Mathematics

CLC number: O193

Bifurcation and Stability Analysis of Time-Delayed Wheelset System under White Noise Excitation

白噪声激励下时滞轮对系统的分岔和稳定性分析

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

^† Corresponding author. E-mail: Zhangjg7715776@126.com

Received: 11 January 2024

Abstract

Considering the impact of time delay in the lateral stiffness of the primary suspension and stochastic disturbances of equivalent conicity on the wheelset system, a stochastic time-delayed wheelset system is established. The wheelset system is transformed into a one-dimensional Itô stochastic differential equation using central manifold and stochastic averaging methods. The analysis of the system's stochastic stability is conducted through the maximum Lyapunov exponent and singular boundary theory. The combination of the stationary probability density method and numerical simulation is employed to discuss the types and conditions of stochastic P-bifurcation in the wheelset system. The results indicate that changes in speed and time delay induce stochastic P-bifurcations in the wheelset system, while changes in noise intensity do not lead to stochastic P-bifurcations. Both time delay and equivalent conicity affect the critical speed of the wheelset system, and the critical speed gradually increases with the decrease of time delay and equivalent conicity.

摘要

考虑到主悬挂侧向刚度时滞和等效锥度的随机干扰对轮对系统的影响, 建立一个随机时滞轮对系统。利用中心流形和随机平均法将轮对系统化为一维Itô随机微分方程, 运用最大李雅普诺夫指数和奇异边界理论对系统的随机稳定性进行分析, 利用平稳概率密度法和数值模拟相结合来判定轮对系统随机分岔的类型和条件。结果表明, 速度和时滞的改变会诱导轮对系统发生随机P分岔, 而噪声强度不会使轮对系统发生随机P分岔, 时滞和等效锥度会影响轮对系统的临界速度, 且临界速度随着时滞和等效锥度的减小而逐渐增大。