Study On The Stochastic Nonlinear Dynamics Of Wheelset

With the rapid development of domestic and international high-speed rail and high-speed trains, much more severe challenges and requirements are put forward for vehicle-track system dynamics. As well known, deterministic view is widely used in physical, engineering, biological and economic fields, but with the development of science and technology, descriptions of the practical problems are required to be more accurate. Therefore, the influence of stochastic factors cannot be ignored easily, for some actual process analysis it is necessary to investigate in the stochastic view instead of deterministic view. For the modern rail vehicles, since high speed has become the core of high-speed railway technology, stochastic factors should be taken seriously, which play an important role in system stability, ride comfort, derailment safety, structural reliability, and train air dynamics issues. Because the rail vehicle research in the past mainly focused on the deterministic framework, while the stochastic nonlinear dynamics studies mainly focused on the system response and qualitative behaviors are rarely involved, this thesis attempts to do further research in this area, mainly including:(1) the building of physical and mathematical model:this paper considers track stochastic irregularity excitation based on primary and secondary action mechanism, that is, stochastic external excitations and randomly parametric excitation, and the structure frequency dependent stochastic parametric excitations. The modeling of elastic restraint wheelset system is transferred from Lagrange system to Hamilton system. With the Hamiltonian (from the energy view, the stochastic response problem analysis of multi-factor is transformed into single-factor energy analysis), dynamic behavior research is conducted. Meanwhile Ito stochastic differential equations with Hamiltonian of the elastic constraints wheelset system are established, which are represented as one-dimensional diffusion process using stochastic averaging method, and average Ito stochastic differential equation which dominated the process has been obtained.(2) The study of stochastic stability, bifurcation and experimental determination method:based on quasi non-integrable Hamilton system theories and Oseledec multiplicative ergodic theorem, maximal Lyapunov exponents of the system are obtained thus and local stability conditions of the random system are got. Through the analysis of one-dimensional singular boundary diffusion patterns, global stability conditions of the random system are obtained Using averaged probability density and joint probability density of system response, stochastic Hopf bifurcation types, D-bifurcation (dynamic bifurcation) and P-bifurcation (phenomenological bifurcation) bifurcation conditions are obtained, and the stochastic stability and deterministic stability are compared and analyzed. Experimental determination methods of the bifurcation points and derailment safety conditions are given, which have been applied to realistic experimental data analysis. The experimental results and theoretical analysis results have a good match which verifies the correctness of the methods and the feasibility of application in specific railway lines.(3) First reliability investigation of transversing derailment failure:based on stochastic stability and stochastic bifurcation analysis, this paper obtains the first passage derailment failure reliability destruction conditions of elastic constraints wheelset system, gets the backward Kolmogorov equation met by the system reliability function, the generalized Pontryagin equation met by averaged first passage time and the conditional probability density equation of first passage, studies the influence of first passage failure on system configurations as well as the dynamical behavior after failure combined with the initial conditions and boundary conditions using numerical methods.(4)Stochastic nonlinear optimal control study:with stochastic dynamic programming by targeting higher system reliability and longer first-passage time, stochastic nonlinear optimal control analysis is carried out on the elastic constraints wheelset system, and control effectiveness and strategy are discussed in detail. In addition, nonlinear stochastic optimal control of the elastic constraints wheelset on stochastic system stabilization is discussed.