Multi-parameter bifurcation study of shimmy oscillations in a dual-wheel aircraft nose landing gear

Abstract

We develop and investigate a mathematical model of an aircraft nose landing gear with a dual-wheel configuration. The main aim here is to study the influence of a dual-wheel configuration on the existence of shimmy oscillations. To this end, we consider a model that describes the torsional and lateral vibrational modes and the non-linear interaction between them via the tyre-ground contact. More specifically, we perform a bifurcation analysis (with the software package auto) of the model in the two-parameter plane of forward velocity of the aircraft and vertical load on the nose landing gear. This two-parameter bifurcation diagram allows one to identify regions of different dynamics, and the question addressed here is how it depends on two key parameters of the dual-wheel configuration. Namely, we consider the influence of, first, the separation distance between the two wheels and, second, of gyroscopic effects arising from the inertia of the wheels. For both cases, we find that with increasing separation distance and wheel inertia, respectively, the lateral mode becomes more stable and the torsional mode becomes less stable. More specifically, we present associated bifurcation scenarios that explain the transitions between qualitatively different two-parameter bifurcation diagrams. Overall, we find that the separation distance and gyroscopic effects due to wheel inertia may have a significant influence on the quantitative and qualitative nature of shimmy oscillations in aircraft nose landing gears. In particular, the torsional and the lateral modes of a dual-wheel nose landing gear may interact in a quite complicated fashion.