Research on Stochastic Stability of Suspension Wheelset System under Gauss White Noise

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (19) : 49-56.

Zhang Bo , Zeng Jing, Liu Weiwei

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Abstract

The Gauss-White-noise parametric random excitation is considered in the nonlinear suspended Wheelset System. According to Hamilton System and Stochastic differential equation theory, and the model can be expressed as a quasi-non-integrable Hamiltonian System in form of Ito Stochastic differential equation. The equation can be reduced to One dimensional diffusion Ito average stochastic differential equations by the stochastic averaging methods, So the solution of the original system convergence in probability to the one-dimensional Ito diffusion process. The global stochastic stability conditions were also obtained by judging the modality of the singular boundary. At last, the stochastic P bifurcation and D bifurcation are researched, the stochastic P bifurcation diagram and the stochastic limit cycle are obtained. The results show that the random excitation drift forward the critical speed and the critical speed significantly decreased when the intensity of random excitation increased. And the P bifurcation leads to the most possible limit cycle,while the D bifurcation leads to a non-limit cycle unstable hunting in the sense of probability.
Keywords:the stochastic averaging methods; the singular boundar; the stochastic P bifurcation diagram; the stochastic limit cycle

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Zhang Bo,Zeng Jing, Liu Weiwei. Research on Stochastic Stability of Suspension Wheelset System under Gauss White Noise[J]. Journal of Vibration and Shock, 2015, 34(19): 49-56

References

[1] 刘宏友．高速列车中的关键动力学问题研究.[D]．成都：西南交通大学，2003．
Liu Hongyou. Study on Key Dynamics Problems of High-speed Train [D]. Chengdu: Southwest Jiaotong University, 2003.
[2] 曾京. 车辆系统的蛇行运动分叉及极限环的数值计算[J]. 铁道学报,1996,(3) : 13-19.
Zeng Jing. Numerical computations of the hunting bifurcation and limit cycles for railway vehicle dydtem [J].Journal of the China railway society.
[3] 刘伟渭，戴焕云，曾京.弹性约束轮对系统的随机稳定性研究[J]. 中国机械工程,2013.
LiuWeiwei, Dai Huanyun, Zeng Jing. Research on Stochastic Stability of Elastic Constraint Wheelset System [J]. China mechanical engineering, 2013.
[4] 黄世凯.轮对运动稳定性的机理研究.[D]. 成都：西南交通大学，2013．
Huang Shikai. Study on the stability of wheelset system [D]. Chengdu: Southwest Jiaotong University, 2013.
[5] Khasminskii R Z. A limit theorem for the solutions ofdifferential equations with random right-hand sides. Theory of Probability and Application, 1966, 11: 390-405.
[6] Utz von Wagner. Nonlinear dynamic behaviour of arailway wheelset. Vehicle System Dynamics[J], 47:5, 627-640
[7] 朱位秋，几类非线性系统对白噪声参激与（或）外激平稳响应的精确解[J]. 应用数学和力学，1990，11 (2)：155-164.
Zhu Wei-qiu. Exact Solutions for Stationary Responses of Several Classes of Nonlinear Systems to Parametric and/or External White Noise Excitations [J]. Applied Mathematics and Mechanics, 1990,11(2) ：155-164.
[8] ZhuWQ,YangYQ. Stochastic Averaging of Quasi-non-integrable Hamilton System[J].ASME Journal of Applied Mechanics.1997,64:157-164.
[9] 朱位秋，非线性随机动力学与控制—Hamilton 理论体系框架[M]. 科学出版社，2003.
Zhu WQ. Nonlinear stochastic dynamics and control --Hamilton theoretical system framework [M]. science press , 2003.
[10] 刘先斌，陈虬，陈大鹏. 非线性随机动力系统的稳定性和分岔研究[J]，力学进展, 1996,26(4):437-452.
Study on stability and bifurcation of nonlinear stochastic Dynamic system [J]. Advances in mechanics.1996,26(4):437-452.
[11] 葛根. 矩形薄板振动的随机分岔和可靠性研究[D]. 天津大学博士学位论文,2009.
Ge gen. Research of stochastic bifurcation and reliability on rectangular thin plate vibration system [D]. Tianjin: Tianjin University, 2009.