Train-track Stochastic Dynamics With Consideration Of Temporal-spatial Variation Effects

Due to the longitudinal traction of a locomotive and rolling stocks,the dynamic interaction between the train and the tracks are the set of actually nonlinear dynamics behaviors with the traits of spatial randomicity and temporal evolution.As the direction-guiding and supporting system of a moving train,the infrastural type,the material form and environmental status of the track subsystem are naturally varied in space.This variation will directly cause the spatial variability of train-track systems in physics,mechanics and geometries.Besides,the train-track interaction is a dynamic and cyclic process in a long-term aspect.Accompanied by the train operation,temporal evolution effects are formed once highlighting the material damage,fatigue and performance degradation,etc.From above statements,it can be congnised that the train-track temporal-spatial vibration analysis virtually requires the approaches characterizing the interrelation,association and evolution of system parameters,excitations and dynamic behaviors at specific time-space scales.Generally the temporal-spatial behaviors of a train-track system possess the characteristics of high dimensionality,correlation and uncertainty.Therefore,the scientific and unified characterizations are the foundation for achieving the highly efficient stochastic analysis for train-track systems.For further approaching to the real physical and mechanical status of train-track systems,and perfecting the researches on motion attitude,statistical characteristic,dynamic evolution under temporal-spatial stochastic status for train-track systems.The vibrational analysis researches for train-track temporal-spatial system is urgently needing to be conducted.Based on the mathematical framework and fundamentals of train-track coupled dynamics,this current thesis mainly solved the following issues and conducted extensive work by adopting multi-disciplinary methods,as follows,(1)In classical train-track dynamics models,force equilibrium-and mode superpositionbased methods were applied to build the dynamic model,moreover,the wheel/rail contacts in normal and tangential directions respectively employed Hertz contact theory and nonlinear creep thoery.For further enriching the methodologies in the construction of track-track interaction models,the energy-variational principle and finite element method were introduced.In the dynamic model,the wheel/rail displacement compatibility and force equilibrium requirements were guaranteed,based on which,matrices-coupled dynaimc equations for motions of train-track interactions were built.In the time-domain numerical integrations,no iterative procedures were required even in large time step size.Moreover,some improvements were achieved in two classes of fully-coupled models:? To the first class model(an improved wheel-rail keep-contact model): the two-dimensional(2-D)wheel-rail constraint equation was extended to three-dimensional(3-D);the difficiencies of previous wheel-rail rigid-contact models on wheel-rail contact geometric relationship at 3-D space and wheel-rail separation were improved.? To the second class model(Hertzian contact model): the Hertz nonlinear wheel-rail contact force has been equivalently formed into the dynamic stiffness matrices by nonlinear stiffness coefficeints.(2)Aiming at the longitudinal and nonuniform characteristics of track structures,Karhunen-Loève(K-L)expansions were applied to express the discrete random variables as assembles of independent random variables to reduce the random samples based on the theory of orthogonal expansion of the random filed.For inversely estimating the system status,a state estimation method was developed based on the basic principle of particle filter.Except the system parameters,multiple works were also conducted on track irregularities,which are the most important system excitation.To not only achieve the sample extraction from massive data and temporal evolution analysis but also investigate the technical basis on dynamic reliability,long-term prediction,etc.,a probabilistic model and spectral evolution model were proposed respectively.The above work laid the foundation for reasonably expressing the temporal-spatial characteristics of train-track systems.(3)The temporal-spatial characteristics of train-track systems were discretized to a series of controlling parameters,and being imported into the deterministically computational model,the train-track temporal-spatial vibration analysis model was accordingly constructed.For further solving the problems on modeling the longitudinal varying track parameters and long length computations,a cyclic calculation method was developed,where the advantages of the finite element method in constructing complex models can be played.(4)The main ability of train-track temporal-spatial vibration analysis model was its consideration of the system's temporal-spatial characteristics,where the system excitations possess ergodicity,probability and randomicity.Therefore,extensive studies could be conducted by combining multi-disciplinary methods,for example,dynamic reliability,response relationship,long-term prediction,sensitivity analysis,system state estimation.