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

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.