摘要
研究了二元机翼非线性颤振系统的Hopf分岔.应用中心流形定理将系统降维,并利用复数正规形方法得到了以气流速度为分岔参数的分岔方程.研究发现,分岔方程中一个系数不含分岔参数的一次幂,故使得分岔具有超临界和亚临界双重性质.用等效线性化法和增量谐波平衡法验证了所得结果.
The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated with the flow speed as a bifurcation parameter. The center manifold theory and complex normal form method were used to obtain the bifurcation equation. Interestingly, for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical. It is found, mathematically, this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter. The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method.
出处
《应用数学和力学》
EI
CSCD
北大核心
2008年第2期181-187,共7页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10772202)
教育部博士学科点专项基金资助项目(20050558032)
广东省自然科学基金资助项目(07003680
05003295)
关键词
非线性颤振
HOPF分岔
超临界
亚临界
极限环振动
nonlinear flutter
Hopf bifurcation
supercritical
subcritical
limit cycle oscillation
