Abstract:

Considering track random irregularity and their structure random parameters,an elastic wheel system was established with Hamilton function form of the Ito stochastic differential equation.According to the stochastic averaging method the Ito stochastic differential equation was expressed as one-dimensional diffusion process,the maximal Lyapunov exponent was calculated by quasi non-integrable hamiltonian theory and Oseledec multiplicative ergodic theory,the local stochastic stability conditions were obtained;the stochastic global stability conditions were also obtained by judging the modality of the singular boundary.The results show that,the stability of the system is mainly composed of inner multiplicative excitation control,and also changed with the external excitation.Different random strength effects on the wheelset system have different instability critical speed,compared with no-considering stochastic factors of wheelset
system identified only one instability critical speed the essential difference is between.

Key words: quasi non-integrable Hamilton system, Ito stochastic differential equation, Oseledec multiplicative ergodic theorem, singular boundary

摘要：

在考虑轨道随机不平顺激励和自身结构参数随机因素作用的前提下建立了弹性约束轮对带Hamilton函数的伊藤随机微分方程组,根据拟不可积Hamilton系统的随机平均法把该方程组表示为一维扩散的平均伊藤随机微分方程。运用Oseledec乘性遍历定理求解了系统的最大Lyapunov指数并得到了系统的随机局部稳定性的条件;通过分析一维扩散奇异边界的性态得到了随机全局稳定性的条件。结果表明,系统的稳定性主要由内在乘性激励控制,但又随着外在激励的改变而改变;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。

关键词: 拟不可积Hamilton系统, 伊藤随机微分方程, Oseledec乘性遍历定理, 奇异边界