Two-parameter bifurcation analysis of an aircraft nose landing gear model

The Hopf-Hopf bifurcations of an aircraft nose landing gear model are investigated in this paper based on two pairs of continuation parameters. It is shown that due to the effect of higher-order terms, there exists a deviation between the bifurcation curve of the original system and the bifurcation curve of its truncated amplitude system, which results in a contraction in the bistable region compared with the previous work. Two codimension 3 strong resonant points can be detected on the Neimark-Sacker bifurcation curve. Period-3 and period-4 limit cycles with torsional-lateral shimmy can emerge when the vertical force and the taxiing velocity are chosen near the resonant points. The occurrence of 1:3 and 1:4 resonant Hopf-Hopf bifurcations can induce tire-ground vibrations in torsional and lateral direction, which can greatly degrade the performance and safety and possibly destroy the airstrip. So it is of significance to investigate the resonate behaviors of the aircraft nose landing gear to ensure the safe landing.