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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 被引量：1

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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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。 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.
作者 梁建术 陈予恕
机构地区 天津大学
出处 《应用力学学报》 CAS CSCD 北大核心 2002年第4期62-67,共6页 Chinese Journal of Applied Mechanics
基金 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)
关键词 MELNIKOV方法 能量-相位准则 Silnikov轨道 全局分岔 Melnikov theory, the energy phase criterion, Silnikov orbit, Global bifurcation.
分类号 O322 [理学—一般力学与力学基础]
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参考文献14

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同被引文献7

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应用力学学报
2002年 第4期

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