Abstract:A revised Bingham model for MRF damping is used to describe the nonlinear damping force of vehicle suspension. The nonlinear stiffness of tire is in a form of squared relations. An analytical solution for the two DOF vehicle system's dynamical response is obtained by averaging method, which is verified by the numerical solution. In addition, the effect of system parameters on the dynamical tire force is also studied. It is found that with the increase of C1, Fy and V0 in the revised Bingham model, the tire force decreases and the effect of C1 and Fy on the tire force is greater than that of V0 ; the effect of square nonlinearity of the tire stiffness on the tire force is small. The results of this study may be relevant to the vehicle vibration control and the avoidance of road damage.