非线性颤振极限环稳定性判别的复数正规形法

陈衍茂; 刘济科

非线性颤振极限环稳定性判别的复数正规形法

中山大学应用力学与工程系, 广州 510275

基金项目: 高等学校博士学科点专项科研基金(20050558032);高等学校优秀青年教师教学科研奖励计划(2001);广东省自然科学基金(05003295)资助项目

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出版历程
- 收稿日期: 2006-03-16
- 修回日期: 2007-01-19
- 刊出日期: 2007-04-28

Application of complex normal form method for stability judgement of limit cycle of nonlinear flutter

Department of Applied Mechanics and Engineering, Zhongshan University, Guangzhou 510275, China

摘要

摘要: 研究了一类含立方非线性二元机翼颤振系统的分岔现象.应用Hopf分岔定理验证了系统在颤振临界点必发生Hopf分岔.利用中心流形定理将系统降维, 然后应用Hopf分叉的复数正规形法判别了极限环的稳定性, 所得结果与数值解吻合.
- 航空、航天推进系统 /
- 非线性颤振 /
- Hopf分叉 /
- 中心流形 /
- 复数正规形
Abstract: The bifurcations of the flutter system of a 2D airfoil with cubic nonlinearity were investigated in this paper.Hopf bifurcation theory was applied to verify Hopf bifurcation at the critical point of flutter.The high-dimensional system was transformed into a lower-dimensional one by center manifold theorem.And,the complex normal form method of Hopf bifurcation was used to analyze the stability of the limit cycle,with the results consistent with numerical solutions.
- aerospace propulsion system /
- nonlinear flutter /
- Hopf bifurcation /
- center manifold /
- complex normal form

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参考文献(11)

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