Abstract Summary
Hyperloop is a new emerging transportation system that is in the development stage. Its design minimises the air resistance by having the vehicle travel inside a de-pressurised tube (near vacuum) and eliminates the wheel-rail contact friction by using an electro-magnetic levitation system (similar to the ones used by Maglev trains). By doing so, it can potentially reach much higher velocities than conventional railways, thus being a climate-friendly competitor to air transportation. It is well known that a vehicle travelling on a supporting structure can become unstable when its velocity exceeds a certain critical velocity. Instability leads to excessive amplification of the response, which can lead to derailment in extreme cases. This is rarely the case in conventional railway tracks, but the Hyperloop vehicle, due its predicted very high velocities, can very well exceed the critical velocity in the system. Consequently, knowing in which velocity regimes the Hyperloop system can be unstable is of high practical importance for its design. Previous studies have investigated this by simplifying the supporting structure (tube, pillars, soil, etc.) to a single degree-of-freedom system. While this approach is a good starting point, it neglects the frequency/wavenumber and vehicle velocity dependent reaction force of the supporting structure. This study aims to investigate the influence of correctly representing the reaction force on the stability of the system. To this end, the Hyperloop is modelled as an infinite beam continuously supported by a visco-elastic foundation (the periodic nature of the supports is neglected at this stage) subject to a moving mass. The interaction between the mass and the supporting structure occurs through an electro-magnetic force governed by a conventional proportional and derivative (PD) control. This study can help engineers designing the Hyperloop system avoid undesired excessive vibrations that can lead to fatigue problems and, in extreme cases, to derailment.
