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

This paper deals with the analysis of vibrations induced by a moving bogie passing through a single-layer model of a railway track. The emphasis is placed on the possibility of unstable behavior in the subcritical velocity range. All results are presented in dimensionless form to cover a wide range of possible scenarios. The results are obtained semi-analytically, however the only “numerical” step is related to solving the roots of polynomial expressions. No numerical integration is used, and therefore even completely undamped scenarios can be easily solved, as damping is not necessary for numerical stability. The vibration shapes are presented in the time domain in closed form. It is concluded that increased foundation damping aggravates the situation, but in general the danger of instability in the subcritical velocity range of moving bogie is less than two moving masses, especially for higher mass moments of inertia of the bogie bar and primary suspension damping. It is also tested how the obtained results were changed by considering a Timoshenko-Rayleigh beam instead of Euler-Bernoulli. Although some cases may seem academic, it has been shown that instability in the supercritical velocity range cannot be assumed as guaranteed.