Effects of Steady Angle of Attack on Nonlinear Flutter of a Delta Wing Plate Model

Limit cycle oscillations (LCO) have been observed in flight for certain modern high performance aircraft. The nonlinear physical mechanism responsible for the LCO is still in doubt, even to the point of it not yet being determined whether the nonlinearity is principally in the flexible elastic structure of the aircraft or due to the fluid behavior in the surrounding aerodynamic flow field. One observation from flight tests is that by changing the angle of attack of aircraft, the flight velocity at which LCO begins may be raised or lowered and that the amplitude of the LCO may be reduced. It has been suggested that this sensitivity to angle of attack indicates the nonlinearity is in the fluid rather than in the structure. In the present paper we show that such effects of an angle of attack change can be the result of a structural nonlinearity. Specifically an investigation to determine the effects of a steady angle of attack on nonlinear flutter and limit cycle oscillation of a delta wing-plate model in low subsonic flow has been made. A three-dimensional time domain vortex lattice aerodynamic model and a reduced order aerodynamic technique are used and the structure is modeled using von Karman plate theory that allows for geometric strain-displacement nonlinearities in the delta wing structure. The results provide new insights into nonlinear aeroelastic phenomena not previously widely appreciated, i.e. limit cycle oscillations (LCO) for low aspect ratio wings that have a plate-like nonlinear structural behavior. The effects of a steady angle of attack on both the flutter boundary and the LCO are found to be significant. For a small steady angle of attack, α0 ≤ 0.1°, the flutter onset velocity increases, while for larger α0 it decreases. Moreover, as α0 increases, the maximum LCO amplitude decreases substantially. Such effects have been observed by Bunton and Denegri in flight flutter experiments. It is noted that the present theoretical results do not prove that the LCO phenomena observed in flight are due to structural nonlinearities; however, the results of the present analysis are consistent with those observed in flight and do show that a structural nonlinearity can give rise to the observed effects of angle of attack on LCO.