Bifurcation analysis on the hunting behavior of a dual-bogie railway vehicle using the method of multiple scales

A bifurcation analysis is performed on a nonlinear railway vehicle having dual-bogies to examine the coupling effect of the bogies on the vehicle's hunting behavior. Because of the coupled nature of these bogies, a pair of complex conjugate roots exists in the linearized system close to the origin in addition to the most dominant pair of roots at the hunting speed. Using these four principal modes and a scaling parameter introduced in a novel way, the original systems of equations are converted into new equations whose linear portions exhibit monofrequency oscillations. The solutions near the hunting speed are constructed with an asymptotic expansion of a small perturbation parameter using the method of multiple scales.Steady state solutions are sought near the hunting speed and the corresponding limit cycle behavior is investigated. The stability of these limit cycles is characterized using Lyapunov's indirect method for the steady state solutions, which is also a novel approach. To support the stability results validity, a series of numerical simulations are performed. Bifurcation diagrams for the lateral motion of the vehicle system are then obtained, and the effects of nonlinearity on the vehicle's hunting behavior are thoroughly examined.