Effects of time delay on the excited nonlinear quarter and half-car models with jumping nonlinearities

Abstract Nonlinear vehicle dynamics are omnipresent and significantly affect driving performance and safety. In particular, jumping vehicles exhibit strong nonlinearity that can cause severe vibrations and steering instabilities. In this study, the dynamics of nonlinear jumping vehicle models with and without a time delay are investigated to understand their general characteristics. Quarter- and half-car models incorporating jumping nonlinearity are employed in which delayed feedback was introduced as an active suspension control. Numerical simulations are performed under periodic and random excitations. The results reveal several novel findings regarding jumping vehicle systems. First, sudden discontinuous transitions from chaotic to nonchaotic dynamics are observed in the bifurcation diagrams of both models. A general relationship between the time period of the periodic motion and forcing period is also identified. This relationship is also validated in a forced Duffing oscillator with a time delay, which exhibits a generic effect. In the presence of a delay, both in-phase and out-of-phase motions occur, particularly between the front and rear, even under simultaneous excitations. From a practical perspective, in-phase motion between the front and rear is undesirable. Thus, achieving out-of-phase motion within a specific range of delay parameters is important for improved ride performance.