Research on hunting stability and bifurcation characteristics of nonlinear stochastic wheelset system

Peng WANG, Shaopu YANG, Yongqiang LIU, Pengfei LIU, Xing ZHANG, Yiwei ZHAO

doi:10.1007/s10483-023-2963-6

Applied Mathematics and Mechanics >

2023 , Vol. 44 >Issue 3: 431 - 446

DOI: https://doi.org/10.1007/s10483-023-2963-6

Articles

Research on hunting stability and bifurcation characteristics of nonlinear stochastic wheelset system

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1. State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
2. School of Traffic and Transportation, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
3. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

Received date: 2022-08-19

Revised date: 2022-11-21

Online published: 2023-02-27

Supported by

the National Natural Science Foundation of China (Nos. 11790282, 12172235, 12072208, and 52072249) and the Opening Foundation of State Key Laboratory of Shijiazhuang Tiedao University of China (No. ZZ2021-13)

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Abstract

A stochastic wheelset model with a nonlinear wheel-rail contact relationship is established to investigate the stochastic stability and stochastic bifurcation of the wheelset system with the consideration of the stochastic parametric excitations of equivalent conicity and suspension stiffness. The wheelset is systematized into a one-dimensional (1D) diffusion process by using the stochastic average method, the behavior of the singular boundary is analyzed to determine the hunting stability condition of the wheelset system, and the critical speed of stochastic bifurcation is obtained. The stationary probability density and joint probability density are derived theoretically. Based on the topological structure change of the probability density function, the stochastic Hopf bifurcation form and bifurcation condition of the wheelset system are determined. The effects of stochastic factors on the hunting stability and bifurcation characteristics are analyzed, and the simulation results verify the correctness of the theoretical analysis. The results reveal that the boundary behavior of the diffusion process determines the hunting stability of the stochastic wheelset system, and the left boundary characteristic value $c_{\rm L}=1$ is the critical state of hunting stability. Besides, stochastic D-bifurcation and P-bifurcation will appear in the wheelset system, and the critical speeds of the two kinds of stochastic bifurcation decrease with the increase in the stochastic parametric excitation intensity.

Key words： stochastic wheelset system; stochastic average method; singular boundary; hunting stability; stochastic Hopf bifurcation

Cite this article

Peng WANG, Shaopu YANG, Yongqiang LIU, Pengfei LIU, Xing ZHANG, Yiwei ZHAO . Research on hunting stability and bifurcation characteristics of nonlinear stochastic wheelset system[J]. Applied Mathematics and Mechanics, 2023 , 44(3) : 431 -446 . DOI: 10.1007/s10483-023-2963-6

References

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