含外激励van der Pol-Mathieu方程的非线性动力学特性分析1)
NONLINEAR DYNAMIC ANALYSIS OF A VAN DER POL-MATHIEU EQUATION WITH EXTERNAL EXCITATION1)
含外激励van der Pol-Mathieu方程的非线性动力学特性分析1) |
| 黄建亮, 王腾, 陈树辉 |
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NONLINEAR DYNAMIC ANALYSIS OF A VAN DER POL-MATHIEU EQUATION WITH EXTERNAL EXCITATION1) |
| Huang Jianliang, Wang Teng, Chen Shuhui |
| 图2 $\omega=1.0$时含外激励van der Pol-Mathieu方程含有3个周期解, 其中 $k_1=0.01$, $k_2=0.01$, $k_3=0.05$和$f=0.01$: (a) 第一个稳定周期解的时间历程图; (b) 第二个稳定周期解的时间历程图; (c) 3个不同周期解的相图; (d) 两个稳定周期解的频谱图 |
| Fig.2 Three different periodic solutions of the van der Pol-Mathieu equation with external excitation for $\omega=1.0$ with $k_1=0.01$, $k_2=0.01$, $k_3=0.05$, and $f=0.01$: (a) Time history of the first stable periodic response; (b) time history of the second stable periodic response; (c) phase plane portraits of the three solutions; (d) Fourier spectra of the two stable periodic response |
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