Shimmy dynamics of a towed wheel system subjected to colored stochastic excitations

This paper examines shimmy dynamics in a towed wheel system in case of colored noise excitations. Shimmy, a usually harmful self-excited oscillation, is traditionally studied in deterministic systems where bistability, chaotic, and transient chaotic oscillations may appear. Since these systems are often subjected to stochastic excitations from road or wind irregularities, we introduce random disturbances into the simplest mechanical model of shimmy and analyze the dynamical behaviors using bifurcation analysis and Monte Carlo method. The results show that the random excitations lead to stochastic P-bifurcation and random transitions, causing the system to alternate between rolling and slipping states. Also, the increased noise intensity shortens the mean first passage times. The proposed methodology provides a toolbox for engineers to estimate the probabilities of catastrophic oscillations in towed wheels and attached structures subjected to real-life stochastic perturbations.