Bifurcation And Chaotic Motion Of Nonlinear Mechanical Vibration System

In the actual engineering environment,there are many kinds of nonlinear factors,such as the frictional force encountered in the mechanical working process,and the gap between the mechanical parts caused by the assembly and so on.These will make the dynamic behavior of mechanical system in actual work process more complex than single linear system.It is precisely because of these nonlinear factors that often affect the mechanical equipment's strength,safety and service life.At the same time,we also made use of these nonlinear characteristics to create some mechanical devices to serve our life.Therefore,it is necessary for us to study the dynamic characteristics of this kind of nonlinear system,reduce the adverse effects on our life,and make full use of this characteristic to serve our production practice.In this paper,a relative collision vibration system with two degrees of freedom and a relative collision vibration system with three degrees of freedom are established from the train brake system and the coupler buffer device.Through the force analysis of these two kinds of systems,the differential equations of motion of the system are established,the analytic solution of the system is derived by the semi analytic method,and the Poincaré mapping of the system is established by combining the boundary conditions of the system.The numerical simulation test is carried out in the MATLAB system,and the specific transition path of the system from the periodic motion to the chaotic motion is mainly analyzed,and the different parameters of the system occur in the system.The influence of variation on the nonlinear dynamic behavior of the system is discussed.At the same time,the image of the system simulation test is analyzed,and the theoretical reference of the parameters optimization of the two kinds of systems is provided from the angle of nonlinear dynamics.The third chapter is mainly from the train braking system,considering the dynamic process of the train braking,the train's brake shoe and the wheel are equivalent to two protons in the model,and a class of relative collision vibration system with two degrees of freedom is established and studied.The research results show that the system mainly leads to chaotic motion through the way of Hopf bifurcation,doubling bifurcation or combining two kinds of bifurcations.And the influence of the system parameters and the system dynamics is studied.The results show that with the increase of these two parameters,the Hopf bifurcation and the bifurcating bifurcation values of the doubling bifurcation will be reduced,and the dynamic behavior changes of the system have a greater influence on the system.The fourth chapter mainly takes the train's coupler buffer device as the research background.Considering the longitudinal impact of the train and the gap between the couplers,a kind of dynamic system of the relative collision vibration system with three degrees of freedom is established.The results of the numerical simulation of the system showthat the Hopf bifurcation will occur in the doubling bifurcation first and then to the chaotic motion under the appropriate parameters.The types of bifurcations are the same,but from the perspective of Poincaré cross section,they have different ways of transferring.Finally,the influence of two mass ratios on the dynamic behavior of the system is compared.The results show that the mass ratio has a greater influence on the dynamic behavior of the system.