多频激励Duffing-van der Pol系统振动状态研究

赵志宏;张明;杨绍普;邢海军

振动与冲击 ›› 2013, Vol. 32 ›› Issue (19) : 76-79.

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PDF(1221 KB)
振动与冲击 ›› 2013, Vol. 32 ›› Issue (19) : 76-79.
论文

多频激励Duffing-van der Pol系统振动状态研究

  • 赵志宏1,张明2,杨绍普2,邢海军2
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Duffing-van der Pol system vibration behavior under multi-frequency excitation

  • Zhao Zhihong 1,Zhang Ming2, Yang Shaopu2, Xing Haijun2
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摘要

通过多尺度法对Duffing-van der Pol系统的幅频响应特性进行研究,多频激励改变了单频激励条件下系统的振动状态。与Duffing系统相比,Duffing-van der Pol系统不但使系统主共振曲线发生了偏移,而且系统的振幅也发生了变化。经过分析得出了Duffing-van der Pol系统主共振幅频特性曲线的偏移和振幅的改变与加入的多频激励的幅度和频率有关。利用Matlab对Duffing-van der Pol进行了数值仿真,仿真结果得出多频外激励改变了原有单频激励的振动状态,并且随着多频激励的幅值和频率的改变,系统的振动状态出现了一定规律的变化。对比研究了解析分析与数值仿真结果,得出的结论比较一致。

Abstract

Using the multiple-scale method, amplitude-frequency response characteristics of a Duffing-van der Pol system were analyzed. Multi-frequency excitation changed the vibration behavior of the Duffing-van der Pol system under single-frequency excitation. Compared with the Duffing system, Duffing-van der Pol system not only makes the curve of the system deviation, but also changes the amplitude of the system. It is shown that the changes of Duffing-van der Pol system amplitude-frequency curve depend on multi-frequency excitation amplitude and frequency. Through the numerical calculations of the Duffing-van der Pol system, it is shown that multi-frequency excitation changes the vibration behavior of the Duffing-van der Pol system under single-frequency excitation; moreover, with the change of the amplitude and frequency of the external excitation, the vibration behavior of the Duffing-van der Pol system has certain change. The conclusions of the experimental are verified with numerical simulations.



关键词

Duffing-van der Pol系统 / 非线性 / 多频 / 分岔 / Lyapunov指数

Key words

Duffing-van der Pol system / nonlinear / multi-frequency / bifurcation / Lyapunov exponent

引用本文

导出引用
赵志宏;张明;杨绍普;邢海军. 多频激励Duffing-van der Pol系统振动状态研究[J]. 振动与冲击, 2013, 32(19): 76-79
Zhao Zhihong;Zhang Ming;Yang Shaopu;Xing Haijun. Duffing-van der Pol system vibration behavior under multi-frequency excitation[J]. Journal of Vibration and Shock, 2013, 32(19): 76-79

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