Instability of a Moving Bogie: Analysis of Vibrations and Possibility of Instability in Subcritical Velocity Range

This paper analyzes vibrations induced by a moving bogie passing through a single-layer railway track model. The emphasis is placed on the possibility of unstable behavior in the subcritical velocity range. All results are presented in dimensionless form to encompass a wide range of possible scenarios. The results are obtained semi-analytically, however, the only numerical step involves solving the roots of polynomial expressions. No numerical integration is used, allowing for the straightforward solution of completely undamped scenarios, as damping is not required for numerical stability. The vibration shapes are presented in the time domain in closed form. It is concluded that increased foundation damping worsens the situation. However, in general, the risk of instability in the subcritical velocity range for a moving bogie is lower than that of two moving masses, particularly for higher mass moments of inertia of the bogie bar and primary suspension damping. The study also examines how the results change when a Timoshenko-Rayleigh beam is considered instead of an Euler-Bernoulli beam. Although some cases may appear academic, it is demonstrated that instability in the supercritical velocity range cannot be assumed to be guaranteed.