Stochastic response and stability analysis of nonlinear vehicle energy-regenerative suspension system with time delay

Abstract

With the rapid development of new energy vehicles, a novel vehicle energy-regenerative suspension for simultaneous vibration suppression and energy harvesting has become one of the key development directions of the next generation of vehicle design. In order to improve the performance of suspension system, the time-delayed feedback control is applied to the novel suspension system subjected to different external excitation. At the same time, there are few studies related to the stochastic dynamics of nonlinear vehicle energy-regenerative suspension system with time delay. This paper studies stochastic response and stability of nonlinear vehicle energy-regenerative suspension with time-delayed feedback control under the excitation of Gaussian white noise. First of all, a stochastic dynamic model of the nonlinear vehicle energy-regenerative suspension with time delay system is established. Secondly, using the stochastic averaging method based on generalized harmonic function, the steady-state probability density function (PDF) of amplitude is obtained. The accuracy of the presented approach is verified through the comparison of analytical and numerical solutions. In addition, through combining the stochastic averaging method with the Khasminskii method, the top Lyapunov exponent (TLE) of the system is obtained, and then the influence of time delay and system parameters on the asymptotic Lyapunov stability is discussed. Finally, the effects of time delay and system parameters on system performance are also studied.