Complete bifurcation behaviour of aeroelastic systems with freeplay

Abstract

Over the last couple of decades, a significant amount of research has been carried out on the aeroelastic behaviour of aeroelastic systems with freeplay. It has been established that such systems can undergo Limit Cycle Oscillations (LCO), both periodic and aperiodic. It has also been shown that several LCOs can occur at the same flight conditions, depending on initial conditions. A lot of the work has been applied to a pitch-plunge airfoil with a control surface and freeplay in the control rotation spring but, even for this simple model, the complete LCO behaviour has not been calculated. In this work, a combined approach using equivalent linearization, a shooting-based numerical continuation scheme and branch following is used to calculate the full bifurcation behaviour of such a system. It is shown that the primary LCO branches depend on the underlying linear systems but that there are two branching points from which secondary periodic solution branches emanate and wrap themselves around the primary branches. Up to 13 different LCOs can coexist at a single flight condition. The system undergoes Hopf, fold, flip and Neimark-Sacker bifurcations and the proposed solution method can identify and all of them.