Stochastic stability of an elastically constrained wheelset system under additive and multiplicative color noise excitations

This study investigates the nonlinear dynamic response of an elastically constrained wheelset system, considering the impacts of excitation factors such as track irregularities and control parameters of the wheelset itself. A dynamic model of the wheelset system is established under both multiplicative and additive colored noise excitations, focusing on the system's stability and bifurcation behavior. By applying the stochastic averaging method for quasi-non-integrable Hamilton systems, the model is simplified to a one-dimensional Itô stochastic differential equation. Based on the singular boundary theory and the three-exponential method, the types and conditions of the stability and bifurcation of the system are assessed theoretically. Numerical simulations are conducted to analyze the effects of various parameters on the system's stability, the critical speed for stochastic bifurcation, and the changes in the topology of the probability density function. The results demonstrate that the system's stability and the type of bifurcation are primarily governed by internal excitations. Variations in control parameters lead to changes in the critical speed for instability and alter the type of bifurcation. We reveal the bifurcation trends of the system through time history diagrams, Poincaré sections, and bifurcation diagrams. The system exhibits rich dynamic bifurcation characteristics as parameters vary. Notably, when affected by multiple parameters, the system transitions from periodic to chaotic states in the period-doubling bifurcation manner on the two-parameter plane, with bifurcation structures changing accordingly with parameter variations.