Chaotic Motion in a Nonlinear Car Model Excited by Multi-frequency Road Surface Profile

In order to solve the problem that existing nonlinear suspension models have not considered chaotic motion in primary and other resonances, and numerical calculation model is too simplified to capture the accurate critical conditions for the chaotic motion, a nonlinear suspension model and its new paths of chaos are investigated. Primary resonances, secondary resonances, and combined resonances are performed using multiple-time scales method. Based on the Melnikov functions, the critical conditions for the chaotic motion of the nonlinear system are found, which is 0.246 7 for the primary resonance, and 0.338 8 for the secondary resonance. The effects of parameters on chaotic range are considered, and results show that nonlinear stiffness of suspension k ₂ has the largest impact on the chaotic range while damping coefficient C ₁ has the smallest one. The chaotic responses on the area of the primary and secondary resonances are discussed via Lyapunov exponents and numerical integration of the equations of motion. It is found from Lyapunov exponents and Poincaré maps that motions are chaos over critical conditions, and has shown two very different paths of chaos on the primary and secondary resonances. Chaotic motion patterns in the primary and secondary resonances are obtained with more accurate critical conditions, which is a necessary complement to nonlinear study in nonlinear suspension mode.