立方非线性机翼非零平衡点极限环颤振的研究  

Study of limit cycle oscillation on nonzero equilibrium points for Airfoil with cubic nonlinearities

作　　者：郝淑英[1] 刘海英[1] 张琪昌[2] 

机构地区：[1]天津理工大学机械工程学院,天津300191 [2]天津大学机械学院力学系,天津300072

出　　处：《天津理工大学学报》2007年第2期1-4,共4页Journal of Tianjin University of Technology

基　　金：国家自然科学基金(10372068)

摘　　要：本文深入研究了在不可压缩流中有立方非线性刚度的二元机翼颤振系统关于非零平衡点发生Hopf分岔的情形.采用中心流行理论对原系统降维得到分岔点处中心流形约化方程,再对约化方程进行化简得到Hopf分岔的A规范形,应用谐波平衡法分析广义气流速度对机翼颤振系统分岔特性的影响,并研究了系统参数对非零平衡点极限环颤振的影响.Hopf bifurcations of a two-degree-of-freedom airfoil with cubic nonlinear aeroelastic stiffness in incompressible flow on nonzero equilibrium points are investigated. The dynamical behaviors of bifurcation points are determined by using the method of successor function. The normal form method is applied to reduce a four-dimensional system to a two-dimensional system, which is on center manifold. Harmonic balance method can analysis the bifurcations of the airfoil flutter with respect to the airspeed. The effect of the system parameters on the stability and amplitudes of limit cycle oscillations are investigated.

关 键 词：极限环颤振 中心流形 规范形理论 谐波平衡法 

分 类 号：O322[理学—一般力学与力学基础]