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The dynamic model of the automobile shimmy system considering the sinusoidal road roughness excitation is established, and the response characteristic of the shimmy system is investigated with numerical simulations. Based on the complexification-averaging (CX-A) method, the slow flow equations of the shimmy system are obtained, and the shimmy angle of the front wheel is available on the basis of the analytical solution of the system. In addition, the bifurcation theory is applied to evaluate the stability of periodic solutions of the shimmy system exposed to the road roughness excitation. Finally, the laws of energy transfer between relevant subsystems of the shimmy system at various speeds are analysed. The suppression mechanism of the automobile shimmy by the damping of the steering system and the damping of the suspension at various speeds is also investigated. The conclusions provide theoretical supports for better anti-shimmy design, thereby improving the stability of the automobile.

Hopf bifurcation and energy transfer of automobile shimmy system with consideration of road roughness excitation