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| RESPONSE OF PARAMETRICALLY EXCITED DUFFING-VAN DER POL OSCILLATOR WITH DELAYED FEEDBACK | |
| 作者姓名： | 李欣业 陈予恕 吴志强 宋涛 |
| 作者单位： | School of Mechanical Engineering Hebei University of Technology，Tianjin 300130，P. R. China，School of Mechanical Engineering，Tianjin University，Tianjin 300072，P. R. China，School of Mechanical Engineering，Tianjin University，Tianjin 300072，P. R. China，Department of Graduate Student，Shandong Institute of Architecture and Engineering，Jinan 250014，P. R. China |
| 基金项目： | Project supported by the Scientific Research Foundation for Returned 0verseas Chinese Scholar of Ministry of Eduction, China （No.2006-331） |
| 摘 要： | The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance. It is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node (SN) or Hopf bifurcation (HB) as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results. |
| 关 键 词： | 自激振动 煤粉 震荡器 延时反馈 |
| 收稿时间： | 2005-07-12 |
| 修稿时间： | 2006-08-28 |
Response of parametrically excited Duffing-van der Pol oscillator with delayed feedback |
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| Xin-ye Li Doctor,Yu-shu Chen,Zhi-qiang Wu,Tao Song.RESPONSE OF PARAMETRICALLY EXCITED DUFFING-VAN DER POL OSCILLATOR WITH DELAYED FEEDBACK[J].Applied Mathematics and Mechanics(English Edition),2006,27(12):1585-1595. | |
| Authors: | Xin-ye Li Doctor Yu-shu Chen Zhi-qiang Wu Tao Song |
| Institution: | 1. School of Mechanical Engineering, Hebei University of Technology,Tianjin,300130, P. R. China 2. School of Mechanical Engineering, Tianjin University, Tianjin,300072, P. R. China 3. Department of Graduate Student, Shandong Institute of Architecture and Engineering,Jinan,250014, P. R. China |
| Abstract: | The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance. It is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node (SN) or Hopf bifurcation (HB) as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results. |
| Keywords: | Duffing-van der Pol oscillator principal parametric resonance time delay feedback control bifurcation |
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