更宽的有效减振频带宽度, 为了进一步降低共振峰幅值, 在负刚度吸振器系统耦合时滞反馈控制. 对负刚度时滞反馈控制动力吸振器系统进行等峰优化设计, 优化设计的准则是:第一和第二共振峰的峰值相等; 同时兼顾两个目标, 一个目标是在优化时的最大共振峰幅值小于被动负刚度吸振器系统的反共振峰幅值, 另一目标是在优化时共振峰幅值与反共振峰幅值差小于被动吸振器系统. 接着, 通过设计和调节负刚度系数、吸振器阻尼系数和时滞反馈控制系数对控制系统进行等峰优化设计. 最后, 在降低幅值的同时, 分析结构参数对有效减振频带宽度的影响. 经过等峰优化之后, 选择本文的一组结构参数与两个典型的模型进行对比. 为了定量比较不同模型的降幅效果, 定义了减幅百分比, 研究发现在有效减振频带区间内减幅百分比超过40%以上. 结果表明, 通过等峰优化准则对结构参数进行优化设计和调节增益系数和时滞量, 共振峰幅值的减幅百分比也近似达到40%, 也可以调节增益系数和时滞量, 使得幅频响应曲线具有较宽的有效减振频带和较低的共振峰幅值与反共振峰幅值的差值. 

EQUAL-PEAK OPTIMIZATION OF DYNAMIC VIBRATION ABSORBER WITH NEGATIVE STIFFNESS AND DELAY FEEDBACK CONTROL

Compared with the traditional dynamic vibration absorber, negative stiffness dynamic vibration absorber has better damping capacity and wider effective damping frequency bandwidth. The time-delay feedback control is coupled into negative stiffness dynamic vibration absorber system to further reduce the amplitude of the resonant peak and increase the bandwidth of the effective damping frequency. In the present paper, the time-delay feedback control dynamic vibration absorber system with negative stiffness is designed by equal-peak optimization. The optimal design criteria are as follows: the peak values of the first and the second resonance peaks are equal; two objectives are considered at the same time, one is to optimize the maximum resonance peak amplitude to be less than the anti-resonance peak amplitude of the passive negative stiffness absorber system, and the other is to optimize the difference between the resonance peak and the anti-resonance peak to be less than the passive absorber system. Then, the equal-peak optimum design of the control system is carried out by designing and adjusting the negative stiffness coefficient, the damper coefficient of vibration absorber and the time-delay feedback control coefficient. Finally, the effect of structural parameters on effective damping frequency bandwidth is analyzed under the condition of reducing amplitude of resonant peak. A set of structural parameters are selected and compared with two typical models based on the results of equal-peak optimization. In order to quantitatively compare the reduction effect of different models, the amplitude reduction percentage is defined. It is found that the percentage amplitude reduction is over 40% in the effective damping frequency band. The results show that the percentage reduction of the resonance peak amplitude also approximates to 40% by optimizing the structural parameters and adjusting the gain coefficient and time delay. In addition, the amplitude-frequency response curve has wider effective damping frequency bandwidth and a lower difference between the amplitude of the resonance peak and the amplitude of the anti-resonance peak by adjusting gain coefficient and time delay.