Double grazing bifurcations of the non-smooth railway wheelset systems

There are numerous non-smooth factors in railway vehicle systems, such as flange impact, dry friction, creep force, and so on. Such non-smooth factors heavily affect the dynamical behavior of the railway systems. In this paper, we investigate and mathematically analyze the double grazing bifurcations of the railway wheelset systems with flange contact. Two types of models of flange impact are considered, one is a rigid impact model and the other is a soft impact model. First, we derive Poincaré maps near the grazing trajectory by the Poincaré-section discontinuity mapping (PDM) approach for the two impact models. Then, we analyze and compare the near grazing dynamics of the two models. It is shown that in the rigid impact model the stable periodic motion of the railway wheelset system translates into a chaotic motion after the gazing bifurcation, while in the soft impact model a pitchfork bifurcation occurs and the system tends to the chaotic state through a period doubling bifurcation. Our results also extend the applicability of the PDM of one constraint surface to that of two constraint surfaces for autonomous systems.

Period-1 to Period-2 Motions in a Discontinuous Oscillator

In this paper, grazing bifurcations on bifurcation trees in a discontinuous dynamical oscillator are discussed. Once the grazing bifurcation occurs, periodic motions switches from the old motion to a new one. Thus, grazing bifurcations on a bifurcation tree of period-1 to period-2 motions varying spring stiffness are presented in a discontinuous oscillator with three domains divided by circular boundaries. The stability and bifurcations of period-1 and period-2 motions are discussed. From analytical predictions, periodic motions are simulated numerically. Stiffness effects on the periodic motions are discussed. Such studies will help one understand parameter effects in discontinuous dynamical systems, which can be applied for system design and control.