在非线性悬挂轮对系统中加入了Gauss白噪声参激,通过Hamilton系统理论和随机微分方程理论,将系统转化为拟不可积Hamilton系统伊藤随机微分方程组,根据拟不可积Hamilton系统的随机平均法,把该方程组降维为一维扩散的平均伊藤随机微分方程,使原系统的解依概率收敛到一维伊藤扩散过程。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。最后对系统的D分叉和P分叉行为进行了研究,并画出了随机P分叉图和随机极限环图。结果表明,随机项的作用使系统的临界速度发生漂移,随着噪声项强度增大,临界速度显著降低。P分叉后系统表现为最大可能意义上的随机极限环振荡,而D分叉后统表现为概率1意义下不稳定的非极限环随机振荡。
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
关键词
随机平均法 /
奇异边界 /
随机P分叉图 /
随机极限环图
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脚注
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