中文摘要：

以三自由度二元机翼为研究对象,将浮沉位移和俯仰位移方向的非线性刚度简化为立方非线性,对于存在间隙的控制面采用双线性刚度代替.考虑准定常气流,建立气动弹性运动方程,通过数值模拟构造峰值-峰值图,反映其在不同气流速度下的振动特征.通过弧长数值连续法构造系统的分岔图,结合Floquet算子研究其稳定性及其分岔类型,所得分岔图和数值模拟的结果相吻合.由分岔图可得系统由于控制面双线性的存在,导致机翼结构振动形态多变,存在多个分岔点和多个不稳定区间,不仅存在极限环振动和非光滑准周期振动,而且在某些不稳定区间出现混沌现象.

英文摘要：

A 3-DOF aeroelastic model was built for 2D rigid airfoils with control surface. This model was simplified with cubic nonlinear stiffness in heave and pitch, where the freeplay con- trol surface was replaced with bilinear stiffness. According to the quasi-steady aerodynamic the- ory, the motion equations for the system was established. The peak-to-peak value diagram was used to depict the global dynamic properties of the airfoil at different flow velocities, and the arc-length numerical continuation method together with the Floquet multiplier was applied to construct the bifurcation diagram and study the aerodynamic stability. The bifurcation diagram matched the peak-to-peak value diagram well. The results show there are various dynamic be- haviors due to freeplay nonlinearity. The aeroelastic model yields complicated limit cycle oscil- lations, quasi-periodic motions and chaotic phenomena when the angular displacement of the control surface reaches the clearance limit.