用规范型直接法研究立方非线性机翼的颤振

研究了在不可压缩流中具有立方非线性俯仰刚度的二元机翼的颤振问题。首先，对系统平衡点进行了特征值分析，得到在Hopf分岔点附近的颤振参数方程。然后，应用规范形直接法的Maple推导程序，计算得到Hopf分岔的规范形．并数值模拟验证了超、亚临界类型分岔情形下响应对初值的依赖性。最后．分析了线性和非线性刚度系数对颤振响应拓扑结构的影响。

Study on Flutter of an Airfoil with Cubic Non-Linearity Using Normal Form Direct Method

This paper studies the flutter of a two-dimensional airfoil in the incompressible flow with cubic non-linearity in the plunging direction. Firstly,the characteristic value of the system in the neighborhood of an equilibrium point was analyzed. The parametric equations of the flutter were obtained in the vicinity of a Hopf bifurcation point. Then,the normal form of the Hopf bifurcation was deduced by applying the Maple procedure of a normal form direct method. The dependence of response on initial values was certified by numerical analysis in the supercritical and subcritical situations. Finally,the influences of the linear and non-linear stiffness coefficients on the topological structure of flutter responses were analyzed.