Hyperloop has emerged as a promising mode of transportation and has attracted strong interest from student teams and start-ups. Its potential lies in enabling faster and more sustainable transport. At the same time, the technology and characteristics of the hyperloop system may also lead to different instability mechanisms. This study focuses on two of these, namely electromagnetic instability and wave-induced instability. Previous studies have generally considered either conventional control strategies or simplified models of the vehicle-guideway dynamics. This study contributes by investigating the effect of an advanced control strategy, Model Predictive Control (MPC), on both sources of instability. MPC is applied because of its predictive nature and its ability to handle constraints.

The analysis first considers a simplified 1.5-degree-of-freedom (DOF) system to study the effect of MPC on electromagnetic instability. An eigenvalue analysis was conducted to examine the influence of the MPC parameters. It is found that linear MPC does not achieve stabilisation. Therefore, a nonlinear MPC is designed and compared with a PD controller, showing improved control performance.

To capture the influence of vehicle velocity on system stability, an infinite guideway with coupled vehicle-beam interaction is considered, allowing anomalous Doppler waves to arise at high velocities. In the supercritical velocity regime, where wave-induced instability becomes dominant, numerical simulations show that MPC can maintain stability for suitably tuned controller parameters over a wider range of velocities. Compared with the PD controller, MPC appears better able to achieve fast convergence while also suppressing wave-induced instability.

Overall, MPC showed improved control performance relative to the PD controller and appears to be a promising control strategy for application in magnetically levitated high-speed transportation systems. However, more research is needed to make nonlinear MPC feasible for real-time implementation. A more formal and comprehensive study of the stability of the vehicle is also needed.
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This dissertation investigates how external vibrations can be used to influence and control friction. While friction is essential in many systems, it also leads to energy loss, wear, and inefficiencies. Traditional lubrication has limitations, making vibration-based methods a promising alternative. The study explores how factors such as excitation frequency, phase, load application, and system dynamics affect friction behaviour, as well as the interaction between friction and vibrations, including potential instabilities. By using more realistic system models, the research highlights the importance of system flexibility and dynamic properties, contributing to a deeper understanding of friction in complex systems and offering insights for practical applications. ... Read more

In the Netherlands there are many waterways where bridges or locks are situated within the navigation way of inland waterway vessels. To protect these civil structures from potential collision risks, protection structures are placed around them. In this research, a commonly used protection structure, the steel piled fender structure, is analyzed under impact events, followed by a comparison with the design methodology prescribed in the Dutch codes. In the Netherlands, design guidance is provided by the "Richtlijnen Ontwerp Kunstwerken", abbreviated as ROK. The ROK adopts a design formula for the required energy absorption capacity of fender structures from the EAU 2012. By applying the principle of work, the required energy absorption capacity can be converted into an equivalent static load that incorporates dynamic effects. This allows the soil-fender structure system to be designed using static analysis.

In this research, a triangular-shaped fender structure with fixed geometrical properties is examined. Additionally, the bow structure of a CEMT class IV ship is included to capture the interaction between the ship and the fender structure during impact events. The aim of this study is to obtain a transient response of the system, investigate the interaction between the ship, soil, and fender structure during dynamic impact events, and evaluate this against the design methodology prescribed in the Dutch codes.

To determine the transient response, two different models are developed. A simplified dynamic model based on linear beam theory is constructed. In this model, the problem is reduced to two-dimensional space, where the fender structure is modeled as a 2D frame partially supported by linear elastic foundations representing the surrounding soil. The ship's bow structure is simplified as a mass-spring system attached to the frame structure. Furthermore, a non-linear finite element model (NLFE) is developed in three-dimensional space. The NLFE model includes the full geometry of the fender structure of interest, with the ship's bow structure modeled up to the most frontal bulkhead, and the soil is represented by a series of non-linear discrete springs.

Before performing NLFE impact simulations that account for the full interaction between the ship, soil, and fender structure, an extensive sensitivity study was conducted on the individual models, showing expected behavior. Impact simulations performed during the sensitivity study were used to set up the impact configuration for the final head-on and oblique impact simulations, in which the ship, soil, and fender structure behave flexible simultaneously, allowing full interaction.

A comparison between the simplified model and the head-on impact simulation from the NLFE model revealed different peak responses. The response of the NLFE model was dominated by significant plastic deformations, resulting in larger peak displacements compared to the simplified model. However, during the initial stage of impact loading, dominated by elastic deformations, both models showed good agreement.

Finally, NLFE simulation results are compared to the design methodology prescribed in the Dutch codes. The energy absorption observed in the fender-soil system from the NLFE simulations is compared to the required energy absorption capacity according to the codes. For the head-on impact scenario, significant crushing of the ship's bow led to reduced energy absorption by the fender-soil system. In the oblique impact simulation, the NLFE model predicted higher energy absorption by the fender-soil system compared to the code requirements. There are numerous differences in modelling assumptions between the NLFE model and the method prescribed in the codes. Moreover, the NLFE model includes simplifications of the real-world problem that may lead to an overestimation of the absorbed energy by the fender-soil system. Therefore, extending the NLFE model by removing simplifying assumptions remains highly recommended.
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This thesis presents a modelling framework to describe the non-smooth dynamic response of solid media in the time domain under dynamic loading conditions, such as those typically found in soil-structure and ice-structure interaction. The approach divides the medium into two domains: a near-field domain capable of capturing nonlinear phenomena, and a surrounding linear far-field domain. The near field is modelled as a discrete lattice incorporating rheological elements, such as springs, dashpots, and dry-friction elements, for example enabling stick-slip behaviour.
The far-field domain is incorporated through a boundary integral formulation that accounts for the domain's properties solely at the interface with the near field, allowing for accurate wave transmission and minimal reflections at the boundary. Boundary integral equations (BIEs) are derived for both continuous and discrete representations of the far field, including one of the first derivations of BIEs for finite or semi-infinite discrete particle systems.
To address the computational challenges of time-domain simulations involving nonlinearities, a novel mixed time-frequency domain (MTFD) method is introduced. This non-iterative hybrid approach combines the efficiency of frequency-domain methods during periods of linear behaviour while accounting for the changing properties of the lattice over time whenever a nonlinear event occurs.

Results demonstrate the effectiveness of lattice models and discrete-based BIEs in capturing non-smooth dynamics, while highlighting the importance of robust numerical implementation. The proposed framework offers a promising tool for simulating wave propagation in nonlinear media and supports improved analysis and design in civil, geotechnical, and offshore engineering applications.
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The renewable energy sector is experiencing rapid growth, with offshore wind energy gaining significant global importance. Designing bottom-fixed offshore wind turbines (OWTs) with monopile (MP) foundations in seismic-prone regions, particularly in coarse-grained soils, presents challenges due to the risk of soil liquefaction during earthquake excitations. Current design practices for soil-structure interaction modelling address seismic pore pressure effects by accounting for the net decrease in soil shear modulus resulting from the development of excess pore water pressure.
This thesis examines the cyclic contour diagrams framework (CDF) for its capacity to predict excess pore water pressure (EPP) build-up in coarse-grained soils under seismic conditions. The framework is assessed by employing PM4Sand in PLAXIS2D to produce the cyclic contour diagrams for a coarse-grained material. This material is then used to perform site response analysis (SRA) on a soil column in PLAXIS2D. Subsequently, a total stress SRA is conducted using DEEPSOIL V7.0 to obtain the equivalent cyclic stress ratio (CSR) and the number of cycles by employing a best-match soil material similar to the one utilized in the PLAXIS analysis. By analyzing the cyclic stress history obtained from the SRA, the equivalent number of cycles and cyclic stress ratios are applied to the material's cyclic contour diagrams. Finally, the predictive capabilities of the method to predict the EPP calculated in the PLAXIS model are assessed.
Two case studies illustrate the framework's practical application. The first case focuses on Akita Port, Japan, which experienced significant damage during the 1983 Nihonkai-Chubu earthquake. The CDF was able to accurately predict liquefaction severity, validating the method. The second case study involves an offshore wind farm in the Netherlands, examining how liquefaction impact monopile foundation designs. The study highlights the importance of incorporating soil degradation because of liquefaction into the design of offshore wind turbines.
The findings indicate that the CDF is a viable tool for evaluating liquefaction potential in coarse-grained soils under seismic loading in engineering practice.
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This research focused on applying vibration-based model updating to estimate the structural properties of high-rise buildings using a discrete Timoshenko beam model. Previous studies by Moretti et al. [1] and Taciroglu et al. [2] showed limitations in estimating the structural properties of buildings using model updating with a uniform Euler-Bernoulli beam model or a uniform Timoshenko beam model. Both models were not able to describe the third measured bending mode accurately after updating. Moreover, with the uniform Euler-Bernoulli beam model, when only the lowest two bending modes were used to fit the model, the estimates of the rotational stiffness of the foundation around the y-axis, Kr,y, showed significant uncertainty after model updating, with a Coefficient of Variation (CV) of 46.9%. Therefore, this research aimed to improve the accuracy of structural property estimations for high-rise buildings by using a more detailed model.
The model updating method applied in this research was an indirect vibration-based technique, which adjusted the input parameters of the chosen model to minimize the difference between the model output and the measured data. Both the model output and the measured data were in the shape of natural frequencies and mode shapes. The technique was applied to two high-rise buildings: the residential tower New Orleans, which is bending-dominant in behavior, and the office tower Delftse Poort, which is shear-dominant in behavior and exhibits irregular stiffness across its height. The discrete Timoshenko beam models used to approximate the dynamic behavior of these buildings were created using the Finite Element (FE) models of the buildings.
The research findings highlighted several key aspects essential for obtaining more accurate estimations of the structural properties of high-rise buildings. For a more accurate estimation of parameter Kr,y, it is of importance to incorporate shear deformations in the model and to account for irregular stiffness along the height. For the New Orleans, using the discrete Timoshenko beam model led to estimates of parameter Kr,y with low uncertainty, indicated by a Coefficient of Variation of 6.91%. This was an improvement compared to the study by Moretti et al. [1], which showed a Coefficient of Variation of 46.9% using the uniform Euler-Bernoulli model.
Moreover, obtaining accurate values for the bending stiffness was crucial for achieving more precise estimations of the structural properties. It was challenging to determine the bending stiffness values using the FE models. These challenges posed a problem for model updating, as the initial structural property ratios were maintained for both high-rise buildings. Maintaining these ratios gives weight to the initial structural property values. These values must be correct. Otherwise, model updating is limited by the incorrect ratios and will not be able to accurately match the measured modal properties.
For the Delftse Poort, more pure bending modes were needed for better accuracy. The discrete Timoshenko beam model was unable to match the measured second bending mode in the y-direction, as it exhibited twisting, which the model could not represent due to its limitation to pure bending modes. Furthermore, since the discrete Timoshenko beam model requires a single displacement value per height but multiple sensors were used to measure displacements, the measurements had to be averaged. This averaging process may led to a mode shape that deviates from the actual behavior, resulting in an inaccurate representation of reality. ... Read more

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. ... Read more

The Hyperloop concept tackles the challenges conventional transport modes face, despite the considerable research gap. This research reduces the gap by focusing on the dynamic response of the periodically supported Hyperloop tube since the Hyperloop greatly exceeds the operational speed of traditional transport modes. Complexity is incorporated to obtain a detailed dynamic response using a finite element method. Progress has been made in incorporating the moving reference frame within the model with recommendations for the numerical stability of the transient analyses. Despite the computational inefficiency of the conventional non-moving reference frame, the model is utilised to conduct a parametric study. The study examines correlations between the stiffness properties of various Hyperloop elements, including the tube, rail, and the interface between the Hyperloop tube and column. These correlations are analyzed based on the system's response at the pod's location and the intersections between the tube segments. Here, the velocity of the pod is of paramount importance. Within the operational velocity range, only one critical velocity is identified, despite the system's infinite number of natural frequencies. The only dynamic amplification, identified as the main critical velocity, can be shifted beyond the operational range by increasing the overall structural stiffness. The shift can be realised due to the positive correlation with the main critical velocity and a negative correlation with the displacement difference at the interface between two tube segments relative to the structural stiffness. Within the research, the soil and pod interactions with the Hyperloop structure are excluded, leading to potential resonance with no risk of instability. The limitation can be addressed by modelling the pod as a mass-spring system and the soil as a two-dimensional medium. The files developed for the finite element models and the parametric study are available on GitHub (https://github.com/dedenner3/MasterThesis_Hyperloop). The files support reproducibility and further exploration of the methods described. ... Read more

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. ... Read more

Underground tunnels are important infrastructures due to diverse applications in civil engineering. The dynamic behavior of the underground tunnels when exposed to seismic waves or the passage of high-speedmoving trains is of particular interest. Amplifications of displacements and stress concentrations may occur due to wave scattering and wave interference. Engineers concern about the vibration stability of moving trains as so-called anomalous Doppler waves may be generated when trains move at high speeds; the corresponding energy is fed into the vibration of the vehicle. Therefore, the traintrack- soil interaction should be properly considered to predict when the vehicle vibration becomes unstable. This thesis aims to present a semi-analytical solution for the response of a half-space with an embedded tunnel subject to seismic waves and to analyse the vibration stability of high-speed trainsmoving through that underground tunnel. Previous studies indicate that the method of conformal mapping is a promising analytical method to solve the two-dimensional (2D) wave scattering problem due to its computational efficiency and accuracy. Thus, the first objective of this thesis is to extend the method of conformal mapping to three-dimensional (3D) case and systematically evaluate its performance. Results reveal that inaccurate results maybe obtained, particularly at high frequencies. This observation motivates the second objective of this thesis, which focuses on verifying the accuracy of the specific application of the method of conformal mapping in which thewaves scattered fromthe half-space surface are represented by cylindricalwaves that originate from an image source of a priori unknown intensity. To this end, a simpler 2D model is considered, involving a cylindrical cavity embedded in an elastic half-space subject to a harmonic anti-plane shear wave. The performance of the indirect Boundary Element Method (indirect BEM) is evaluated too for this model in view of the choice of the appropriate solution method for the second type of dynamic problem considered in this thesis. For this second type of dynamic problem, due to the identified inaccuracies at high frequencies for the 3D problem, the indirect BEM is utilised to investigate the stability of vibrations of an oscillator moving at high speeds through a tunnel embedded in soft soil, which is the third objective of this thesis… ... Read more

Railway tracks are subjected to constant degradation in terms of geometry, and wear and tear of the track components (rails, sleepers, fasteners, trackbed layers, etc.). Over the years, trains have evolved immensely, but the track infrastructure has not kept pace. With rapid advancements in vehicle technologies, the design of rail infrastructure must cope with the challenges associated with the operation of railway tracks. In addition, railway transition zones (RTZs) degrade even faster (4-8 times) than normal tracks, leading to higher maintenance and operational costs. RTZs are areas where railway tracks cross stiffer structures (e.g., roads, bridges, culverts). The amplified degradation in RTZs is mainly attributed to abrupt changes in vertical stiffness and to differential settlement, resulting in amplified and non-uniformtrack responses. Even though the dynamic behavior of RTZs differs from that of normal tracks, the design of track components in these zones remains similar to normal tracks, with some modifications at the superstructure and/or substructure levels to mitigate the transition effects. There have been several attempts to mitigate the adverse effects of dynamic response amplification in RTZs, but they have proven either marginally effective or counterproductive. Therefore, a comprehensive design methodology for RTZs is needed that addresses the main degradation mechanisms leading to amplified degradation of these zones.

In this paper-based thesis, a novel methodology is proposed to design and evaluate railway transition zones. For this purpose, detailed analysis and design optimization is performed for a bridge-embankment transition using various two-dimensional and three-dimensional finite element models, different vehicle models, and surrogate models (using polynomial chaos expansion). Firstly, the proposed methodology establishes a robust design criterion to design and evaluate RTZs. The criterion relates the magnitude and uniformity (spatial and temporal) of the total strain energy in the trackbed layers to the permanent deformation of RTZs. This novel energy-based criterion is used to evaluate the most commonly used mitigationmeasures at the superstructure and substructure levels and to investigate the key phenomena governing RTZ design. Based on insights obtained from these analyses, a preliminary design of a novel transition structure called SHIELD (Safe Hull-Inspired Energy Limiting Design) is proposed. The second phase of the work is dedicated to identifying the most influential design parameters leading to optimized geometry of SHIELD and the desiredmaterial characteristics. The third phase involves the performance evaluation of optimized SHIELD subjected to critical loading conditions (e.g., critical and supercritical velocities, different directions of movement, hanging sleepers, non-straight rail) and SHIELD is shown to be a robust design solution for all conditions under study. In the end, the use of SHIELD is extended to another type of an embankment-bridge transition (with ballast running over the bridge) where it is shown to be equally (compared to embankment-bridge transition with no ballast layer over the bridge) efficient in mitigating the transition effects, and a laboratory experiment is designed to test the effectiveness of the proposed design criterion and methodology. A robust design methodology for RTZs is proposed in this work, which aims to minimize operation-induced degradation and can be adapted to different transition types and sitespecific conditions. A preliminary optimized design of SHIELD is proposed, which has been shown to be effective in mitigating dynamic amplifications in RTZs under both ideal and non-ideal conditions. The results and conclusions presented in this work demonstrate the promise of SHIELD as an intervention for railway transition zones, outline the next steps toward its practical implementation, and highlight the challenges that need to be addressed in future research.
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Due to the current climate crisis, railway transport is receiving increased attention owing to its capability of running fully on electricity, which can be generated from renewable sources. High-speed railway networks and the new concepts, such as Hyperloop, are already competing with road and aviation transport. However, the increased demand on railway transport causes an acceleration in infrastructure degradation leading to an increased frequency of maintenance and repair operations. Consequently, what before was considered normal "wear and tear" of the infrastructure is quickly turning into serious challenges causing disruptions to the normal operation of traffic.

When it comes to track degradation, the so-called transition zones require significantly more frequent maintenance than the regular parts of the railway track. Transition zones in railway tracks are areas with substantial variation of track properties (e.g., foundation stiffness) encountered near rigid structures such as bridges, tunnels, culverts, or rail-crossings. The occurrence of differential settlements at transition zones has been known for a long time and a multitude of mitigation measures have been designed to cope with this problem. Nonetheless, the mitigation measures have had just limited success and in some cases have even exacerbated the problem. Although the failure of some mitigation measures stems from inadequate design and poor implementation, overall, the lack of efficiency of mitigation measures can be attributed to the lack of understanding of the main mechanism(s) that drive(s) the differential settlement. Therefore, to design efficient mitigation measures, one needs to advance the understanding of the physical processes leading to differential settlements at transition zones. This constitutes the first objective of this dissertation.

The settlement mechanisms are studied in this dissertation through models rather than in-situ measurements or lab experiments. The majority of previous studies have used models to (i) understand and (ii) predict the response of railway tracks at transition zones. Researchers aiming at (i) have usually used simplified phenomenological models in which system characteristics that are not of interest are excluded. More recently, the models' complexity has increased tremendously by incorporating many system characteristics, making these models ideal for (ii), but less ideal for (i) due to the many mechanisms simultaneously at play. This led to the second objective of this dissertation, which is to investigate the effect of specific characteristics of the railway system on the degradation at transition zones. In other words, the second objective entails improving the simplified models by incorporating additional characteristics and determining which of these characteristics is of importance and which can be neglected.

Naturally, this dissertation can only focus on a few of the many aspects involved in this complex problem, and the two main constraints are presented in the following. Improving the maintenance operations themselves by employing new technologies could lead to a reduction in the maintenance frequency. However, to develop a long-term solution, one should aim at eliminating the root cause. Therefore, this dissertation investigated the \emph{initiation} phase of the settlement, and not the accumulation phase. Furthermore, this dissertation focused on the differential settlement stemming solely from the amplification of stresses and strains that occur at transition zones, which is significant at relatively large train velocities. Consequently, this dissertation has not treated other sources of differential settlements, such as the different rates at which autonomous settlement develops in the open-track and at the man-made structure.

Using a simple phenomenological model representative of the railway track, Chapter 2 demonstrates that the response amplification at transition zones is caused by the interference between the steady-state field and the free field generated by the transition process. Consequently, the more pronounced the free field, the larger the resulting amplification. It also shows that the soft-to-stiff and stiff-to-soft transitions have significantly different behaviour, strongly suggesting the need of different mitigation measure designs for the two types of transition. Finally, the transition radiation energy is shown to be invariant between the soft-to-stiff and stiff-to-soft scenarios, finding which was unexpected considering the above-mentioned difference in behaviour.

Investigating the vehicle-structure interaction, Chapter 4 demonstrates that the amplification of the wheel-rail contact force caused purely by a change in foundation stiffness and damping (i.e., a track without initial imperfections) can be significant. Previous literature studies concluded the opposite; however, these studies considered only quasi-static velocities and small effective changes in foundations properties. The findings presented in this chapter, thus, supplement earlier findings to offer a more complete picture. Nonetheless, even though the vehicle-structure interaction leads to a stronger transition radiation, it leads to a reduction of the response amplification at the critical locations in transition zones where settlement is usually observed.

Chapter 5 identifies three response amplification mechanisms at transition zones in systems that have a periodic nature. The amplification is the product of a system with periodic nature and with a local inhomogeneity, and if one of these characteristics is omitted, the amplification does not occur. While these mechanisms can be influential for the railway over-head wires and for the emerging Hyperloop transportation system, they have a negligible influence in the conventional railway track. Consequently, for investigations focused on transition zones and response amplification at low frequencies, the periodicity of the railway track can be successfully approximated by the equivalent continuously supported one without neglecting influential amplification mechanisms.

Chapter 6 introduces the ballast settlement and investigates its influence on the transition process. It shows that the development of the initial settlement leads to a redistribution of the transition radiation energy during the transition not only between frequencies, but also between the soft and stiff media. This redistribution is mainly attributed to the separation between the beam and foundation at the settlement location. Consequently, if the developed settlement is not large enough to allow for this separation, the influence of the nonlinear foundation on transition radiation is negligible.

Chapter 8 investigates the influence of the foundation nonlocality on transition radiation. It shows that the nonlocality of the soil layer has an increasingly pronounced effect on the steady-state response with its decreasing shear stiffness. Consequently, modelling the nonlocality of the supporting structure can be important for railway tracks founded on soft soils. Furthermore, for ballasted tracks founded on soft soils, the response amplification at transition zones can be more pronounced in the soil layer than in the ballast layer depending on the transition type. This is caused by the vertical stiffness of the ballast layer can be significantly larger than the one of the soil. This finding suggests that soil settlement should be accounted for if the long-term behaviour is to be correctly represented.

The investigation of several mechanisms of response amplification at transition zones performed in this study has led to a deeper understanding of the mechanisms leading to differential settlement at transition zones in railway tracks. This knowledge can serve future researchers and engineering in designing more efficient mitigation measures.
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In transition zones, railway tracks experience significant inhomogeneity in their mechanical properties—more specifically in vertical stiffness. In such areas, conventional tracks (soft tracks) are typically encountered with other engineering structures with noticeably larger stiffness, such as bridges and culverts (stiff tracks). This inhomogeneity together with the passage of high-speed trains leads to amplification in dynamic response, which in turn results in faster degradation and higher cost of maintenance at transition zones. In practice, various mitigation measures have been adopted which have led to improvement in track performance to a certain degree.

This thesis is mainly focused on the feasibility of using the tuned mass damper (TMD), as a novel mitigation measure, for improving the aforementioned undesired behavior. Additionally, the efficiency of two already existing corrective measures, namely auxiliary rail and under sleeper pad (USP), is investigated at transition zone.

The track is modeled as an infinite one-dimensional Euler-Bernoulli beam resting on a piecewise-homogeneous and continuously distributed Kelvin foundation. For each mitigation measure, semi-analytical solutions are derived through the Fourier transform method. Regarding TMD analysis, mechanical parameters are optimized by an evolutionary algorithm (NSGA-II), in which the discrepancy between the soft and the stiff tracks’ wavenumbers is minimized. In regard to auxiliary rail, two configurations with multiple number of extra rails (ERs) are evaluated; ERs over soft track only, and ERs over all domains. Additionally, USPs with different stiffness are considered for their arrangement along the track. The efficiency corresponding to each mitigation measure is mainly evaluated through dynamic amplification factor (DAF) and power input.

The system with TMD demonstrates a significant reduction in DAF amplitude corresponding to the load velocity for which the optimization is performed. This improvement is also evident for velocities close to the aforementioned load speed. In fact, the addition of TMD results in presence of a free propagating wave behind the load and decreasing the critical velocity in the corresponding system. The outcomes corresponding to power input suggest a significant reduction in potential damage to the foundation due to the employment of TMD.

Furthermore, the application of ER leads to improvement in dynamic performance of the track by increasing the critical velocity to a larger value, at which the corresponding DAF indicates no reduction. In addition, considering more than one ER along the track does not lead to a noticeably better result compared to when only one ER is added. Moreover, applying ER over soft track leads to inhomogeneity in bending stiffness and mass corresponding to the beam element at transition point. Therefore, the system with ER over all domains indicates a better dynamic behavior. Potentially, less damage to the foundation can be signified in the system with ER according to the power input response.

Finally, USP can significantly affect the equivalent stiffness of the track. It is concluded that the efficiency of USPs in mitigating the amplified response is strongly dependent on their stiffness and arrangement along the track, as well as the stiffness variation in the supporting structure; improper design of USPs alignment can adversely result in even more amplified responses.
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In the Netherlands, there is an increasing need to create residential spaces in its already crowded cities to accommodate the growing population. Constructing high-rise buildings is one way to try to solve the issue. However, high-rise buildings are sensitive to wind-induced vibrations. The accurate prediction of the dynamic response is important in high-rise building design. In building design practice, calculating the dynamic response of high-rise buildings under wind loading typically involves simplifying the structure as a single degree of freedom system, characterised by the first eigenmode properties and subjected to a white noise spectrum. The damping and natural frequency of the building substantially impact its dynamic response. These parameters are challenging to predict with accuracy. Additionally, in the presence of soft soils, soil-structure interaction can play an important role in energy dissipation and influence the structure's natural frequency. In practice, soil-structure interaction is either disregarded or simplified.
In order to assess the effect of soil-structure interaction on the dynamic response of the building, this study models in a robust manner: the foundation, the tower structure, and the wind load. This newly developed model is addressed as the HF model. The investigation consists of a case study and a parametric study. Additionally, this study compares the predictions by the newly developed model with those obtained with a model as specified in the Eurocode. The case study provides a comparison between the models and the measured dynamic response of the New Orleans Tower. The parametric study looks into the influence of soil stiffness and material damping on the dynamic response of high-rise buildings. Furthermore, it investigates how these parameters affect the dynamic response of structures with various slenderness ratios.
The case study was used to demonstrate that the developed model accurately predicts the measured dynamic response of the New Orleans Tower in the along-wind direction. For all the examined dynamic properties, the error compared with the measurements was lower than 7%. In the case of the Eurocode model, the results demonstrate that, when using the natural frequency estimation recommended by the Eurocode, it provides a 30%–35% underestimation of the peak acceleration compared to measurements. This Eurocode model overestimates the natural frequency and overall damping, which causes it to underestimate peak acceleration. However, the natural frequency determined in the design phase of the New Orleans Tower was significantly lower than the value obtained with the recommended estimation method in the Eurocode. With this lower natural frequency, the peak acceleration is overestimated by around 50%. This underestimation of the natural frequency and overestimation of the damping provided acceptable conservative results. Although this showcases the importance of accurate predictions of both natural frequency and damping, having poor predictions that cancel out each other’s effects is not desirable.
The results from the parametric study support the findings from the case study. This shows that the case study’s findings apply to the more extensive range of building configurations investigated in the parametric study. In general, the Eurocode model, for slender structures on soft soil, overestimates the natural frequency and overall damping, which causes it to underestimate peak acceleration.
The parametric study revealed that the building's first natural frequency and global damping ratio are significantly influenced by the soil stiffness and soil material damping, which can result in various effects on the peak acceleration. In the case of soil material damping, not considering it at all or considering a higher value could lead to 20% overestimation and 40% underestimation of peak acceleration, respectively. Soil stiffness had more intricate effects since it affected the natural frequency and the amount of energy dissipated by the soil radiation damping, the soil material damping and the structure material damping. For particular combinations of parameters, soil stiffness had up to a 40% increase in the peak accelerations compared to the fixed foundation.
The results of this research show that the soil stiffness and soil material damping, for the ranges of properties relevant to the Netherlands, significantly influence the accurate predictions of the wind-induced dynamic response of high-rise buildings. Especially, there was found a higher influence on the dynamic response for the extreme cases of high slenderness ratio structures on very soft soils. ... Read more

The Hyperloop is a high-speed means of transport, consisting of a bullet-shape vehicle travelling in a quasi-vacuum tube, electrically powered and moving through an electromagnetic levitating system. This allows the reduction of air resistance and wheel-rail contact friction, which translates in higher speeds for smaller power inputs. In the Netherlands, the Dutch company Hardt Hyperloop, has developed a new design concept of such technology, by means of electromagnetic suspension systems, unlike the most commonly applied levitating techniques.

The main aim of this project is to investigate the stability of the electromagnetic suspension levitation system, study the effect that the implementation of an error-based closed-loop control system has on the system dynamics and investigate the vehicle-structure interaction once a control system has been applied to the system.

Along these lines, the overall infrastructure-vehicle system is modelled through an equivalent two degrees of freedom system. In this manner, the inherent instability of the electromagnetic system is confirmed and the initial vehicle dynamics are highlighted. Afterwards, an error-based closed-loop PD-control system that applies to the system definition and reacts on the uncontrolled system dynamics is implemented and the effect of the control parameters on the dynamics and the stability of the system is studied. A certain stability region in the parametric space is derived, which ensures the stability of the system for significant perturbations of the vehicle from its equilibrium point. Besides, the existence of a subcritical bifurcation with respect to the parameter combination is demonstrated. The safety margin in the time delay of the controller response is studied, so as to define a slack time that accounts for not only processing and sampling delays, but also unforeseen events. Finally, the vehicle-infrastructure interaction is studied and its stability is ensured, by means of the previously defined control scheme.
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The stability analysis of electromagnetic suspension system applied to Hyperloop in simplified two degrees of freedom system has been studied deeply where the track-beam is regarded as a point mass and the effects of velocity and beam are neglected. However, there is little reference on the study of the interaction between electromagnetic suspension system and wave effects.

The main aim of this thesis is to investigate the dynamic behavior of the EMS vehicle-beam coupled system using the one-dimensional model, and illustrate the combined effects of the EMS and guideway on the vehicle instability at different horizontal velocity by comparing with results of EMS system in simplified model and mechanical system in one-dimensional model.

Along these lines, the tube is modelled as an infinite long Euler-Bernoulli beam resting on a homogenous viscoelastic foundation and the vehicle is modelled as a point mass. The response of the system is obtained both numerically and analytically. The values of control gains are determined based on the equivalent simplified two degrees of freedom EMS system. A representative mechanical system is designed to show the anomalous Doppler waves effects. It is found that for inappropriate values of control gains which will cause instability of vehicle at static state, the one-dimensional guideway has positive effects which can stabilize the vehicle at certain range of subcritical velocity, whereas for appropriate values of control gains the EMS system can counteract the wave-induced instability and keeps the vehicle stable at even supercritical velocity. Finally, a method to linearize the system is presented which allows eigenvalue analysis.
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The instability of a moving mass / oscillator due to surpassing the velocity of the minimum group wave velocity (in a continuous homogeneous structure) has been studied extensively and is well understood. In contrary to that, Parametric Instability of a moving mass / oscillator on a continuous periodic structure has been studied less extensive and therefore the mechanism behind the instability is unknown. Literature that is avaiable on this topic mainly focuses on continuous periodic inhomogeneous structures, namely where the foundation is modeled as a continuous periodic inhomogeneous structure. Even less well studied are models where instead of a continuous periodic inhomogeneous foundation discrete periodic supports have been used. So far as known to the author there has also been no studies where the discrete supports are coupled through a medium. In order to solve the transition curves discerning the stable and unstable domains concerning the parametric instability of a moving mass / oscillator the analogy with the Mathieu equation is used, which tells us that the solution on those transition curves will be periodic with once or twice the period of the parametric excitation. In this thesis we have focussed on studying the use of the analogy on continuous structures founded upon periodic supports.

The Mathieu equation describes the motion of a parametric oscillator, for example a pendulum with a length that periodically varies over time. The theory that predicts the solution to the Mathieu equation is called Floquet theory and ascociated with the solution are the Floquet exponents, these exponents dictate whether the solution will be periodic and bounded or unbounded. By solving for the Floquet exponents of the Mathieu one sees that for an increase of the amplitude of the parametric excitation the system will experience a greater exponential growth. For a greater mistuning between the parametric excitation and the natural frequency of the equivalent non-parametrically forced equation we see that the system will experience a smaller exponential growth. Outside the instability domains the solutions will be bounded and periodic and contain a wide variety of frequencies. When damping is introduced, the value of the damping coefficient (if written in the canonical form of a viscously damped single degree of freedom equation) will be subtracted from the value of the undamped Floquet exponents and by that result in an upward shift and narrowing of the transition curves. Furthermore, outside the instability domains we will see two regions: the first lies close the the transition curves and is asymptotically stable with a period equal to that of the transition curve, the second covers the remaining stable region and is asymptotically stable and periodic with a wide variety of frequencies.

Regarding the Parametric Instability of a moving mass / oscillator we have studied three different models: a continuous Euler-Bernoulli beam on periodic spring supports, a continuous Euler-Bernoulli beam on periodic supports that are complex (i.e. modeled as an oscillator between two springs), and a continuous Euler-Bernoulli beam on periodic supports that are founded upon a 2-dimensional lattice. Of these models we have conducted a parametric study as to study what the effects are of the various parameters. We have seen that whenever the ratio between the stiffness of the supports and that of the beam is increased, the instability domains will shift to higher velocities and become wider. For certain combinations also 'islands' of instability may appear, where these 'islands' indicate stable areas between regions of instability. If damping is introduced into the system, this will generally narrow the instability domains and shift them to higher values of the mass and lower values of the velocity. However, for certain parameter combinations adding damping will lead to a widening of the instability domain. In the case of a moving oscillator the instability domains will narrow and be shifted to lower values. If the support is modeled with a mass it will affect the general trend of the transition curves through its own resonance, hence for a complex structure it is advised to model the supports with the correct dynamic equations. Last but not least, if the supports are coupled through a medium (a 2-dimensional lattice in this case) one will generally see a similar effect as adding damping has.

In this thesis we have also studied three real world cases: a regular railway track, a high-speed railway slab-track, and the Hyperloop. In the first case we have seen that Parametric Instability will most likely have no influence. For the slab-track, being much more stiff, Parametric Instability will be important. However, a more extensive study with several cases must confirm this. In the last case, namely the Hyperloop, we have seen that for a moving mass the instability domains are relatively large as compared with the other cases. We have also studied the Parametric Instability of a test-pod, which showed that its instability domains that are negligible. Of course, this was merely a test-pod not capable of transporting people, hence when a larger pod is studied it may be expected that the instability domains may not be neglected. ... Read more

An important subject in the research on the behaviour of railway structures is the validation of numerical models by means of in-track measurements. Many forms of track measurements have taken place all over the world, mainly in the sense of strain and acceleration measurements, but a more unexplored area is that of the direct measurement of stresses in the ballast.
The aim of this research is to find the best way to equip a railway sleeper with measuring instruments in order to use it for validation of computational models. The sleeper must be able to measure the the vertical velocity of the sleeper as well as the normal stresses on the ballast-sleeper interface over time.

In order to predict the quantities to be measured, a finite element model was build for this research with the Kratos open source software package. The model comprises one single sleeper on top of a volume of ballast, both in solid elements. A dynamic load was applied vertically on top of the sleeper to simulate the passing of a double axle bogie. Linear elastic springs were fixed on top of the sleeper to represent force of the rail pulling the sleeper back to its initial place.
In order to analyse the effect of hanging sleepers, interface elements were used in between the ballast and the sleeper to simulate hanging gaps. The idea is that these elements transfer no stresses when the surfaces are physically separated, and adopt Mohr-Coulomb criteria as soon as the surfaces approach each other. This method turned out to be very difficult to implement, despite numerous discussion with the software engineer it was not possible to script this in the FE software in such a way that all calculations converged without any errors.
During the modelling of the sleeper, it was found that the forces on the sleeper are highly dependent on the resistance of the rail. The rails have such a high bending stiffness that they hardly show any curvature over the length of only a few meters, so the sag of the rail is mainly dependent on the behavior of the surrounding sleepers. It was concluded that, to get a good picture of the behaviour, it is not sufficient to model only one individual sleeper, but it is necessary to look at a larger part of the railway track in order to involve the coupling between the sleepers.
The results from the computational model were used to determine the magnitude range and the frequency domain of the values to be measured, in order to be able to select the right measuring instruments. The results were also used to select the right positions for the sensors on the sleeper. Due to the constraints described above, a certain margin of uncertainty has been adopted.

The vertical speed of the sleeper is best measured with accelerometers, the large amount of previous applications of this type of measurement has shown that this measurement works well and will not lead to problems.
It was considered to use pressure cells for the measurement of interface stresses, though this device turned out to be difficult to fix at the sleeper and it gives very little information on the distribution of stresses. It was concluded that the best way to measure the ballast-sleeper interface stresses is by using the matrix based tensile surface sensor (MBTSS). This instrument is able to capture the stress distribution on a surface over time, by measuring the electrical current flow through a matrix of conductive lines, the current is resisted when certain forces are applied on the surface. Tekscan is a manufacturer that offers a wide range of MBTSS types, including sensors previously used in railway measurements. A certain protection will be needed to protect the sensor from being damaged by the ballast particles.
Previous applications of MBTSS in railway structures showed the calibration of the sensor to be very difficult. This presumably has to do with the way the stresses are distributed over the sensor surface. Since the stresses of the ballast are often compressed to very small contact points, it should be made sure the stresses will not get lost between the sensels, that are the points on the surface where the stress magnitudes are measured. The advice is to cover the MBTSS with an under sleeper pad, this is a relatively stiff mat that, in addition to offering protection to the sensors, also spreads the ballast forces. Laboratory tests will have to be performed in advance of the field measurement to test whether a correct calibration is possible. It can not be made sure that a fully successful calibration method will be found and therefor additional measurements are recommended for a validation for the stress magnitudes. A first validation can be found by equating the sum of the vertical forces with the mass times the acceleration of the sleeper. To find the sum of the vertical forces, the load on top of the sleeper at the rail-sleeper connection, has to be measured as well. This can be realized by placing MBTSS between the baseplate of the rail and the sleeper. Similar measurements described in literature proved this type of measurement to be feasible. Furthermore, the result of the acceleration measurement will have to be used here as well. A second validation can be performed by determining the moment distribution over the length of the sleeper, this can be conformed to the magnitude and distribution of the vertical stresses on the sleeper. The most reliable way to perform this validation is by using fiber measurements to find the moment distribution over the whole of the length. The most important positions over the length of the sleeper are under the rails and in the middle of the sleeper, because the peaks in the moment distribution are expected here based on the computational model calculations.
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The offshore wind industry is a quickly growing market because the increasing demand for clean energy sources. Large wind speeds and the abundance of potential wind farm locations make Offshore Wind Turbines an interesting solution. Because of high continuous dynamic loading and extreme environmental conditions, the structural design requires a detailed assessment, especially in the Fatigue Limit State. In this thesis, the focus lies on improving the modeling of monopile foundations for Offshore Wind Turbines, which could pave the way towards more efficient foundation design.

The conventional method of modeling the monopile foundation of an Offshore Wind Turbine is with a nonlinear elastic distributed spring stiffness along the monopile (using p-y curves). Damping related to the soil is considered through either global damping (like Rayleigh damping) or local viscous damping. However, the response of the soil around the monopile under wind and wave loading is better described through a nonlinear hysteretic (rate-independent) model, which is computationally demanding to model in the time domain. Next to that, a conventional frequency domain method can not be combined with any nonlinearity. Therefore, linear elastic models are used to model the soil response in frequency-domain simulations.

The goal of this thesis is to combine a nonlinear hysteretic soil model with a frequency-domain analysis. A response amplitude-dependent linearization of the nonlinear hysteretic element is made. The combination of the response amplitude-dependent element with an iterative solution strategy, the Equivalent Linear method, is shown to approximate a nonlinear time-integration under both harmonic and multiharmonic loading, as long as the nonlinearity is limited.

A nonlinear hysteretic model is fit to available soil reaction data and a response amplitude-dependent linearization is generated. A Finite Element model that can be combined with the Equivalent Linear method is set up and verified with a case study structural model of an Offshore Wind Turbine. The model is subjected to (high) Fatigue Limit State wave loading. The results are compared to both a conventional frequency-domain method (with a linear elastic small-strain soil model) and a nonlinear time-domain method (with a nonlinear elastic soil model). The deflections and deflection spectra in the foundation found through the Equivalent Linear method correspond to results from the nonlinear time-domain method, provided the influence of higher harmonics is limited and the response has a similar amplitude throughout the analyzed time window.

Results from the Equivalent Linear method show that the main frequency of the first resonance peak is around 2% smaller than the first natural frequency of the system, which is consistent with the results found through the nonlinear time-domain method. The identified soil damping in the first mode is 0.64-0.8% critical (4-5% log. dec.), which is similar to other literature. By combining observed system properties with literature about fatigue damage estimation, a hypothesis is stated: the fatigue damage in the foundation calculated through an Equivalent Linear method with a nonlinear hysteretic soil model will be lower than the fatigue damage calculated through a nonlinear time-domain method with a nonlinear elastic soil model.

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Areas of railways with considerable variation of track properties encountered near structures such as bridges and tunnels are referred to as transition zones. Degradation rates at these transition zones are higher compared to the remaining railways. These high degradation rates result in high maintenance expenses. In order to come up with solutions that reduce this degradation and thus also the expenses it is needed to have an understanding of the underlying mechanisms in the railway tracks. This is done by formulating a mathematical model of the railway track which can then be analyzed. Researchers have been using different models for this purpose.

The choice is often made to model the railway track an elastically supported beam. This elastic foundation represents the supporting structure of the railway tracks and its stiffness is based on static load cases. This 1D model is often used due to its relative simplicity compared to other more complicated multidimensional models. This model has been thoroughly analyzed and it has turned out to have an important constraint which is its inability to result in a critical velocity that makes sense for railway tracks. The critical velocity of a railway track is that velocity at which waves travel near the surface of the subsoil of the supporting structure. A vehicle that moves with a velocity close to the critical velocity of the railway track causes a strong amplification of the response. Another important constraint of this model is the fact that there is no possibility to directly adjust the stiffness properties of the different components of which the railway track exists individually.

It is opted in this thesis to adjust the previously mentioned 1D model by the addition of a distributed mass and an extra elastic layer. The upper elastic layer represents the pads and the lower elastic layer represents the remaining of the supporting structure. The idea behind the addition of the distributed mass is to include the activated mass of the supporting structure by the moving load. This is done in order to take the dynamical behavior of the supporting structure into account and thus obtain realistic critical velocities. The idea behind the addition of an elastic layer is that it enables to adjust the stiffness of the pads individually. By using this model one can thus modify the stiffness of the pads at transition zones and study whether it is possible to decrease the degradation which is the initial goal of all studies on transition zones.

In this thesis the adjusted model is analyzed thoroughly for different physical phenomena. Such analyses cannot be found in the literature, to the best of the authors knowledge. The system response has been investigated for a uniformly moving load of a constant magnitude. This has been done for homogeneous properties of the elastic layers and for an abrupt jump in the stiffness of the lower layer. Attention has been given to both the displacement fields of the rails and energy propagation in the system. Also a numerical model has been formulated for other load cases and stiffness properties. In order to simulate infinite system behavior non-reflective boundary conditions have been derived and applied to the numerical model. It has been found that indeed a far more realistic critical velocity can be obtained by making use of the adjusted model. It has furthermore turned out that the system response at a transition zone are very similar for both models for the same ratio of load velocity to the critical velocity. The adjusted model has been investigated extensively in this thesis and it can thus be used as a reference work for future researchers that wish to apply the model. The research that should be performed next in the authors view is to investigate the possibility of reducing the degradation at transition zones by adjusting the stiffness of the pads. ... Read more