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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.
Taking the three-degree-of-freedom binary wing as the research object, the nonlinear stiffness in the direction of drifting displacement and the pitch displacement is simplified as cubic nonlinearity, and the bilinear stiffness is used instead of the control plane with the clearance. Considering quasi-steady airflow, the aeroelasticity The equation of motion is constructed by numerical simulation of the peak-peak diagram, which reflects its vibration characteristics under different airflow velocities. The bifurcation diagram of the system is constructed by arc-length numerical continuous method and the stability and bifurcation type are studied by Floquet operator. The results of bifurcation and numerical simulation agree with each other.By the bifurcation diagram, the bilinear existence of the control plane results in the change of the vibration of the wing structure, the existence of multiple bifurcation points and multiple unstable intervals, There are not only the limit cycle vibration and the nonsmooth quasi-periodic vibration, but also the chaos phenomenon in some unstable regions.