轨道随机激励对弹性约束轮对随机稳定性与随机分岔的影响

刘伟渭; 戴焕云;曾京

振动与冲击 ›› 2013, Vol. 32 ›› Issue (21) : 170-177.

PDF(2650 KB)
PDF(2650 KB)
振动与冲击 ›› 2013, Vol. 32 ›› Issue (21) : 170-177.
论文

轨道随机激励对弹性约束轮对随机稳定性与随机分岔的影响

  • 刘伟渭1,2, 戴焕云1, 曾京1
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Infuluence On Stochastic Stability and Stochastic Bifurcation Of Elastic Constraint WheelsetSystem Subjected To Rail Stochastic Excitation

  • LIU Wei-wei1,2,DAI Huan-yun1,ZENG Jing1
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摘要

考虑轨道随机不平顺激励与结构自身随机参激建立了弹性约束轮对系统的伊藤随机微分方程组,运用拟不可积Hamilton系统理论和奇异边界性态求解了系统的随机局部稳定性和随机全局稳定性,通过分析稳态概率密度和联合概率密度得到了模型的随机Hopf分岔类型并讨论了分岔的条件。可知,分岔的发生不仅受到系统固有参数的影响同时也受随机因素的影响,即使满足一定的分岔条件分岔也并不一定会发生,系统分岔的发生是以概率特征来体现的,这和只能考虑系统固有参数下的确定性分岔有着明显差别;另外,不同随机强度下轮对系统有着不同的失稳临界速度,这和不能考虑随机因素作用下的确定性轮对系统只有一个确定的失稳临界速度有着本质区别。

Abstract

Considering track random irregularity and their structure random parameters to establish the elastic wheel system with Hamilton function form of the Ito stochastic differential equation; According to the quasi non-integrable hamiltonian theory and oseledec multiplicative ergodic theory, the local stochastic stability conditions had been obtained; the stochastic global stability conditions had also been obtained by judging the modality of the singular boundary; the stochastic Hopf bifurcation was analyzed from Steady-state probability density and joint probability density. The results show that, different random strength effect on the wheelset system has different instability critical speed, compared with non-considering stochastic factors of wheelset system identified only one instability critical speed is essential difference between, even if certain bifurcation conditions are satisfied, bifurcation does not have to occur. The possibility of occurrence of bifurcation is evaluated by the probability calculated.



关键词

伊藤随机微分方程 / 拟不可积Hamilton系统 / 稳态概率密度 / 随机Hopf分岔

Key words

Ito Stochastic Differential Equation / quasi non-integrable Hamiltonion system / steady-state probability density / Stochastic hopf bifurcation

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刘伟渭; 戴焕云;曾京. 轨道随机激励对弹性约束轮对随机稳定性与随机分岔的影响[J]. 振动与冲击, 2013, 32(21): 170-177
LIU Wei-wei;DAI Huan-yun;ZENG Jing. Infuluence On Stochastic Stability and Stochastic Bifurcation Of Elastic Constraint WheelsetSystem Subjected To Rail Stochastic Excitation [J]. Journal of Vibration and Shock, 2013, 32(21): 170-177

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