超音速流中结构非线性二元机翼的复杂响应研究

COMPLICATED RESPONSE OF A 2-D WING WITH STRUCTURAL NONLINEARITY IN SUPERSONIC FLOW

基于活塞理论计算作用在二元机翼上的气动力,采用拉格朗日方程建立系统的运动微分方程。通过平衡点的Jacobi矩阵的特征方程求出了系统的Hopf分叉点,研究了带有立方非线性俯仰刚度二自由度机翼系统在典型参数下的稳定极限环颤振和混沌响应。结果表明,在超过一定的流体速度后,系统平衡点的个数及稳定性均发生了变化;随着流速的增大,在积分初始值较小时,系统出现混沌等极为复杂的响应。

Based on the piston theory, the aerodynamic forces on 2-D wing are calculated. The aeroelastic equations of the wing are established by using the Lagrange equation. The stable limit cycle flutter and chaotic responses of the wing with cubic nonlinear pitching stiffness in supersonic flow are studied by using Hopf bifurcation theory and numerical simulation. The results show that the number of equilibrium points and stability of the system are changed with the increasing flow velocity. Moreover, the complicated responses such as chaos occur when the initial values of numerical integration are very small.