In this paper, we investigate the response of a cavity embedded in an elastic half-plane (2D) subjected to a harmonic SH wave. In previous work, the method of conformal mapping and the indirect boundary element method (indirect BEM) were employed to solve the 3D wave scattering from a cylindrical tunnel embedded in a half-space. Inaccurate results were obtained particularly at high frequencies (method of conformal mapping). Therefore, in this study we focus on a comparison of the two methods with the method of images, which serves as a benchmark solution. Through a systematic evaluation, we confirm that the two methods accurately work within the complete considered ranges of the dimensionless frequency and the embedded cavity depth. This suggests that representing the waves scattered from the free surface by cylindrical waves in the method of conformal mapping is the cause of the inaccuracies at high frequency in the 3D problem; the cylindrical waves are probably not able to fully capture all wave conversions taking place at the free surface. The presented results reveal significant effects of the system parameters on the responses. The system's response curves display nearly equally spaced resonances, which is in line with those of the 1D shear layer subject to bedrock motion, while similar response curves for the 3D case do not have this feature.

Railway transition zones (RTZs) are subjected to amplified degradation leading to high maintenance costs and reduced availability of tracks for operation. Over the years, several mitigation measures have been investigated to deal with the amplified degradation of these zones. However, to ensure the robustness of a design solution, it must be evaluated for critical conditions arising due to certain loading and track conditions. In this paper, the critical load conditions arising due to different velocities (sub-critical, critical and super-critical), the direction of the moving load, the combination of inertial effects and track imperfections (non-straight rail and hanging sleepers) and passage of multiple axles (using a comprehensive vehicle model) are investigated for an embankment-bridge transition. The results are then compared against the recently proposed design of a transition structure called SHIELD (Safe Hull Inspired Energy Limiting Design) to evaluate its performance under these critical conditions using various vehicle models and finite element models of the RTZs. It was found that the novel design of the transition structure effectively mitigates dynamic amplifications and results in smooth strain energy distribution across sub-critical, critical, and super-critical velocity regimes in both directions of movement implying that the expected operation-induced degradation will be as uniform as possible in longitudinal direction. Furthermore, even though this transition structure is designed to deal with initial track conditions (perfectly straight track), its superior performance is not confined to tracks in perfect condition; it also efficiently addresses adverse effects from track imperfections such as hanging sleepers and non-straight rail. In the end, this work demonstrates the robustness of the design solution for all the critical conditions under study.

Transition zones, characterized by significant variation in track properties (e.g., foundation stiffness) near rigid structures like bridges and tunnels, necessitate more frequent maintenance compared to standard track sections due to higher levels of differential settlements observed at transition zones. Field measurements on one-way tracks reveal asymmetric settlement patterns (i.e., different settlement in the soft-to-stiff vs. stiff-to-soft transitions), yet existing literature often investigate either one or the other transition type without investigating the potential limited validity of results. This study investigates the similar aspects as well as the dissimilar ones regarding the behaviour of soft-to-stiff and stiff-to-soft transitions. Modelling results show that the behaviour of the two transitions can be considerably different. These results strongly suggest that for a mitigation measure to be efficient, it may be necessary to have different designs for the two types of transition wherever possible (i.e., in one-way tracks). This study can help researchers and engineers understand the different degradation patterns obtained using more complex models or from field measurements.

In this paper, we study the stability of a simple model of a hyperloop vehicle resulting from the interaction between electromagnetic and aeroelastic forces for both constant and periodically varying coefficients (i.e., parametric excitation). For the constant coefficients, through linear stability analysis, we analytically identify three distinct regions for the physically significant equilibrium point. Further inspection reveals that the system exhibits limit-cycle vibrations in one of these regions. Using the harmonic balance method, we determine the properties of the limit cycle, thereby unraveling the frequency and amplitude that characterize the periodic oscillations of the system's variables. For the varying coefficients case, the stability is studied using Floquet analysis and Hill's determinant method. The part of the stability boundary related to parametric resonance has an elliptical shape, while the remaining part remains unchanged. One of the major findings is that a linear parametric force can suppress or amplify the parametric resonance induced by another parametric force depending on the amplitude of the former. In the context of the hyperloop system, this means that parametric resonance caused by base excitation—in other words by the linearized parametric electromagnetic force—can be suppressed by modulating the coefficient of the aeroelastic force in the same frequency. The effectiveness is also highly dependent on the phase difference between the modulation and the base excitation. The origin of the suppression is attributed to the stabilizing character of the parametric aeroelastic force as revealed through energy analysis. We provide analytical expressions for the stability boundaries and for the stability's dependence on the phase shift of the modulation. Finally, we emphasize that suppressing parametric resonance through an added, linear state-dependent force with the coefficient having the same period as the original force can be achieved in other physical systems too.

Maglev and the newer Hyperloop technologies are advanced transportation systems that eliminate wheel–rail friction using electromagnetic suspension/levitation. The electromagnetic suspension is inherently unstable and requires a control strategy for safe operation, which has been previously studied in the context of Maglev. However, the interaction between electromagnetic instability and another instability mechanism, known as wave-induced instability, occurring at high vehicle velocities, has not been explored. This interaction between two distinct instability mechanisms is the focus of this study. From a practical perspective, this study examines the stability of magnetically suspended vehicles (e.g., Maglev or Hyperloop) in relation to vehicle velocity and control gains. To account for this, this study properly includes the infinite guideway, thus allowing vehicle velocity to influence system stability. The results show that at sub-critical velocities, the guideway's reaction force helps suppress perturbations and stabilize the system, with instability driven solely by improper electromagnetic control. However, at super-critical velocities, wave-induced instability drastically reduces the stable parameter space. This study further proposes a methodology to distinguish the contribution of each instability mechanism to the overall system stability, which is important for efficient mitigation measures. The findings reveal that beyond a certain super-critical velocity, wave-induced instability dominates much of the control-gain plane, with the control strategy effective in only limited regions. In conclusion, the study recommends revising control design strategies, as solely focusing on maximizing energy dissipation through control can trigger wave-induced instability. A more effective approach balances energy dissipation with avoiding the activation of wave-induced instability by steering clear of problematic vibration frequencies. These insights provide guidance for improving control strategies.

A novel nonlinear 1-D gradient model has been previously proposed by the authors, combining (i) the higher-order gradient terms that capture the influence of material micro-structure and (ii) a nonlinear softening material behavior through the use of a hyperbolic constitutive model. While the previous study focused on the existence and properties of solitary-type waves, the current study focuses on the characteristics of the transient wave propagation in the proposed model. Findings show that as nonlinearity increases, the bulk of the wave slows down, and its shape becomes more distorted in comparison to the response of the linear system. The energy analysis reveals that, unlike the linear system, the nonlinear one continuously exchanges energy, in which the kinetic energy decreases over time while the potential one increases. Furthermore, the spectral (wavenumber) energy density of the nonlinear-elastic system presents peaks at large wavenumbers. However, these are eliminated when a small amount of linear viscous damping is added indicating that they are not physically relevant. A notable feature that persists despite the presence of damping is the formation of small-amplitude waves traveling in the opposite direction to the main wave. Generalized continua, like gradient elasticity models, miss the small energy scatter by the micro-structure. This study shows that adding material nonlinearity to a homogeneous generalized continuum can capture reverse energy propagation, though at much smaller magnitudes than the main wave. These findings shed light on the characteristics of the transient wave propagation predicted by the proposed nonlinear 1-D gradient model and its applicability in, for example, predicting the seismic site response.

The Boundary Element Method (BEM) based on the linear potential flow theory has shown to produce accurate results at low computational costs in numerical modelling of the hydrodynamics of Wave Energy Converters (WECs). WAMIT, Nemoh and Capytaine are some of the most popular frequency domain BEM solvers used in the response analysis of various WECs. Hydrodynamic Analysis of Marine Structures (HAMS), another open-source BEM solver gaining traction, has been applied to the analysis of single WECs considering rigid body motions providing highly accurate solutions at lower computational costs as compared to other solvers. This research extends its current capabilities to model structures with constraints by applying the generalized modes approach. Results presented include of a cross-model validation with commercial solver WAMIT, of the hydrodynamic coefficients and exciting forces considering flap converter. Furthermore, a comparison is shown with popular open-source solver Capytaine for the same case, since it has parallelization.

Wave energy has immense potential and can provide at least twice as much electricity as globally produced now due to its high energy density. Apart from the vast accessibility of the resource, waves are more predictable and available throughout the year when compared to other forms of renewable energies. This makes the development and utilization of wave energy tech-nologies immensely important, in order to meet the renewable energy targets, an example of which is the 40GW by 2050 set as the offshore energy strategy of the European Commission. For wave energy to become a commercially viable power source, in-dividual wave energy converters (WECs) need to be deployed in large numbers similar to what can be seen in the wind in-dustry. Therefore, numerical tools simulating multiple inter-acting devices becomes highly relevant. This research utilizes the new open-source Boundary Element Method (BEM) based solver HAMS-MREL to analyse the hydrodynamic interactions of mono-array farms of point absorbers inspired by the state-of-the-art Corpower C4 point absorber device in various configurations subjected to waves in different directions. The obtained responses are used to estimate the power absorbed by the arrays in different configurations to obtain the Array Power Matrices, which can be used to study the variability of the q-factors in different sea states and different directions. Furthermore, the obtained Array Power Matrices are used to estimate the power absorbed by the array configurations in the North Sea. This can be a powerful tool for the analysis of the best wave energy farm configurations as it employs a computationally efficient frequency domain-based solver.

Railway transition zones present a major challenge in railway track design mainly due to abrupt jumps in stiffness and differential settlements that result from crossing stiffer structures such as bridges or culverts. Despite numerous efforts to mitigate these transition effects at both the superstructure and substructure levels, a comprehensive solution remains elusive. Substructure-level interventions have demonstrated some effectiveness but are often cost-prohibitive and challenging to implement in existing operational railway transition zones. In contrast, mitigation measures at the superstructure (rail, sleepers, rail-pads, under-sleeper pads) level can be easily installed but have shown limited improvement in site measurements. This study evaluates the influence of different sleeper configurations in transition zones and reduced sleeper spacings on the operation-driven dynamic amplifications in railway transition zones, employing a recently proposed criterion based on the total strain energy in the track-bed layers (ballast, embankment, and subgrade). In addition to this, the influence of the loss of contact between sleepers and ballast (i.e., hanging sleepers), which typically results from the differential settlement, is studied. The first part of the paper provides useful insights regarding the interventions (and/or initial design) in the sleeper configuration and spacing, whereas the second part of the work highlights the need for interventions to deal with the loss of contact between sleeper and ballast. A 2-dimensional finite element model of an embankment-bridge transition was used for the analysis. The results show that it is not possible to mitigate the transition effects completely using the interventions involving sleeper spacing and configuration.

Ocean wave energy has immense potential and can provide at least twice as much electricity as globally produced now due to its high energy density. In order to efficiently extract this energy and make this commercially viable, Wave Energy Converters (WECs) need to interact with the resource in an optimized way for the expanse of sea states. This interaction is critical to power production by these devices and hence an accurate modelling of this is paramount. The Boundary element method (BEM) based on the linear potential flow theory has yielded accurate results at low computational costs when compared to complex Computational Fluid Dynamics methods. Hydrodynamic Analysis of Marine Structures (HAMS) and Capytaine are recently developed open-source BEM frequency domain solvers, originally created for large marine structures. These solvers have since been utilized for studying wave energy converters, though, for very few converter geometries. Owing to the implementation of parallelization in both HAMS and Capytaine, both these solvers could be capable for significantly lower computational costs as compared to the traditional BEM solvers such as Nemoh. This research aims to compare hydrodynamic coefficients and computational costs in Nemoh, HAMS and Capytaine for various WEC geometries.

The increasing demand for renewable energy sources is driving a significant rise in the adoption of offshore wind energy. Offshore wind turbines are typically supported by large foundation piles driven into the seabed. The primary method of installation is by hydraulic impact hammers. However, this method generates excessive underwater noise among other drawbacks. Consequently, alternative techniques are being explored by both researchers and industry. One promising alternative is vibratory driving, which theoretically produces less underwater noise compared to impact driving. Nevertheless, there remains a substantial amount of energy transmitted into the water column, particularly from the higher harmonics of the driving frequency. While energy at the fundamental frequency is essential for efficient driving, the energy associated with higher harmonics does not contribute to this efficiency and can significantly increase radiated underwater noise. To address this issue, this study proposes a mitigation strategy to block energy transfer at super-harmonic frequencies in the pile-water-soil system. To selectively target these frequencies without affecting the fundamental one, a mitigation approach utilizing locally-resonant metamaterials is proposed. This involves integrating a transition piece between the vibratory hammer and the pile, that incorporates periodically inserted multiple-degrees-of-freedom systems. By manipulating the natural frequencies of these periodic inclusions, the transition piece forms band-gaps at the relevant super-harmonics. Initial findings indicate that this design has the potential to effectively mitigate noise and vibration at targeted frequencies. Nonetheless, further investigations employing more sophisticated models are necessary to confirm these outcomes.

In recent times, railway transportation has received increasing attention, particularly for its ability to operate entirely on electricity sourced from renewable sources. However, the growing demand for railway services has transformed previously acceptable issues into significant challenges, disrupting normal traffic operations. One such issue is ground-borne vibration especially in urban and inter-urban locations. This study explores the efficacy of a novel mitigation technique, termed a "metawedge," in reducing ground-borne vibration at the receiving end. The metawedge consists of a series of periodically arranged barriers that act as resonators. Unlike traditional metamaterials, each resonator within the metawedge possesses slightly different natural frequencies compared to its neighbours. With an appropriate choice of this variation, incoming Rayleigh (surface) waves are converted into body waves, redirecting energy deeper into the ground. Simulation results demonstrate that the metawedge can significantly diminish vibration levels with just a few resonators. Additionally, unlike conventional single trenches, which effectively mitigate vibrations only at specific angles of incoming waves (outside the critical cone), the metawedge remains efficient within this cone. While a theoretical proof-of-concept has been previously presented by the authors, this study makes a step forward by proposing a realizable design. Consequently, this work showcases the potential and feasibility of metamaterials to address present and future challenges in railway transportation.

The paper presents a monolithic finite element model for the hydro-visco-elastic analysis of floating membranes interacting with ocean waves. The formulation couples linearised potential flow and viscoelastic membrane equations, offering a versatile tool for modelling arbitrarily shaped floating membranes in varying sea-bed topography. The paper also presents a wet modal analysis for the coupled problem, accounting for the added mass and stiffness of the surrounding fluid. This model is used to study the dependence of the wet natural frequencies of floating membranes on the material properties. It is also used to analyse the reflection, transmission, scattering and absorption of ocean wave energy by 1D and 2D floating membranes. Notably, the paper underscores the impact of proportional material damping on these observed phenomena. The results highlight local peaks in the viscoelastic behaviour at the calculated wet natural frequencies, and demonstrate the outward dispersion of incoming wave around finite 2D membranes. Furthermore, the model is employed to examine the interaction of viscoelastic membranes with other structures, such as a monopile, under the influence of ocean waves. This comprehensive investigation contributes to a deeper understanding of the fluid–structure interaction inherent to certain floating solar, wave-energy converter and floating breakwater technologies.

The Gentle Driving of Piles (GDP) is a new technology for vibratory (mono)pile installation that is based on simultaneous application of low-frequency/axial and high-frequency/torsional vibrations. In this paper, a numerical modelling framework, that has been developed and successfully applied to axial vibratory driving, is employed to study GDP. In that manner, the major driving mechanism of this method is comprehended on the basis of field observations and numerical analyses. As regards the numerical model, the pile is described as a thin cylindrical shell and the soil medium is treated as a linear elastic layered half-space. The pile-soil coupling is realized via a history-dependent frictional interface, that accounts for friction force degradation due to the accumulation of loading cycles at the soil material points. The redirection of the friction force vector due to the high-frequency torsion manifests as the main driving mechanism of GDP. Finally, the soil disturbance during installation is compared for the cases of GDP and axial vibratory driving, showcasing the dissimilar characteristics of the induced soil motion.

Offshore wind energy holds significant promise as a solution in the energy transition. However, installing offshore pile foundations can generate substantial levels of underwater noise, posing potential risks to marine life. This paper examines the influence of asymmetric impact forces and pile inclination on producing underwater noise and seabed vibrations based on cases of a small- and large-diameter monopile. The study focuses on scenarios involving inclined and eccentric forces and tilted piles. The analysis reveals that non-symmetrical conditions significantly impact the sound pressure levels around the ring frequency of the pile due to various noise generation mechanisms. However, it is observed that the vertical component of the impact force predominantly contributes to the generation of underwater noise, primarily due to its considerably higher amplitude.

In this paper, we delve into the dynamics of an electromagnetically suspended mass from a rigid support. The study employs a 1.5-degrees-of-freedom system which serves as a simplified model for a Hyperloop vehicle traveling in a tube. Through linear stability analysis, we analytically uncover three distinct regions for the physically significant equilibrium point. Further inspection reveals that the system exhibits limit-cycle vibrations in one of these regions. Employing the harmonic balance method, we determine the properties of the limit cycle, thus unravelling the frequency and amplitude characterizing the periodic oscillations of system’s variables. We also present preliminary findings regarding the influence of the steady aeroelastic force on the stability of the system.

Railway transition zones are critical regions in railway infrastructure that are subjected to excessive operation-driven degradation due to energy concentration within these zones. This work presents a heuristic approach to optimise the geometry of the transition structure and investigate its influence on the strain energy distribution in the railway transition zones (RTZs), with a specific focus on embankment-bridge transitions equipped with a newly proposed ’Safe Hull-Inspired Energy Limiting Design (SHIELD)’ transition structure. For this purpose, a number of three-dimensional finite element models are used to analyze different geometric profiles of SHIELD in a systematic manner. By altering SHIELD's geometry across longitudinal, transversal, and vertical directions, the influence of the different geometric profiles on the total strain energy distribution across the trackbed layers (ballast, embankment, and subgrade) is studied in terms of spatial and temporal variations. The results establish the contribution of geometry to energy redistribution in all three directions and present an optimum geometry for the type of transition under study. It is found that among all the profiles, the longitudinal geometric profile of SHIELD has the most significant impact on the strain energy distribution, while the transversal profile primarily influences the ballast layer, and the alteration of vertical profiles enhance the local redistribution of strain energy in the vicinity of the transition interface. The preliminary optimisation (heuristic approach) presented in this work provides the starting point for full-scale optimisation to obtain tailored shapes of transition structures such that there is neither a concentration of energy nor an obstruction in the flow of energy in RTZs.

Railway transition zones (RTZs) experience higher rates of degradation compared to open tracks, which leads to increased maintenance costs and reduced availability. Despite existing literature on railway track assessment and maintenance, effective design solutions for RTZs are still limited. Therefore, a robust design criterion is required to develop effective solutions. This paper presents a two-step approach for the formulation of a preliminary-design criterion to delay the onset of processes leading to uneven track geometry in RTZs. Firstly, a systematic analysis of each track component in a RTZ is performed by examining spatial and temporal variations in kinematic responses, stresses and energies using a finite element model of an embankment-bridge transition. Secondly, the study proposes an energy-based criterion to be assessed using a model with linear elastic material behavior and states that an amplification in the total train energy in the proximity of the transition interface is an indicator of increased (and thus non-uniform) degradation in RTZs compared to the open tracks. The correlation between the total strain energy (assessed in the model with linear material behaviour) and the permanent irreversible deformations is demonstrated using a model with non-linear elastoplastic material behavior of the ballast layer. In the end, it is claimed that minimising the magnitude of total strain energy will lead to reduced degradation and a uniform distribution of total strain energy in each trackbed layer along the longitudinal direction of the track will ensure uniformity in the track geometry.

The Hyperloop is an innovative transportation system that is currently under development. It minimizes air resistance by enclosing the vehicle in a de-pressurized tube and eliminates wheel-rail contact friction through the use of an electromagnetic suspension/levitation, similar to Maglev trains. This design can potentially achieve much higher velocities compared to traditional railways, positioning the Hyperloop as an environmentally friendly alternative to air transportation.

A potential challenge for Hyperloop is ensuring the dynamic stability at large velocities, where multiple instability sources can be present. An apparent source is the electro-magnetic suspension (adopted by some designs) making a control strategy mandatory to ensure stability even at quasi-static velocities. A less obvious instability mechanism is that the vibration of a vehicle on an elastic guideway can become unstable when surpassing a critical velocity.

The authors have previously investigated the interplay between the electro-magnetic and wave-induced instability mechanisms and showed that the stability space changes significantly above a certain velocity. In other words, the control strategy can ensure the overall system stability only for a very limited range of its gains. The cause for this drastic change was attributed to the wave-induced instability mechanism. Metrikin demonstrated that this instability arises with the radiation of anomalous Doppler waves, which introduce more energy to the vehicle's vibration than normal Doppler waves radiate away from the vehicle. The current study demonstrates that the change of stability domain is indeed caused by the anomalous Doppler waves. While identifying unstable velocity regimes is practical for Hyperloop design, gaining insight into the contribution of individual instability mechanisms can be crucial for efficient mitigation.

Transition zones, characterized by significant variation in track properties (e.g., foundation stiffness) near rigid structures like bridges and tunnels, necessitate more frequent maintenance compared to standard track sections due to higher levels of differential settlements observed at transition zones. Field measurements on one-way tracks reveal asymmetric settlement patterns (i.e., different settlement in the soft-to-stiff vs stiff-to-soft transitions), yet existing literature often investigate either one or the other transition type without investigating the potential limited validity of results. This study investigates the similar aspects as well as the dissimilar ones regarding the behaviour of soft-to-stiff and stiff-to-soft transitions. Modelling results show that the behaviour of the two transition can be considerably different. These results strongly suggest that for a mitigation measure to be efficient, it may be necessary to have different designs for the two types of transition wherever possible (i.e., in one-way tracks). This study can help researchers and engineers understand the different degradation patterns obtained using more complex models or from field measurements.