Subcritical Limit Cycle in Airfoil Aeroelastic System with Freeplay: Prediction and Mechanism

This paper investigates the aeroelastic system of an airfoil with freeplay in pitch, with emphasis on the subcritical limit cycle (LC) that appears below the linear flutter velocity. The lowest flow velocity for the onset of LC, called the LC boundary, is predicted accurately by the eigenvalue analysis of an auxiliary generalized Jacobian such that it has a pair of purely imaginary eigenvalues. By analyzing the change in linear flutter velocity with respect to the remaining stiffness of the freeplay, an interesting finding is revealed whereby the lowest flutter velocity is just the LC boundary. Based on this feature and the generalized Jacobian, a mechanism responsible for the subcritical LC is elucidated, that is the flutter velocity decreases (but does not increase, as expected) with the remaining stiffness increasing.