Abstract Summary
The parametric instability of a moving mass / oscillator has been studied in literature for a continuous periodic inhomogeneous Euler-Bernoulli beam, a periodic discretely supported string, and a periodic discretely supported Timoshenko beam. It was found that the parametric instability was caused by the radiation of Anomalous Doppler waves and small parametric studies to the influence of various parameters were done. In this present study, we used a periodic discretely supported Euler-Bernoulli beam and a more extensive study on the effects of various parameters was performed. For example, it was shown that in the case of an Euler-Bernoulli beam we have no destabilisation by viscosity, the instability zones merely become smaller. Results also point towards a possible relation between the dispersion characteristics of the periodic structure and the instability zones: the former dictates the possible travelling waves through the infinite kinematic invariants, which may be either anomalous or normal Doppler, that contribute to the (de)stabilisation of the moving mass / oscillator. Furthermore, the rail-sleeper system was coupled with a 2D discrete lattice that models either ballast or a slabbed track and the underlying soil foundation. By which we found that for a moving train on ballasted track parametric instability will be very unlikely: the radiation damping simply prohibits the mass becoming unstable. On the contrary, a high speed train on a slabbed track could still be unstable. This analysis also showed that the coupling of the supports through the medium likely has an effect on the instability domains.
