Theoretical and experimental investigation of a structurally and aerodynamically nonlinear pitch and flap wing

This paper presents and experimental and theoretical investigation of a novel nonlinear aeroelastic system. It consists of a wing with pitch and flap degrees of freedom, suspended from a leaf spring secured in a nonlinear clamp. Both the structural and the aerodynamic forces acting on the wing can be nonlinear, depending on the amplitude of oscillations. Wind tunnel experiments show that the system undergoes a supercritical Hopf bifurcation that leads to small amplitude limit cycle oscillations. At a particular airspeed, the pitch amplitude jumps to a much higher value and dynamic stall starts to occur. Three mathematical models of the system are formulated, one based on linear aerodynamics
and two based on the Leishman-Beddoes dynamic stall model. The objective of the modelling is to determine whether the jump in pitch oscillation amplitude is due to dynamic stall. The predictions for amplitude, frequency and mean angle of the limit cycle oscillations are compared to the experimental observations. All three models predict the small amplitude oscillations with satisfactory accuracy. The complete Leishman-Beddoes model predicts the occurrence of a jump in pitch amplitude but the magnitude of this jump is signi cantly overestimated. The other two models completely fail to model the jump. The failure of the Leishman-Beddoes model to predict the correct post-jump oscillation amplitude may be due to the values selected for the model parameters.