含有时滞控制的准零刚度隔振器动力学分析

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (13) : 49-55.

论文

含有时滞控制的准零刚度隔振器动力学分析

李东海赵寿根何玉金李涛

作者信息 +

Dynamical analysis of a QZS vibration isolator with time-delay control

LI Donghai ZHAO Shougen He Yujin LI Tao

Author information +

文章历史 +

摘要

准零刚度隔振器可以通过正负刚度并联来实现。本文研究了一种由三弹簧系统并联而成的准零刚度隔振器在简谐力激励下的动力学特性，并引入线性位移时滞控制策略。通过平均法分析得到系统在简谐力激励下的响应特性，并利用一阶李亚普洛夫近似稳定理论和劳斯-赫尔维茨准则分析了受控系统的稳定性和跳跃现象以及Hopf分叉现象。研究结果表明，时滞控制可以有效地改善准零刚度系统的稳定性，并且能够抑制系统跳跃现象的发生；通过选择合适的控制参数，可以避免系统发生Hopf分叉现象。

Abstract

A quasi zero stiffness (QZS) vibration isolator can be realized through parallel connection of a positive stiffness and a negative one. Here, the dynamic features of a QZS vibration isolator composed of two oblique springs and a vertical spring under the simple harmonic excitation were studied. Introducing the linear displacement time-delay control strategy, the dynamic response characteristics of the system under the simple harmonic excitation were obtained with the averaging method. The first-order Lyapunov approximate stability theory and Routh–Hurwitz criterion were adopted to analyze the stability, jump phenomenon and Hopf bifurcation of the controlled system. The results showed that the time-delay control strategy can effectively improve the stability of the QZS vibration isolator; jump phenomenon and Hopf bifurcation can be avoided through choosing appropriate control parameters.

导出引用

李东海赵寿根何玉金李涛. 含有时滞控制的准零刚度隔振器动力学分析[J]. 振动与冲击, 2018, 37(13): 49-55

LI Donghai ZHAO Shougen He Yujin LI Tao. Dynamical analysis of a QZS vibration isolator with time-delay control[J]. Journal of Vibration and Shock, 2018, 37(13): 49-55

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