Summary
A wing flap with free play interacting with the flow is is studied using the latest ideas in non-smooth dynamical systems theory in this paper. Piecewise linear spring is used to model the restoring moment due to the freeplay in rotational hinge. The non-smoothness in such a piecewise-smooth system (PWS ) will create enormous interesting dynamical behaviours. High contact stiffness assumption is used to further simplify the model as impacting hybrid system and the restitution coefficient is to characterize the hardness of the impact. Special bifurcations like BEB (boundary equilibrium bifurcation), fold, grazing bifurcation are found in the simulation. We observed a Hopf-like bifurcation, period one LCOs (limit cycle oscillations) born after the BEB. Regarding such phenomenon, only results of planar system are given in the literature and we first come up with a semi-analytical method to determine the existence and stability of the in such higher dimensional system ($n>2$). The numerical continuation is used to track and unfold the bifurcations of the LCOs and the transition to the chaotic attractor is investigated. The conclusion is that the free-play can introduce different attractors in the system, and the softer impact will suppress the single impact LCO.
