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.
It stochastic differential equations of an elastic constraint wheelset system were established considering rail random irregularity excitation and the system＇s random parametric excitation. The stochastic local stability and the stochastic global stability of the system were solved using guasi non-integrable Hamihonian system theory and the behavior of singular boundaries. The stochastic Hopf bifurcation of the system was obtained through analyzing the steady-state probability density and the joint probability density, and the bifuraction occurrence conditions were discussed. The results showed that under different random strengths the wheelset system has different critical speeds to lose stability, while the system has only one critical speed to lose stability if no stochastic factors are considered, so there is an essential difference between the two cases; even if a certain bifurcation condition is satisfied, a bifurcation may not occur, the occurrence possibility of the system＇s bifurcation is evaluated with the features of probability.
出处
《振动与冲击》
EI
CSCD
北大核心
2013年第21期170-177,196,共9页
Journal of Vibration and Shock
基金
国家“973”计划项目(2011CB711106)
自然科学基金(51005189)
国家“863”计划项目(2012AA112002)
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
Ito stochastic differential equation
quasi non-integrable Hamiltonian system
steady-state probabilitydensity
stochastic Hopf bifurcation
