Response, Bifurcation and Reliability Analysis of Vehicle Suspension Systems Under Random Cosinusoidal Road Excitation

As critical damping components of vehicles, suspension systems play an essential role in maintaining vehicle stability and enhancing ride comfort. This paper studies the dynamic behaviors and reliability of the suspension system. First, based on Newton’s second law, a single-degree-of-freedom suspension system model is established through simulating the rough road fluctuations as a combination of typical cosinusoidal road excitation and Gaussian white noise. Then, considering the linear damping and nonlinear damping, respectively, the dynamic evolution and first-passage failure of the system under primary resonance and 1/3 subharmonic resonance conditions are examined by the path integral method. The influence mechanisms of dampings, road surface excitation amplitude and noise intensity on the dynamics of suspension systems are explored. The results demonstrate that reduced damping, increased road excitation amplitude and higher noise intensity collectively impair system stability. Crucially, the system’s response to these parameters is governed by the resonance type. Within a certain range, under primary resonance, road amplitude predominantly affects displacement, whereas under 1/3 subharmonic resonance, it significantly alters both displacement and velocity distributions, even inducing stochastic P-bifurcation. These findings provide valuable insights into the design and optimization of vehicle suspension systems for improving performance and reliability.