| 一类含平方、立方非线性项1:2内共振两自由度系统的全局分岔 |
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| 引用本文： | 梁建术,陈予恕.一类含平方、立方非线性项1:2内共振两自由度系统的全局分岔[J].应用力学学报,2002,19(4). |
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| 作者姓名： | 梁建术 陈予恕 |
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| 作者单位： | 天津大学,天津,300072 |
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| 基金项目： | 国家自然科学基金资助项目 (重大 19990 5 10 )，国家重点基础研究转项经费资助 (G19980 2 0 3 16)，博士点基金资助 (D0 990 1) |
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| 摘 要： | 研究了一类含平方、立方非线性项的两自由度系统的全局分岔。首先应用多尺度法求解其平均方程 ,然后通过一系列变换得到一个近似可积的两自由度系统。应用能量 相位准则 ,确定了在哈密顿共振时Silnikov轨道存在的条件。通过数值计算验证了此条件。
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| 关 键 词： | Melnikov方法 能量相位准则 Silnikov轨道 全局分岔 |
Global Bifurcations in a Class of Two-Degree-of-Freedom Systems with Quadratic and Cubic Nonlinearity and 1:2 Internal Resonance |
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| Liang Jianshu,Chen Yushu.Global Bifurcations in a Class of Two-Degree-of-Freedom Systems with Quadratic and Cubic Nonlinearity and 1:2 Internal Resonance[J].Chinese Journal of Applied Mechanics,2002,19(4). |
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| Authors: | Liang Jianshu Chen Yushu |
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| Abstract: | In this paper, global bifurcations in a class of nonlinear dynamical systems is investigated. Firstly, using the method of multiple scales, the amplitude and phase modulation equations are determined. Secondly, a near integrable two degree of freedom system is obtained by a series of transformations. Employing the energy phase criterion, the condition of existence of Silnikov orbits is determined under Hamiltonian resonance. The condition is confirmed by numerical simulations. |
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| Keywords: | Melnikov theory the energy phase criterion Silnikov orbit Global bifurcation |
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