结构和气动非线性机翼颤振分析

STUDY ON AIRFOIL FLUTTER WITH CUBIC STRUCTURAL AND AERODYNAMICAL NONLINEARITY

研究在超音速流中,含有结构和气动立方非线性的二元机翼的颤振.首先,对线性化系统的零平衡点进行特征值分析,表明系统颤振由Hopf分岔而产生;然后应用规范形直接法,推导出Hopf分岔解的规范形,许结合数值模拟分析超、亚临界分岔情形的极限环特点;最后分析了飞行马赫数和非线性刚度系数对分岔拓扑结构的影响,表明具有“硬”弹簧性质的结构及增大悬挂点与质心的距离都有助于提高安全性,而应避免“软”弹簧性质的结构.

This paper studied the flutter of a two ?dimensional airfoil in the supersonic flow with cubic physical and aerodynamic non-linearity. First, the characteristic value of the system in the neighborhood of equilibrium point was analyzed,and the parametric equations of flutter were obtained in the vicinity of Hopf bifurcation point. Then, the normal form of Hopf bifurcation was deduced by applying the normal form direct method,and the dependence of response on initial values was certified by numerical analysis in the super- and sub-critical cases. Finally, study on the topological structure of bifurcation showed that the 'hard' structural non-linearities render the airfoil safer, whereas the 'soft' ones render the airfoil unsafe,and that increasing the distance between the center of mass and the elastic axis appears to be beneficial from the point of view of the aeroelastic response.