Nonlinear dynamic analysis of a quarter vehicle system with external periodic excitation

• A nonlinear vehicle system under harmonic excitation is studied by IHBM.
• The suspension system has nonlinear stiffness of order three and nonlinear damping.
• The IHBM for multi-degree of freedom nonlinear system is deduced.
• Amplitude-frequency curve, bifurcation and spectrum are used to analyze the system.
• The damping coefficient, excitation amplitude and frequency are investigated.

In this paper, a nonlinear dynamic model of a quarter vehicle with nonlinear spring and damping is established. The dynamic characteristics of the vehicle system with external periodic excitation are theoretically investigated by the incremental harmonic balance method and Newmark method, and the accuracy of the incremental harmonic balance method is verified by comparing with the result of Newmark method. The influences of the damping coefficient, excitation amplitude and excitation frequency on the dynamic responses are analyzed. The results show that the vibration behaviors of the vehicle system can be control by adjusting appropriately system parameters with the damping coefficient, excitation amplitude and excitation frequency. The multi-valued properties, spur-harmonic response and hardening type nonlinear behavior are revealed in the presented amplitude-frequency curves. With the changing parameters, the transformation of chaotic motion, quasi-periodic motion and periodic motion is also observed. The conclusions can provide some available evidences for the design and improvement of the vehicle system.