Study On The Nonlinear Dynamic Problems For Railway Vehicle Systems

It already has a long history for the study of railway vehicle systems, but the really systematic and efficient works started from 1960's with the rapid development of the computer science and computational mathematics. The conventional railway vehicle system dynamics has its own features, but it still belongs to the field of multibody system dynamics and is its application on the railway vehicle systems. The railway vehicle system dynamics is a vigorous engineering subject and is developing rapidly these years.Different from conventional methods, a new method is found on the basis of conventional vehicle system dynamics in this dissertation. The vehicle system steady-state solutions depending on the varying parameters are calculated by using the continuation method DERPAR on the basis of Newton-Raphson iterations. As for the periodic solution in the vehicle system, it is discretized by using the finite difference method. At the same time, a parameter is introduced into the system, therefore, the system with the parameter is solved by using the continuation method.The vehicle system dynamic model is setup by using the Newton-Euler principle in the dissertation. The continuation method is applied to the research of the vehicle system dynamic behaviors. The calculations of steady-state solution and periodic solution of vehicle system are carried out with continuation method. The solution diagrams of railway vehicle system with the parameters on the large range are obtained.Continuation method is an algorithm suitable for the evaluation of the dependence of the solution of algebraic equations with a parameter. The difficulties that arise from the singularities of the dynamic system are overcome in the continuous calculations. It has been developed since seventies last century and applied to many scopes, but it is rarely seen its application in railway vehicle dynamics due to the complexity of the vehicle system. In this dissertation the continuation method is introduced into the railway vehicle dynamics.The vehicle system steady-state solutions on the circular curve and transitional track are calculated by using the method. The steady-state case exists in the railway vehicle system during the curve negotiation. Theoretically, it has several limited sets in its dynamical system when railway vehicle runs on the track, among them the steady-state solutions exist. The large range solution diagram of the vehicle system changing with respect to a parameter can be obtained by using the continuation method. Here, the railway vehicle model with varying parameters, in nature, is not a single model, but a set of models. The continuation method just has the merit to deal with this set of vehicle models with varying parameters. The steady-state solutions of vehicle system are studied in the dissertation, and the results of the vehicle system with a single and/or two varying parameters are given. The results do not contain the transient components in numerical integration, because they are steady-state solutions. It can reflect the relationship of the vehicle performance depending on its parameters and is an efficient tool for parameter study of vehicle systems.Secondly, the periodic solutions of vehicle system are also studied using the continuation method. The discretization of the periodic solutions is adapted by the Finite Difference Method (FDM). We convert the boundary value problem (BVP) of ordinary differential equations to a system of nonlinear algebraic equations with parameters. The system of nonlinear algebraic equations is solved by using the continuation method and its periodic solution is obtained. The initial values of the periodic solutions are obtained via numerical integration in time domain. By this method, not only the stable periodic solutions, but also the unstable periodic solutions can be obtained. The stable periodic solutions of railway vehicle system exist objectively in the real world. Even though the unstable periodic motions cannot hold on continuously for a long time, they can be boundaries of attracti...