Bifurcation analysis of vehicle shimmy system exposed to road roughness excitation

The vertical load of the tire has a significant influence on the lateral force, so the influence of the dynamic load on vehicle shimmy should be taken into account. Based on the dynamic model of a quarter vehicle, a three-degrees-of-freedom dynamic model of the shimmy system with consideration of the road roughness excitation is established by applying the second Lagrange equation. The response characteristic of the system is investigated by the numerical simulations. Moreover, the complexification-averaging method is used to obtain the analytical expression of the shimmy angle of the front wheel, and then, the stability of periodic solutions of the system is evaluated based on the bifurcation theory. Finally, the saddle-node bifurcation and Hopf bifurcation of the shimmy system are studied. The influence of the system parameters on the bifurcation characteristic of the system is also investigated, and the results obtained by using the complexification-averaging method are compared with the numerical examples.