Purpose <p>Vehicle shimmy is a self-excited unstable vibration phenomenon and affects vehicle driving stability during driving process. The purpose of this study is to propose an inerter-based nonlinear damping dissipation mechanism (INDDM) and apply it in the vehicle frame to suppress vehicle shimmy.</p> Methods <p>The dynamic model of the vehicle shimmy system with INDDM is established using Lagrange theory, and its bifurcation characteristic is studied through bifurcation analysis. The shimmy suppression performance of the INDDM is analyzed and compared with those of the original suspension and three other vibration dissipation mechanisms. The parametric effects of the INDDM and vehicle structural parameters on the vehicle shimmy performance are investigated and its structural parameters are further optimized using the differential evolution (DE) optimization algorithm.</p> Results <p>The INDDM obtains the best shimmy suppression performance among the original suspension and vibration dissipation mechanisms. The unstable parameter interval is reduced, the maximum front wheel swing angle is decreased, and the vehicle speed interval for vehicle shimmy is narrowed. Vehicle shimmy becomes more likely to occur when the inertance and additional spring stiffness of the INDDM are larger, and the unstable parameter intervals of inertance and additional spring stiffness expand as the vehicle speed increases. A larger tire relaxation length and a smaller vehicle body mass is beneficial for suppressing vehicle shimmy. When the structural parameters of the INDDM are optimized, a full-speed stable parameter interval exists, the vehicle shimmy system remains stable, and the stabilization time when the vehicle shimmy system reaches stability is significantly shortened.</p> Conclusion <p>The INDDM is a novel vibration dissipation mechanism to achieve excellent vehicle shimmy suppression effect and offers guiding significance for vibration dissipation design in vehicle engineering.</p>