This article investigates the methodology and applicability of the statistical linearization (SL) method to incorporating multi-variate non-differentiable nonlinearities, with a focus on floating renewable energy devices. The SL method serves as a highly competitive approach for analyzing floating renewable energy structures, such as wave energy converters (WECs) and floating wind energy turbines, because it inherently combines adequate accuracy and high computational efficiency. The origin of high accuracy comes from its incorporation of nonlinear effects through statistically linearized representations. Yet, the statistically linearized solutions have only been derived and verified for a limited number of nonlinearities of floating renewable energy devices, mostly simply-formed and differentiable in their mathematical expressions. However, floating renewable energy devices usually exhibit a complex dynamic mechanism, in which the relevant nonlinear effects could appear to be highly complex for linearization process to describe. These nonlinear effects could make a significant impact on the system dynamics, exemplified by external machinery force saturation and nonlinear hydrostatics of floaters with a non-uniform geometry. To push forward the boundary of the SL method, it is crucial to demonstrate how it applies to nonlinearities of different features. In this paper, the existing SL method is extended to address the nonlinear effects expressed as multi-variate non-differentiable functions. Several case studies are carried out to exemplify the application of the extended SL approach to the concerned nonlinearities in floating renewable energy devices. The accuracy and computational efficiency of the extended SL approach are evaluated by verifying against the corresponding nonlinear time-domain (TD) and linear frequency-domain (FD) models. Despite the complexity of the given nonlinearities, the relative errors of the SL approach are no more than 6 % while its computational time is comparable to the FD model, being thousands of times faster than the TD model. Comparatively, the FD model leads to a relative error of over 70% in some cases.

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.

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.

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.

The increasing size of offshore wind turbine foundations necessitates innovative approaches for monopile installation. Traditionally performed through impact driving, the challenges of large stresses induced on the monopile and high levels of underwater noise emissions have driven a shift toward vibratory installation methods. This study investigates the vibro-installation process of steel tubular piles in dense saturated sand through controlled lab-scale experiments. The experiments systematically varied penetration rates and driving frequencies to analyze the interaction between the piles and the surrounding soil. The results reveal critical insights into the influence of vibratory parameters on soil resistance and pile drivability, with a specific focus on the response of the pile tip and shaft under different conditions. These findings contribute to improved predictive models for monopile installation, addressing data gaps in offshore conditions and supporting the optimization of vibratory techniques for sustainable and cost-effective wind energy development.

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.

To accelerate the energy transition, offshore renewable energy is increasingly moving toward array deployment. This shift demands accurate, reliable analysis of hydrodynamics and array interactions at low computational cost. Frequency-domain tools, especially those based on the Boundary Integral Equation Method (BIEM), have thus become widely adopted in the renewables community. Hydrodynamic Analysis of Marine Structures-Marine Renewable Energies Lab (HAMS-MREL) is a recently developed open-source multi-body BIEM solver that computes diffraction and radiation problems, yielding hydrodynamic coefficients and excitation forces on structures. The solver has been validated across a range of geometries using experiments, semi-analytical solutions, and cross-model comparisons, demonstrating high accuracy. This study extends HAMS-MREL with several new features—including wave field calculations (free-surface elevation and pressure), global symmetry, irregular frequency suppression, and generalized (dry) modes—all of which have been validated for accuracy and computational efficiency. OpenMP parallelization has been integrated into each feature, delivering significant computational speed-ups ranging from 13.5 to 47.2.

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.

The global market for offshore wind energy is currently experiencing tremendous growth, which is expected to continue in the coming decades. Monopiles are one of the most frequently used foundations for Offshore Wind Turbines (OWTs) and are commonly driven into the seabed using impact hammering. The demand for higher capacity OWTs requires the installation of larger monopiles. As monopiles, however, become bigger their installation with hammering and mitigation of generated noise becomes challenging and costly. To optimize installation and to limit noise emissions, an innovative installation technique known as the Gentle Driving of Piles, GDP, has been developed. This technique combines vertical and torsional vibrations under different frequencies with the main driving assistance coming from the torsional force. This paper presents and discusses the results from a series of lab-scale pile driving tests performed in dense sand using the GDP method. For these tests, a lab-scale GDP shaker has been mobilized. During installation of the scaled piles, the frequencies and amplitudes of the vertical and torsional excitation were varied independently with the objective to increase the penetration speed. The results show improved pile driveability with high-frequency, low-amplitude torsional vibrations and showcase the potential of the GDP method in improving installation performance.

HAMS-MREL is a recently developed open-source BIEM solver, which allows for the solution of the diffraction and radiation problem for multiple floating rigid structures, taking into account their interaction. This has shown to highly accurate when compared with semi-analytical solutions/commercial solver WAMIT, within a computationally efficient framework that is parallelized. The solver is currently capable of providing the hydrodynamic coefficients (added mass and radiation damping) and exciting forces for all 6 rigid body modes per body. With this research, the solver has been extended significantly to include the following features for the multiple body interaction problem 1) Removal of irregular frequencies, 2) Global symmetry, 3) Wave fields and 4) Generalized modes. This study contributes further to the open-source domain with the development of highly accurate numerical tools for the accelerated deployment of offshore renewables.

Railway tracks are subjected to constant degradation over the operational period leading to high maintenance and operation costs. To add to this railway transition zones experience 4–8 times more degradation and need more frequent maintenance compared to normal tracks. Railway transition zones are areas where the railway tracks cross a different transportation modality (road, waterway, etc.) or where the rail experiences major changes in the type of track support structure. Several studies have pointed out that the transition zones show amplified dynamic responses due to abrupt changes in stiffness and differential settlement in these zones. Consequently, an increased deterioration of geometry and material is observed in these zones. Numerous attempts have been made to address the abovementioned factors at the superstructure and substructure level. However, an effective intervention to mitigate the amplified degradation in these zones is missing. In this chapter, an overview of the problem and existing solutions is presented. Moreover, a novel design methodology to design railway transition zones is proposed and discussed in detail. The design methodology includes the formulation of a design criterion, identification of design parameters, investigation of key phenomena governing design and proposing an optimized design solution.

In order to reduce the Levelized Cost Of Energy (LCOE) of Wave Energy Converters (WECs) and make them competitive with conventional energy sources, they would need to be deployed in large numbers as farms similar to Offshore Wind. Given their significant capacity, Offshore wind turbines are often placed at large distances apart, to reduce destructive wake effects, while maintaining a high energy density per unit area. However, WECs within a farm, are much smaller with much lower capacities and stronger inter device interactions due to the presence of a highly dense fluid. Therefore, larger number of WECs can be deployed in closer proximity to produce comparable energy density per unit area. As we move towards hybrid systems with floating solar, wind and wave energy amongst others, efficiency in deployment within an area becomes key. Conventional wave farm concepts that have been extensively studied such as 1) wave farms of different types of WECs (Point Absorber, Attenuator, Flap etc) also referred to as homogeneous arrays (same device in multiple numbers) and 2) wave farms with different sizes and drafts of one type of WEC also referred to as heterogeneous arrays. To date, studies have focused on multiple devices with similar geometries interacting through the same degrees of freedom. With this research, the authors explore mixed wave energy farms, which are wave farms utilizing different types of wave energy converters in the same farm. With the focus on the hydrodynamics and power produced by wave energy converters, this research provides for the first time insights into the interaction of devices, with varying geometries and degrees of freedom, thus entering an entirely new domain of wave farm research.

Railway transition zones (RTZs), where rail tracks undergo abrupt changes in foundation types, represent critical challenges in railway infrastructure due to their higher degradation rates compared to open tracks. This study synthesizes insights from multiple research efforts to propose a robust design solution and an energy-based design criterion for RTZ management. We present a two-step approach to establish the design criterion based on a systematic analysis of each RTZ component, focusing on variations in kinematic responses, stresses, and energies. Based on this analysis, the energy-based design criterion is proposed, asserting that minimizing the total strain energy within the trackbed layers and uniformly distributing it in the longitudinal direction can significantly mitigate uneven track geometry and reduce degradation. A novel safe hull-inspired energy limiting design (SHIELD) is introduced and evaluated against traditional transition structures like approach slabs and transition wedges. SHIELD’s effectiveness in managing energy flow at RTZs is demonstrated, highlighting its potential as a transformative solution in RTZ design. Further, we explore the impact of stiffness variations in both vertical and longitudinal track directions and the temporal changes in material properties on RTZ dynamics, suggesting permissible stiffness ratios to control strain energy amplification. A detailed investigation is thus performed to understand the role of geometry in energy management. The influence of different geometric profiles of SHIELD and standard embankment-bridge transitions on strain energy distributions is studied using 3D finite element models. The findings emphasize the strategic use of geometry to channel and scatter energy, and thus mitigate energy concentrations, enhancing the performance and lifespan of RTZs. In conclusion, this comprehensive research not only highlights the importance of an energy-based design criterion and the innovative SHIELD structure in RTZ management but also underscores the need for further research into the geometric profiles and their interplay with energy flow and mechanical properties. This study lays a foundation for future explorations aimed at optimizing RTZ design, ensuring robustness, and extending the operational life of these crucial railway sections.

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.

The Hyperloop, a developing transportation system, reduces air resistance by housing the vehicle within a depressurized tube and eliminates contact friction by using an electro-magnetic suspension/levitation system. Maintaining system stability poses a challenge due to the exceptionally high target velocities. Consequently, it is important to know apriori the velocity regimes in which the system can be unstable. The authors have recently investigated this aspect by, unlike previous studies, properly accounting for the frequency and velocity dependent reaction force provided by the infinite guideway. Furthermore, that study focused on the interplay between two fundamentally different instability sources, namely (i) the electro-magnetic suspension, and (ii) wave-induced instability, showing that stability domains drastically change above a certain vehicle velocity. The current study presents a methodology to distinguish the contribution of each instability mechanism to the overall system stability, and demonstrates that the wave-induced instability mechanism is causing the drastic stability change at large vehicle velocities. This investigation offers physical insight into the mechanisms that can cause instability in the Maglev/Hyperloop systems, and can help engineers that develop this novel transportation system to avoid excessive vibrations and, in extreme cases, derailment.

This paper studies the mechanism that leads to the reduction of frictional soil reaction forces during pile driving, termed friction fatigue. We focus on axial vibratory driving, an environmentally friendly monopile installation method, and examine two friction fatigue formulations, i.e. a penetration-based and a cyclic memory mechanism. Friction fatigue plays a pivotal role in pile drivability and post-installation bearing capacity for piles installed via axial vibratory driving. Through numerical analyses and validation against field data from onshore experiments, the efficacy of these memory mechanisms is assessed. The results reveal that the proposed cyclic memory mechanism provides consistently more accurate predictions than the corresponding penetration-based approach, offering a promising option for modelling friction fatigue in vibratory driving. This study advances our understanding of friction fatigue in the context of vibratory driving for offshore monopile installation, emphasizing the need for further numerical and experimental works in this topic.

This paper presents the development and testing of a lab-scale Gentle Driving of Piles (GDP) shaker. Conventional impact piling for offshore monopile installation faces challenges due to noise regulations and its adverse marine environmental impacts. The GDP method, which integrates high-frequency torsional vibrations with low-frequency axial vibrations, aims to mitigate these issues. In this work, a new GDP shaker is designed and tested to enhance vibratory pile driving by independently controlling torsional and vertical vibration amplitudes and frequencies. Laboratory tests were conducted using the newly designed shaker for pile driving in sandy soil to evaluate its performance. The results indicate a significant reduction in power consumption and improved pile drivability with high-frequency, low-amplitude torsional vibrations. This study highlights the importance of optimizing dynamic inputs for enhanced pile penetration and reduced environmental impact, showcasing the potential of the GDP method as a promising alternative to traditional impact piling techniques.

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.

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.