Nonlinear dynamic analysis of a unilateral vibration vehicle system with structural nonlinearity under harmonic excitation

In this paper, the nonlinear dynamics and vibration transmission characteristics of a multi-body dynamic model are investigated to examine the performance of a unilateral vibration vehicle system. The nonlinear equation of motion, considering the suspension and tyre characterized by quadratic and cubic nonlinearities, is deduced by Lagrange's equation. Based on the dynamic equation, the nonlinear dynamic behaviors of the vibration system are investigated more precisely by bifurcation diagram, the largest Lyapunov exponent and 3-D frequency spectrum with the effects of external excitation amplitude, tyre nonlinearity and inclined angle. The numerical analysis indicates that the vibration system exhibits a wide variety of rich and interesting dynamic behaviors, namely different motion states and jump discontinuity are observed, and the different routes to chaotic motion via period-doubling bifurcation, inverse period-doubling bifurcation, Hopf bifurcation and saddle-node bifurcation are presented depending on the different system parameters.