超音速结构非线性翼型的颤振分析

Supersonic Flutter Analysis of an Airfoil with Cubic Structural Nonlinearity

对超音速流速中的结构非线性二元机翼进行颤振分析。通过对线化系统在零平衡点的特征值分析得到该系统的Hopf分叉点,应用中心流形定理对原系统降维,并用后继函数法判断分叉点的类别及稳定性;然后应用分支问题的Liapunov第二方法分析了系统的超临界、亚临界Hopf分叉现象,并通过数值模拟验证了理论分析的正确性。

The flutter of anairfoil with structural nonlinearity in the supersonic flow was analyzed. First, Hopf bifurcation points of the linearized system were obtained by analyzing the characteristic value of the system in the neighborhood of equilibrium point, and the centre manifold theory was used to reduced dimensions of the system. The type and stability of the bifurcation points in the subsequent reduced two-dimensional system were analyzed by the method of succeeding function .Then, using the second Liapunov Quantity about bifurcation study, the super and sub-critical Hopf bifurcation of the system were construed. Finally, the theoretic analysis was proved by numerical simulation.