Stability Analysis of Vehicle Shimmy System with Independent Suspension Based on Complexification-Averaging Method

Based on the dynamic model of a quarter-vehicle system, a three degrees-of-freedom (DOF) dynamic model of the vehicle shimmy system with independent suspension is established by applying the second Lagrange equation. Numerical examples are employed to investigate the speed range and frequency characteristic of the vehicle shimmy system, and then the influence of the vertical load of the tire on vehicle shimmy is discussed. The equilibrium equation and characteristic polynomial of the shimmy system are obtained by using the complexification-averaging (CX-A) method, and the stability of the shimmy system is analyzed based on the first approximate stability theory. Furthermore, the boundary condition of Hopf bifurcation is investigated, and the stability boundary of the suspension parameters varying with the vehicle speed is obtained. The relevant conclusions can provide technical supports for the suppression of vehicle shimmy.