具有间隙的二元机翼自激振动的数值分析

Numerical analysis on a self-excited two-dimensional airfoil with freeplay model

利用Runge Kutta法分析了具有不对称间隙的二元机翼自激振动的动力学响应,研究了当U /U L从零逐渐增大到1时系统的周期运动和混沌运动,发现在不对称分段线性系统中存在复杂的运动形式,其中包括从P 1到P 2的倍周期分叉,P 4到P 2,P 2到P 1的倒分岔,同时存在混沌运动形式,而且不同的初值条件所对应的运动形式也有所不同.给出了全局分岔图、局部分岔图、混沌运动的功率谱密度图及3种周期运动的时间历程曲线和相平面图,对于实际的飞行结构设计具有重要的指导意义.

The dynamics response of a self-excited two-dimensional airfoil with freeplay model is analyzed by means of Runge-Kutta method. Bifurcation of periodic motions and chaos are studied when U~*/U~*_L increases from zero to 1 gradually in the system. There are chaos, double-bifurcations from P-1 to P-2, inverse bifurcations from P-4 to P-2 and from P-2 to P-1. The responded motions are changed with the initial value. The globe and local bifurcation diagrams, power spectral density plot of the chaos and the time history plot and phase plane plot of three periodic motions are given, which are instructive to the real design of aircraft structures.