具有操纵面立方非线性机翼的混沌响应

CHAOTIC MOTION OF A TWO DIMENSIONAL WING WITH CONTROL SURFACE CUBIC NONLINEARITY

以二元机翼-操纵面立方非线性系统为研究对象,基于能量方法和活塞理论建立了三自由度二维翼段-操纵面的运动微分方程,采用当量线性化方法计算出系统极限环颤振频率,然后将操纵面孤立成单自由度系统,借用现有的单自由度杜芬振子的混沌运动的解析条件来分析操纵面在极限环颤振频率下的响应情况,从而预估原系统的混沌运动存在区域,并用数值积分方法研究了系统的复杂动力学响应。结果表明:在理论分析所获得的混沌运动区域内,系统确实存在混沌运动,但从数值模拟的结果上看,在上述的区域内,系统还存在一些狭窄的周期窗口。

A two dimension wing with a control surface in supersonic flow is theoretically modeled based on the energy method and piston theory, in which the cubic stiffness in the torsional direction of the control surface is considered. An approximate method of the chaotic response analysis of the nonlinear aeroelastic system is studied, the main idea of which is that under the condition of stable limit cycle flutters of the aeroelastic system, the vibration in the plunging and pitching of the wing can approximately be considered to be simple harmonic excitation to the control surface. The motion of the control surface can be modeled by a nonlinear oscillator of one-degree-of-freedom. Then, the range of the chaotic response of the control surface is approximately determined. The theoretical analysis is verified by the numerical results. However, there are relatively sub regions of periodic motions embedded with the chaotic region.