具有立方非线性机翼颤振的局部分岔

Local Bifurcation for Airfoil with Cubic Nonlinearities

针对飞机飞行时机翼振动问题,研究了在不可压缩流中有立方非线性刚度二元机翼颤振系统的局部分岔,取空气速度和线性俯仰刚度系数作为分岔参数.采用后继函数法对降维后求得系统分岔点类别进行定性分析,结果表明3个分岔点都为稳定的焦点.对分岔点处中心流形约化方程进行化简得到霍普分岔的A规范形,研究了系统参数对极限环颤振的稳定性及幅值的影响,得到了机翼颤振系统在普适开折参数平面的分岔图.发现了抑制颤振振幅和临界颤振速度大小的系统敏感参数,提出了降低颤振幅值和避免不稳定极限环运动的措施.

Local bifurcation of two-degree-of-freedom airfoil with cubic nonlinear aeroelastic stiffness in incompressible flow was investigated.The airspeed and the linear stiffness were taken as the bifurcation parameters.The dynamical behaviors of bifurcation points were determined by using the method of sussessor function.The results indicate all the three bifurcation points are stable focus.The normal form method was applied to reduce a four-dimensional system to a two-dimensional one which is on center manifold.Furthermore,the effect of the system parameters on the stability and amplitudes of limit cycle oscillations were investigated and the universal unfolding bifurcation diagram of the system was obtained.Sensitive parameters of flutter system affecting amplitudes and critical flutter velocities were found.And the measures of reducing amplitudes of flutter and avoiding unstable limit cycle oscillations were provided.