As urbanization intensifies and rail and road traffic increase, infrastructure and buildings face growing challenges from ground-borne vibrations, particularly at low frequencies. Traditional mitigation methods, such as heavy masses or stiff trenches, are often ineffective due to the large wavelengths involved. This research investigates metamaterials—mass–spring systems with viscous damping—as a novel solution capable of attenuating low-frequency vibrations through local resonance. Three metawedge configurations—uniform, wave conversion, and rainbow trapping—were evaluated at a target frequency of 10 Hz, typical of soil vibrations induced by trains and traffic. The wave conversion metawedge proved most effective at mitigating surface vibrations, while the rainbow trapping metawedge minimized impact on the surrounding environment by dissipating rather than redirecting energy. Based on these findings, design criteria were developed, including the relative resonator bandwidth (RRBN), optimal mass range, and resonator spacing considerations. Additionally, the potential of impact-based resonators to enhance energy dissipation by exciting higher frequencies was explored. While promising results were observed in a simplified two-degree-of-freedom system, numerical simulations on a soil domain revealed unexpected amplification, highlighting the need for further investigation. This work establishes a foundation for the practical design of metawedges and identifies directions for future research into nonlinear and impact-based vibration mitigation strategies.

The study explores different system identification techniques that utilize machine learning, including the Restoring Force Surface (RFS) method and Sparse Identification of Nonlinear Dynamics (PySINDy).
These methods have potential to help uncover physical models for soil-pile interaction.
To test these methods , the research first applies them to well-known benchmark systems—simple mechanical models with known nonlinear behaviours. This ensures that the identification techniques work correctly before applying them to real pile-driving experiments.
The experimental data comes from lab-scale vibratory pile-driving tests using strain gauges and accelerometers. The study analyses how forces acting on the pile change over time, focusing on both the tip and shaft resistance. Various mathematical models are tested to see which best captures the nonlinear behaviour.

Understanding the dynamic behaviour of soil is crucial for the design of geotechnical structures, particularly for offshore wind turbine foundations. This study evaluates the performance of a nonlinear numerical model in accurately capturing soil response under dynamic shear loading, comparing its simulated response to experimental data obtained from Resonant Column Tests (RCT). The research systematically investigates the role of higher-order odd harmonics in the numerical solution, assesses the differences between linear and nonlinear models, and validates the nonlinear model against experimental results.

The findings reveal that higher-order harmonics contribute negligibly to the numerical response, simplifying the model's implementation. Furthermore, the nonlinear model effectively captures the resonance shift observed in experimental data, outperforming the linear model, particularly at higher strain levels where soil softening effects become significant. While the model demonstrates a strong correlation with experimental results, discrepancies arise in high-strain scenarios, primarily due to limitations in damping representation. To address this, corrective approaches such as a damping correction factor and strain radius adjustments were explored, improving model accuracy but failing to eliminate errors entirely. The study highlights the necessity of incorporating a strain-dependent damping formulation to enhance predictive capabilities for high-strain soil behaviour.

The results confirm that nonlinear numerical modelling is a valuable tool for capturing essential soil dynamics, but further refinements in damping representation are required to improve alignment with experimental data. Future research should focus on advanced damping models to ensure greater accuracy in high-strain dynamic soil simulations.

This thesis studies the use of metamaterials for mitigating train-induced ground-borne vibrations, a growing issue with the projected increase in train transportation. Traditional mitigation measures such as trenches often fall short, particularly at low frequencies and small incidence angles. Metamaterials, engineered to alter wave propagation properties, offer a novel solution by creating frequency bands that attenuate vibrations. This study begins with an one-dimensional model of an Euler-Bernoulli beam on a visco-elastic foundation, where metamaterials are modeled as local mass-spring-dash pots and single-degree-of-freedom resonators. This model facilitates an analytical study into wave propagation and band gap formation using Floquet analysis, which identified band gaps arising from both local resonances and the periodicity of resonator arrangements.

The study progresses by examining a finite periodic system using a numerical model. This involves comparing the dispersive properties of the finite system with those observed in its infinite counterpart. The results demonstrate an excellent agreement between the two. A significant focus is on the "metawedge", a metamaterial configuration with unit cells varying in natural frequency, allowing for broadband frequency targeting. This configuration enables elastic rainbow trapping and wave-mode conversion, with detailed three-dimensional analysis performed using FEMIX to explore these phenomena further. The three-dimensional model consists out of a homogeneous elastic half-space with single-degree-of-freedom resonators placed on top of the surface. The results demonstrate that the proposed metamaterial solutions are effective in mitigating low-frequency vibrations caused by trains across all incidence angles. The findings indicate that the classic metawedge configuration traps waves, by slowing them down, while the inverse metawedge accelerates waves, facilitating wave-mode conversion.

The maintenance and repairs of transition zones pose significant challenges in the railways industry due to their accelerated degradation rates in comparison to free tracks. These zones, characterized by track property variations, amplify their response when a source travels along the tracks. The resulting amplifications in stress and strain fields lead to differential settlements, affecting both track's stability and passenger comfort. This study investigates the influence of incorporating active control forces and moments at the interface of transition zones to mitigate the excessive degradation of soft domains.

Three 1-dimensional models are developed, which include active control forces and moments as a novel method to minimize the amplification of the response in the soft domain of transition zones, as well as, the derivation of these forces. The purpose of these three models is to give the reader an inside view of the method to derive these active control forces with models that increase in complexity.

The first model involves an Euler-Bernoulli beam resting on a piece-wise inhomogeneous Winkler foundation. The second model extends this by including a shear beam and a second layer of foundation, with the first layer being homogeneous and the second layer piece-wise inhomogeneous (Kerr foundation). The third model is a hybrid model between the first two, on which the soft domain is represented by the description of the second model, and the rigid domain by the description of the first model. Numerical solutions in the time-domain were applied to these models, and the study focused on a transition zone subjected to a constant amplitude moving load with constant velocity, traveling from a soft to stiff domain. The purpose of the first model is to give the reader a general idea on the derivation of a very simplistic model. The second model's purpose is to better represent the different elements of a railway structure, on which the shear beam and the lower layer of springs represent the mobilised soil under the tracks, while the top layer of springs and the Euler-Bernoulli beam represent the ballast, the sleepers and the rail. Finally, the third model was made to represent a transition zones, on which the soil is discontinued due to a man-made structure, e.g. a concrete bridge, which leads the structure under the ballast, in the rigid domain, to be consider infinitely stiff and to be represented just by an Euler-Bernoulli beam on a Winkler foundation.

Findings reveal that the active control forces and moments are capable of fully mitigating the dynamic amplification in soft domains of transition zones, however, they increase the dynamic amplifications in the stiff domain. Moreover, the shape that these forces take over time is dictated by the interaction between both domains of the transition zone, when the interface of the transition zone has continuous elements, the forces take a similar shape to the eigenfield of the system, while when there is discontinuous elements over the interface, the forces take a 'flipping' shape. Furthermore, of the two parameters studied (velocity of the moving load and vertical stiffness), the dominating parameter in the response of the system depends upon the regime that the system is being subjected to. For relatively low and extremely high velocities of the moving load, the system is dominated by the vertical stiffness ratio, while for medium velocities of the moving load, the system is dominated by the velocity of the moving load. Finally, transition zones with discontinuous elements require significantly more energy to be absorbed and added into the system by the active control forces to mitigate the dynamic amplifications in the soft domain of the system.

These thesis offer valuable insights for preliminary designs of active control forces aimed at diminishing the dynamic amplification of soft domains of transition zones railway.

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.

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.

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.

Soil exhibits hysteretic damping. A commonly used implementation of this type of damping are the Masing rules. They consist of a loading and an unloading branch, dened as a piecewise function and having a nonsmooth character. This paper presents a framework how steady-state solutions of the motion of a soil column, with nonlinear hysteretic damping, can be obtained by using a variant of the Harmonic Balance Method (HBM), the Alternating Frequency/Time Harmonic Balance Method (AFTHBM), applied on a discretised soil column (a lattice system). The theoretical background of the method is presented, as well as its application to a soil column with both shear strain-dependent stiness and damping. Results show that the AFTHBM is an efficient method for obtaining steady-state results for nonsmooth nonlinear behaviour, which is in this paper presented by simulations for nonlinear media. The results of the AFTHBM are sensitive to time sampling and convergence tolerances; nonetheless, if these parameters are properly chosen, the application of AFTHBM leads to good results.

Railways and other sources of environmentally induced vibrations often lead to annoyance and sometimes property damage. In this framework, transition zones are deemed as the most sensitive locations on the railway track, especially to high vibrations and impact loads. This causes high maintenance costs and is often very annoying, as the availability of the track gets limited during maintenance processes. One of the main reasons of this problem is the stiffness change of the railway supporting structure which is sometimes abrupt. This thesis will shed some light on the factors playing roles in altering the vibration intensities in level crossings. Moreover, the effects of these factors on ground vibrations will be highlighted. Further on, a model is presented which incorporates all these parameters. This model can be used to predict the change in ground vibrations in level crossings. The objective of this thesis is to determine the influential parameters in terms of the response vibrations in the surroundings of railway tracks. On that account, following an in-depth literature study, and based on the analysis of the measurements performed at Movares, it was suggested to investigate three factors being the ambient temperature effect, the hanging sleeper scenario and the inhomogeneity of foundation and analyze their impacts. The in-situ measurements illustrated a correlation with temperature, where the vibrations are amplified during hot periods and in the summer season. Besides that, the reports indicated the presence of the hanging sleeper scenario, where the suspension between the rails and the foundation is no longer active. It was also reported that locations with inhomogeneous foundations experience higher vibrations than those with quasi-homogeneous foundations. On those grounds, it was decided to study the effects of the hanging sleeper scenario, the ambient temperature and the presence of a slab-track crossing on the track. A complete vehicle/track/soil numerical model has been used in the parametric study in order to assess the factors affecting the response vibrations induced by trains and to quantify their impacts. Along with that, the numerical results have been validated, to some extent, with analytical results. More specifically, the steady-state response obtained with both approaches are compared present a good agreement. The results exhibit that the hanging sleeper phenomenon has a substantial effect on the vibrations. Furthermore, the existence of a level crossing (representing a foundation inhomogeneity) proved to be of significance as well. Lastly, the ambient temperature possesses a limited impact which could turn severe in extreme conditions.

Due to the high cost of long spanned bridges or deep tunnels, the interest into a submerged floating tunnel (SFT) has reemerged. In the last twenty years many studies on the SFT have been performed. This report investigates the interaction between a single vehicle, moving at constant velocity, and the SFT. The research is limited to the dynamic response, of both vehicle and tunnel, in only the vertical direction. The SFT is moored to the bed floor and is further kept in position by the buoyance force.
The main question to be answered is: Does the vehicle’s inertia, the design of the SFT (i.e., the length of the tunnel) or the vehicle parameters, because of this dynamic loading, play a significant role in the Ultimate Limit State of the tunnel or the Service Limit State for passenger.

When a vehicle moves across a bridge, there is always an interaction between the vehicle and the bridge and within the vehicle itself. It is important to predetermine the vibrations in the bridge and vehicle. This way, the Ultimate Limit State (ULS) and Serviceability Limit State (SLS) can be more accurately determined, compared to a static approach. Ultimate Limit State refers to the safety of the bridge and vehicle. Serviceability Limit State refers to the usability of the bridge and comfort of the passengers. The behaviour of a bridge subjected to a moving load has been researched before. In these studies, the moving vehicle was simplified to a one or two degrees of freedom mass-spring system, which might be insufficient. This thesis aims to investigate the influence of a multiple degrees of freedom oscillator, where the wheels, bogies and wagons are taken into account in the model. The main goal for this thesis is to investigate and describe the vibrations when a vehicle crosses a bridge. More specifically, the importance of the inertia of the vehicle will be assessed for the serviceability limit state (SLS), and ultimate limit state (ULS).

In this bachelor thesis a theoretical model is developed for the dynamic loading of a simply supported beam.