Abstract:The nonlinear dynamics of a semi-active suspension system under skyhook control with time delay are studied. First, the approximate analytical solution for the semi-active suspension system is obtained using the averaging method. The numerical solution is also obtained through simulation in Matlab software. The comparison between the displacement transmissibilities for the two methods verifies that the approximate analytical solution has satisfactory precision. Furthermore, the stability analysis for this system is completed based on the Lyapunov stability theory. The results show that the system without time delay is unconditionally stable, while the stability of the delayed system varies periodically with time delay. The variation period is the same as that of the excitation. The results verify that time delay is important in the semi-active suspension system under skyhook control.