Dynamic Analysis Of The Geometrical Nonlinear Model Derived From Bogie

There are a lot of nonlinear vibration problems in modern life, such as theaerospace engineering, the train system. So research on the strong nonlinear systemis a hot topic for several decades. Taylor expansion was used to get the approximatesystem of the nonlinear multiply degree of freedoms system in the past days. Basedon the singularity theory, the approximate system is equivalent to the original systemonly when they are strongly equivalent. So taylor expansion method may lost somedynamic properties of the original nonlinear system. In this paper, averaging methodis used to analysis bolster-spring system instead of taylor expansion. The main workof this paper is as follows:(1) Nonlinear bolster-spring model with three degree of freedoms(DOF) based on thebogie system in the train system is built, in which geometrical non-linearity isconsidered. The governing equations of the bolster-spring system is obtained.Bolster-spring system with three degree of freedom is analyzed numerically.The bifurcation diagram of the three DOF system with different systemparameter is drawn.(2) A two DOF geometrical nonlinear system is built based on the three DOF bolster-spring system, in which the yaw motion is neglected. With different systemparameter, the number of equilibrium point and their stability are obtained.The bifurcation diagrams of the horizontal and vertical direction with differentsystem parameters are obtained numerically. The region where periodicalsolutions of the system exist can be found from the bifurcation diagram.Averaging method is used to obtain the analytical solution of the two DOFsystem. Averaging equation and amplitude-frequency diagram of the two DOFsystem are got and the vibration-parameter relationship is obtained.(3) Oblique coupled oscillator with two DOF is come up with based on the bolster-spring system. With different system parameter D, the number of equilibriumpoint and their stability are obtained. The bifurcation diagrams of the oscillatorwith different system parameters are obtained numerically. The region whereperiodical solutions of the system exist is obtained from the bifurcation diagram.Averaging method is used to obtain the analytical solution of the two degree of freedom oblique coupled oscillator. Averaging equation and amplitude-frequencydiagram of the two DOF system are got and the possible motion of the systemunder different external excitation is drawn.