Investigation of Response Amplification and Dynamic Stability of a Hyperloop System

Abstract

Hyperloop is a high-speed transportation mode that operates through magnetic levitation of so-called pods which are then transported through a tunnel in which a low-pressure environment is created. Due to reduced air resistance and friction, high velocities are achievable. This thesis addresses the behaviour of such a system operating at high velocities, focusing mainly on dynamic stability. The novelty of this study lies hereby in the implementation of a more realistic guideway model in the analysis. This was achieved by modelling the Hyperloop tube as an infinitely long cylindrical shell on a viscoelastic foundation from which the vehicle is suspended through an electromagnetic force, including an active control system.

This study aims to evaluate the system’s stability and its sensitivity to changes in the model by using mainly analytical methods which are supplemented by numerical computations where needed. There are two fundamentally different instability mechanisms studied, namely the electromagnetic instability caused by the inherent unstable nature of the suspension system and the wave-induced instability which originates from the energy feedback of radiated anomalous Doppler waves excited by the vehicle moving at large velocities. The research is motivated by two central questions: (1) What is the influence on the steady-state response when employing the more realistic guideway model? (2) What is the influence on the stability when employing such a model?

To address the first research question, only the steady-state of the guideway is analysed. Hereby, the electromagnetic force as well as the vehicle are disregarded and replaced by a constant moving load. To solve the system, the governing equations are projected on circumferential modes and transformed from space-time to the Laplace-wavenumber domain. This study analyses various scenarios based on their dispersion curves and/or steady-state response compared to a reference case.

For the second research question, the study analyses stability phenomena whereby the response of the guideway is expressed using a convolution of its Green’s function and the unknown electromagnetic force. Linearising the system around its steady-state equilibrium allows a computation and analysis of its eigenvalues which describe its stability. To complement and verify the analysis of the linearised system, a non-linear transient model is solved by using a numerical time-stepping algorithm.


The study highlights that the cylindrical shell model significantly affects the critical velocity, compared to an Euler Bernoulli beam model. Analysing the vehicle-structure interaction through the linearised stability analysis reveals stability concerns primarily driven by wave-induced instability when operating at supercritical velocities. In the subcritical regime, instability is only caused by the electromagnetic suspension, which can be overcome when choosing the right control parameters. To reduce the risk of instability it is advisable to choose the structural dimension such that the system operates at subcritical velocities to avoid the interaction between the two instability mechanisms.

This research advances the understanding of Hyperloop dynamics and its stability, providing a foundation for future studies and practical implementations aimed at developing the novel transportation mode.