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研究了分段刚度描述的间隙约束二元翼段气动弹性系统,取俯仰角最大幅值处为类Poincaré截面,数值计算得到了系统随飞行速度变化的分岔图,发现飞行速度在Ma=0.71~0.75属于跨临界颤振区,而在Ma=0.75~0.95发生极限环震荡.同时通过构造极限环震荡的四维Poincaré映射分析了极限环震荡的稳定性,结合稳定性和运动流形理论,得到极限环震荡的吸引域一般位于极限环内部并用数值方法进行了验证.且跨临界颤振速度区域中存在多种分岔形式以及多解共存现象,例如由双周期运动直接通向混沌、多周期运动与双周期运动共存现象,振动幅值也存在跳跃现象.
The gap-constrained dual-wing aeroelastic system described by piecewise stiffness is studied. Poincaré-like section at the maximum amplitude of pitch angle is obtained. The bifurcation diagram of the system with varying flight velocities is obtained numerically. The results show that the flight velocity is at Ma = 0.71 ~ 0.75 belongs to the transcritical chattering zone, and the limit cycle turbulence occurs in the range of Ma = 0.75 ~ 0.95. The stability of the limit cycle turbulence is also analyzed by constructing a four-dimensional Poincaré map of the limit cycle turbulence. Combining the stability and the theory of the motion manifold, The attracting domain of the limit cycle oscillations is generally located within the limit cycle and verified by numerical methods. There are many bifurcations and coexistence phenomena in the region of transcritical flutter velocity, such as direct chaos from double cycle motion to multi-period The phenomenon of co-existence of movement and double-period movement also has the phenomenon of jumping in vibration amplitude.