Complete bifurcation behaviour of aeroelastic systems with freeplay

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.