Hyperloop is a novel high-speed transportation system that combines electromagnetic suspension with a low-pressure environment within a tubular shell to enable travel velocities well above those of existing high-speed rail. While this concept promises high efficiency and reduced resistance, it also introduces dynamic effects and potential instabilities that become increasingly significant at such speeds. This thesis investigates these phenomena with particular focus on the influence of periodic supports and shell behaviour on the structural response, aiming to provide a more realistic guideway model than those previously adopted in the literature.

The guideway is modelled as a thin-walled cylindrical shell with discrete supports, while the vehicle is represented as a moving mass suspended through a non-contact electromagnetic force governed by a proportional–derivative control system. This setup enables more physically representative modelling by incorporating discrete support spacing and allowing for the inclusion of circumferential pre-stress from the vacuum environment, a feature intrinsic to Hyperloop systems.

Two themes are central to the study. The first concerns the steady-state response of the shell under a constant moving load, which isolates the structural behaviour of the guideway. Using a semi-analytical approach, the governing equations are projected onto circumferential modes, transformed into the frequency–wavenumber domain, and solved with a periodicity condition to reconstruct the steady-state response. This analysis shows that periodic supports strongly modify wave propagation, leading to multiple resonance peaks, including in ranges where operational velocities may lie. As a result, simplified continuous models risk overestimating safe operating speeds and overlooking significant amplifications. The results also demonstrate how geometric and damping parameters affect the critical velocity, offering practical strategies for vibration reduction. Furthermore, the inclusion of circumferential pre-stress is shown to be essential, since vacuum-induced compression reduces the effective stiffness of the shell and shifts the system closer to resonance conditions.

The second theme addresses the stability of the coupled vehicle–structure system, where two distinct instability mechanisms are considered: wave-induced instability from anomalous Doppler waves, and electromagnetic instability from the suspension control system. The periodicity of the support structure enables the potential manifestation of wave-induced instability in the form of parametric instability, which is absent in continuously supported models. The analysis is carried out using a semi-analytical approach that combines Floquet theory, Fourier expansion, and harmonic balance to reformulate the problem as an eigenvalue analysis, from which stability boundaries are identified. The findings highlight the need for careful controller design at operational speeds, with periodicity shown to play a role in shaping instability zones.

Overall, this research demonstrates the importance of accounting for both shell behaviour and support periodicity when assessing the dynamic performance and stability of Hyperloop systems. In doing so, it advances the understanding of Hyperloop dynamics and provides a foundation for future research and the further development of this emerging mode of transportation.

Nations worldwide are striving to meet the climate goals set forth by the Paris Agreement and reduce greenhouse gas emissions, with offshore wind farms (OWFs) playing a crucial role. However, OWF construction generates underwater noise from impact piling, which is harmful to marine life. This study examines the effects of PULSE – a novel mitigation measure acting as a spring-damper system between the hydraulic hammer and monopile – on underwater noise and its interaction with air-bubble curtains. Using the semi-analytical SILENCE model, the complete pile-water-soil system is simulated to evaluate noise levels, with the model’s predictions compared to field data from a recent German project. Results show that PULSE effectively reduces both Sound Exposure Level (SEL) and Peak Sound Level (Lpeak) by shifting acoustic energy from higher to lower frequencies. When combined with air-bubble curtain configurations, noise reductions are greater, but the effectiveness of PULSE diminishes. Consequently, the individual performance of PULSE and air-bubble curtains cannot be linearly added to predict their combined effectiveness. In conclusion, while PULSE effectively mitigates underwater noise, its combined use with air-bubble curtains impacts overall mitigation efficiency and requires careful evaluation.

Several studies have highlighted the negative impact of underwater impact pile driving on
marine life, underscoring the need for effective noise mitigation systems (NMS). While bubble
curtains are commonly used, recent research also focuses on near-pile NMSs. For instance, with resonating devices such as Helmholtz resonators, which are known for their tunability and effectiveness in specific frequency ranges. However, the potential for broadband noise mitigation using arrays of Helmholtz resonators in offshore impact pile driving remains uncertain. This thesis aims to address this research gap.

Locally resonant acoustic metamaterials, characterised by unusual properties such as negative or zero-valued effective mass, have shown potential for broadband noise mitigation. This thesis defines an acoustic metamaterial composed of Helmholtz-type resonators and investigates its combined effects. The study employs the finite element method (FEM) and the lumpedcomponent method to define the resonator characteristics of a reference Helmholtz-type resonator. Subsequently, the boundary element method (BEM) is used to examine the acoustic behaviour of horizontal arrays of Helmholtz-type resonators, appropriately named Helmholtz-type acoustic metamaterials, in the frequency domain. Multiple configurations of these systems are analysed. Finally, a case study approximating the pressure field radiated by a vibrating monopile excited by an impact hammer is conducted in the time domain using the FEM.

The results indicate that Helmholtz-type acoustic metamaterials amplify sound pressure at
frequencies below the natural frequency of the individual resonators and reduce it at frequencies above. Functional grading, achieved by incrementally decreasing the natural frequencies of the individual resonators in steps of up to 3 Hz along each horizontal array, can reduce the low-frequency amplification while maintaining the high-frequency attenuation. In a vertical system of Helmholtz-type acoustic metamaterials similar behaviour is observed. A vertical system comprising of horizontal arrays of 20 resonators with a horizontal spacing of 0.1 meter and a vertical spacing of 1 meter between each array shows a promising balance between attenuation and unwanted amplification. However, the system’s performance is sensitive to maintaining optimal volume of encapsulated air within the resonators, as the target frequency can significantly increase if a large percentage of the encapsulated air is lost. The transient response behaviour aligns with frequency domain observations, showing low-frequency amplification and high-frequency mitigation. Additionally, it is found that the orientation of the resonators does not significantly affect the transient response. Finally, it is important to note that mechanical coupling effects, which are not included in this study, may introduce additional low-frequency interactions.

This study demonstrates the potential of using Helmholtz-type acoustic metamaterials in near-pile NMSs for offshore impact pile driving, emphasising the system’s sensitivity to the frequency of the applied force and the importance of air volume maintenance. The findings suggest that while Helmholtz-type resonators can effectively mitigate noise in specific frequency ranges, careful configuration is crucial for achieving broadband noise mitigation and for minimising the risk of unwanted amplification of the pressure field.

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.

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.

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.

To reduce the construction industry’s negative influence on global climate, emissions related to concrete consumption need to be addressed. This implies reducing the amount concrete used, by creating material-efficient structures. One of concrete’s main advantages is that it can be moulded into virtually any shape. Despite the fact that modern digital design tools enable the effortless design and calculation of lightweight and graceful structures, this potential often goes unrealised. This can be attributed to the challenges associated with constructing intricate and custom geometries using conventional formwork techniques that depend on single-use cut timber or milled foam. Not only do these methods make the construction of these types of structures labour and cost intensive, they also cause them to be wasteful.

KnitCrete, which uses knitted technical textiles as stay-in-place moulds for concrete structures, has proven to be a solution for building doubly curved structures, eliminating the need for time-consuming, costly, and wasteful moulds. However, due to its inherent high flexibility and the challenges of predicting and controlling the geometry during the casting process, the technology relies on coating procedures using high-strength cement paste coating to stiffen the geometry before concrete can be poured.

This research addresses both issues and proposes a design approach, which models the deformation behaviour of the uncoated knitted formwork under concrete pressure to determine the final geometry of flexibly formed concrete structures, hence gaining better understanding on the deformation behaviour of knitted textile formworks and bypassing the stiffening steps during fabrication.

Developing a method to predict the final geometry of flexibly formed concrete structures involves various research disciplines, including material science, and structural mechanics. The research approach is divided into three parts. The first part investigates the stress-strain relationship of various textiles with different knitting patterns, alongside the rheological and mechanical strength properties of different cementitious mixtures. The second stage focuses on developing (semi-)analytical models to predict the deflection behaviour of membranes subjected to varying boundaries, loads, and material properties. Finally, the accuracy of the models are validated by the construction of multiple prototypes.

In conclusion, this thesis introduces a fabrication system that exploits the deflection behaviour of flexible formworks to create funicular shell structures and lays the foundation for implementing (semi-)analytical approaches to model these deformations.

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.

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.

The Dutch government provides a calculation method to determine the risks to society outside the boundaries of institutions handling Dangerous Goods (the risk affecting External Safety). The current method to calculate the risk affecting External Safety for train marshalling yards is deterministic, outdated, and not transparent. This thesis aims to improve the calculation method regarding rear-end collisions in automated marshalling. It provides a reliability-based approach to the study case Kijfhoek and uses a multi-body dynamic model to simulate the collisions. A Monte Carlo simulation is performed implementing over twenty-five parameters to determine the probability of damage in case of a rear-end collision. From the results, a simplified method is designed to assess the probability of damage to the wagon’s structure. This method uses a newly found relation to determine the absorbed energy at the impact interface in case of a collision. Furthermore, the simplified method reduced the calculation to five parameters and an analytically solvable Limit State function. A first-order reliability method shows that the impact velocity is the single most important parameter in determining the probability of damage.
The simplified method also allows for site-specific values and gives insight into the system and the most important parameters. It is recommended that this method, to determine damage to especially tank wagons in rear-end collisions, is used to improve the existing calculation method for determining the risk affecting External Safety.

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.

A new form of high-speed transportation, which involves a magnetically levitated vehicle that travels through a vacuum tube, is currently under development. Those parts of the trajectory along which the tube is supported by columns---which possess both axial and bending stiffness---requires the use of a model that allows to study a form of instability that is inherent to this type of support. Specifically, the stability is studied of a point mass with a lateral and vertical degree-of-freedom that moves with constant velocity along an infinite Euler-Bernoulli beam on coupled lateral-vertical periodically inhomogeneous foundation. The beam model is able to deflect in both the lateral and vertical direction and the concentrated mass is attached to this beam by a lateral and vertical contact spring. With the help of a perturbation method it is shown that the system's vibrations can become unstable. As for the model that only exhibits degrees-of-freedom in the vertical direction, the underlying physical phenomenon is parametric resonance, which occurs because of the periodic variation of the foundation stiffnesses. For the lateral-vertical model, this form of instability is referred to as combination parametric resonance, which yields four instability domains in the velocity-mass parameter space as opposed to the one domain for the vertical-only model. The center lines of these four domains depend strongly on the period of inhomogeneity; the larger the period, the higher the velocity at which instability occurs. Vehicle-structure interaction (i.e. the maglev system) also affects the center lines considerably; including contact springs between the beam and the point mass reduces the velocity at which instability occurs. To obtain the complete instability domains and to be able to investigate the mitigating effect of foundation damping, the method from another paper is recommended to be used for follow-up research.

The strive for cleaner energy sources is one of the most demanding problems the world faces today. The role of offshore wind in the energy transition is becoming increasingly relevant. One of the areas where the industry expects to reduce conservatism and uncertainty in design is the interaction of the foundations of offshore wind turbines with the surrounding soil. Currently, it is known that the dynamic behavior and natural frequencies of the offshore wind turbines in design and in actual measurements do not match. This is mainly the result of inaccuracy and lack of understanding of the soil behavior and the interaction with the foundation piles. Therefore, this study is aimed at developing analytical and numerical methods to describe the nonlinear dynamic soil response as excited by a harmonic excitation representing a Dynamic Cone Pressure Meter. Measuring the dynamic soil properties more accurately and using them in design will reduce the uncertainties and conservatism in the design of foundation piles.

This study is divided in two main parts. In the first part a soil column is modeled. The numerical and semi-analytical methods to describe the one-dimensional linear and nonlinear dynamic soil response to a prescribed displacement are developed. The linear solution is obtained first since it is easier to get and interpret. It is also used to study the extent to which the nonlinearity influences the soil behavior. In the nonlinear analysis strain-dependent shear modulus and damping ratio are used. These are essential input parameters for conducting a ground response analysis. In this study, the curves constructed using the hyperbolic soil model are used for the expressions of strain-dependent shear modulus and damping.

In the second part of the study, the cavity expansion problem is modeled to simulate a Dynamic Cone Pressure Meter (DCPM) that will be used for in-situ investigation of dynamic soil properties. The response of the soil to a prescribed displacement/ stress at the cavity is found using the numerical method and the HBM. Using the HBM different assumed solutions are implemented to study the influence of the higher harmonics. The HBM is assessed for both a finite and an infinite medium, meaning when standing waves and propagating waves are formed respectively.

Overall, the HBM was found to have a comparable level of accuracy with the numerical method in modelling the nonlinear response of the soil column and the cavity problem. The difference results due to the limited number of harmonics used in the HBM and also due to the tolerances of the MALAB solvers used such as bvp5c and ode45. Both methods show that the nonlinearity affects the response considerably. As the nonlinearity increases, the amplitude and the phase shift of the response change. While it may be hard to interpret the results judging from the numerical solution only, they become much easier to understand by comparing them with the harmonic balance method. Moreover, while it takes hours to obtain the numerical solutions for different forcing frequencies, the frequency response function is obtained in a couple of minutes through the harmonic balance method. This shows that the harmonic balance method is a computationally efficient and powerful tool. Overall this study is an important step of the project that aims to develop a prototype of a DCPM for in-situ soil investigations. The DCPM will pave the way for the reduction of uncertainty in the soil-structure interaction models and help the offshore wind industry to increase cost efficiency while harvesting energy from a sustainable natural resource.