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.

Hyperloop is a new high-speed transportation system currently in development. Utilising an electromagnetic suspension within a low-pressure tube, this approach eliminates the traditional wheel-track friction and drastically reduces the air resistance, targeting speeds up to 1000 km/h. Compared to traditional trains and aeroplanes, the Hyperloop is a more sustainable alternative as it produces no greenhouse gas emissions and uses ten times less energy than road and aviation transportation. The Hyperloop, therefore, has great potential to contribute to the goal of achieving climate neutrality by 2050.

Ensuring the stability of the Hyperloop is a critical challenge in its realisation. Multiple instability mechanisms are present in the system: (1) electromagnetic instability, (2) wave-induced instability, and (3) aeroelastic effects, such as galloping. Additionally, the imperfections in the guideway, make the Hyperloop system prone to parametric instability. This thesis primarily investigates how aeroelastic forces and parametric resonance interact with the electromagnetic and wave-induced instability mechanisms, impacting the overall stability of the Hyperloop system.

Based on the results, it can be concluded that the aeroelastic force destabilises the system, where its impact increases as the velocity rises. As the aeroelastic force continuously injects energy into the system, the unstable domain expands. Furthermore, parametric resonance, represented by ellipse-shaped indentations in the stability planes, is observed when the excitation frequency is twice the natural frequency of the system. Based on the control parameter range used for maglev trains, it is found that the stable domain is narrow, with only a small region prone to parametric resonance. Therefore, choosing the control parameters precisely is essential to prevent instability and parametric resonance.

When examining the combined effect of aeroelastic force and the irregular guideway profile, the results show that the aeroelastic force shifts the overall position of the stability boundaries but it does not affect the parametric resonance regions. Instead, the amplitude of the guideway’s irregular profile influences the size of the ellipses and the stable domain. A larger amplitude leads to an expansion of the unstable domain and an increase in the size of the ellipse; therefore, it is advised to maintain a smooth guideway.

This thesis further evaluates the capabilities of analytical expressions for the simpler 1.5 degree-of-freedom (DOF) electromagnetically suspended mass system by comparing it to systems that incorporate the beam dynamics. The results show that the analytical expressions from the 1.5 DOF system cannot approximate the position of the ellipses for the more complicated systems across all velocities. However, beyond the velocities of $1.3v_{cr}$, the analytical expressions effectively approximate the ellipse size. Notably, while the position and size of the ellipse are influenced by the guideway’s surface roughness amplitude, only the size of the ellipse is affected by the amplitude of the oscillations in the 1.5 DOF system. For the more complicated systems, the analytical expressions of the ellipse size relative to the amplitude provide accurate results, making the simplified system a valuable approach for estimating the ellipse size of parametric resonance in systems with beam dynamics.