Abstract <p>This paper establishes a four-degree-of-freedom half-vehicle model with nonlinear springs and dampers to study the nonlinear vibration of a car moving on a rough road. According to D’Alembert’s principle, the nonlinear dynamical differential equations of the vehicle system under sinusoidal road excitation are obtained. A system of first-order differential equations is obtained using nondimensionalization and some techniques for order reduction of nonlinear systems with time. Then it is used to investigate the effects of damping and frequency ratios on the body displacement, pitch angle, and displacements of front and rear wheels. The numerical calculation of the equations demonstrates that the damping and frequency ratios control the nonlinear vibration behavior of the vehicle system. The proposed model can also predict the possible motion state of the vehicle system under sinusoidal road excitation at different velocities. The vehicle system will transform periodic motion into chaotic motion. The conclusions provide some available evidence for the design and improvement of the vehicle suspension system.</p>