Modeling and analysis of rotational freeplay nonlinearity of a 2D airfoil

Aeroelastic flutter is a dynamic instability of fluid-structural system in which the structure exhibits a sustained, often diverging oscillation. Flutter behavior is self-feeding and destructive. Nonlinearities such as freeplay in rigid-body rotational stiffness of the structural system can have an effect on the onset of flutter and its amplitude. In particular there is experimental evidence that as the amount of freeplay increases, the freestream velocity at which the flutter instability occurs decreases. In this paper, we develop a modeling framework that allows us to predict this dependence of flutter velocity on the freeplay parameter. We model the airfoil system with freeplay nonlinearity as a feedback interconnection of linear system and sector bounded nonlinearity. Freeplay in stiffness is practically approximated as a hyperbola nonlinearity. Eigenvalue analysis at equilibrium points is used to predict onset of flutter and characterize a Hopf bifurcation of the system from stable to limit cycle behavior. Spectral analysis us used to characterize the limit cycle behavior. This analysis indicates the flutter onset velocity to be a function of freeplay region length. Follow-on research correlating recently obtained wind tunnel results to a three-dimensional extension of the model is outlined.