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.

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.

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.

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.

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.

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.

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.

Railway induced ground vibrations are of increasing importance for structures and inhabitants in the vicinity of railway tracks. This study investigates the capabilities of a novel mitigation measure, a so-called metawedge, in reducing the ground-borne vibration at the receiver end. A metawedge is series of barriers (i.e., resonators) arranged periodically in the longitudinal direction and each one is offset with respect to the others in depth direction (i.e., while the first barrier is completely on the surface, the last barrier can be completely embedded). The advantage of this countermeasure is that it can convert the incoming Rayleigh (surface) waves into body ones, redirecting the energy content deep into the ground. Simulation results show that the metawedge is capable of significantly reducing the vibration levels with as few as five resonators. Furthermore, while conventional single trenches are efficient as mitigation measures only at a certain angle of the incoming waves (outside the critical cone), the metawedge is efficient inside this cone. Although the metawedge solution is promising, this paper serves solely as a proof of concept, and additional studies are necessary to design realistic resonators that can comply with the low frequencies of the railway induced ground vibrations. Nonetheless, this study shows that metamaterials-inspired solutions can play an important role in addressing present and future challenges of the railway transportation.

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.

Railway transition zones (RTZs) are regions where abrupt track stiffness changes occur that may lead to dynamic amplifications and subsequent track deterioration. The design challenges for these zones arise due to variations in material properties in both the depth (trackbed layers composed of different materials) and longitudinal directions of the track, as well as temporal variations in mechanical properties of materials due to several external factors over the operational period. This research aims to investigate the effects of these variations in material properties (i.e., of the resulting stiffness distributions in vertical and longitudinal directions) on the behaviour of RTZs, assess from this perspective the performance of a novel transition structure called the SHIELD, and establish a methodology for designing a robust solution to mitigate the dynamic amplifications in these zones. Results indicate that stiffness variations in both vertical and longitudinal directions significantly influence the dynamic behaviour of the RTZs. The study also suggests a permissible range of stiffness ratios to control the amplification of strain energy in the most critical components of RTZs, both in the initial state as well as during the operational phase (where material properties may vary over time). Moreover, the proposed methodology offers a valuable tool for the design and evaluation of RTZs and is applicable to various transition types and a broad spectrum of material properties.

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.

Current offshore wind turbine installation and positioning methods require mechanical equipment attached on the lifted components and human intervention. The present paper studies the development of a contactless motion compensation technique by investigating a magnetically controlled pendulum. The technique involves the interaction of a magnetic pendulum with an electromagnetic actuator. Two control modes are considered: the imposition of a desired motion to the mass and the motion attenuation of a prescribed pivot excitation. The numerical model is validated and calibrated against experiments and demonstrates excellent predictive capabilities. The control exerted is effective for a broad range of excitation frequencies and amplitudes. Important parameters associated with the performance of the technique such as the separation distance of the magnets and the saturation of the controller are identified. The controllability regions for effective control depending on the characteristics of the excitation are derived. The force amplitude of the contactless actuator is comparable to currently-used active tugger line control systems, but with the additional advantage of both attractive and repulsive forces. The findings of this paper illuminate the path for the further development of a non-contact control technique which has the potential to increase the efficiency of offshore wind installations.

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, 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 validate 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.

While most recent models of railway tracks include the nonlocal nature of the foundation reaction force, few studies have investigated the influence of its nonlocal nature on the response. Accounting for the nonlocal nature of the foundation force is computationally expensive and increases the complexity of the model, thus, knowing when and when not to account for it is important. This paper aims to shed light on the influence of the nonlocal, both in time and space, reaction force provided by the foundation on the transient response at railway transition zones. To this end, a 2-D system in which the soil layer is modelled as a viscoelastic continuum is compared to an equivalent 1-D system with a local foundation reaction force (i.e., Winkler foundation). Results show that, in general, the response of the 2-D system with shallow and/or stiff soil layers can be well captured by the equivalent 1-D model. However, for medium-to-deep and/or soft soil layers, the nonlocality of the foundation reaction force is influential and the transient response at transition zones cannot be satisfactorily captured by 1-D models. Finally, the ballast settlement is also poorly captured for medium-to-deep and/or soft soil layers, with the main cause being the inability of the 1-D model to separate between ballast and soil stresses, and not the locality of the reaction force.

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.

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.

Periodic fluid-solid layered media exhibit distinctive features that can be utilized in various engineering disciplines, such as selective transmission of guided waves, omnidirectional band-gaps and Fano resonances, depending on the spatial configuration and the material properties of the fluid and solid layers involved. This work utilizes the Thin-Layer Method (TLM) in the study of layered fluid-solid media, by extending the original normal modes-based method to acousto-elastic problems. By means of this development, the band-gap structure of these periodic systems can be analysed and their effect when incorporated in fluid or solid full-/half-spaces can be investigated seamlessly for different periodic arrangements. Conclusively, this study presents a framework to analyse these systems, serving as a basis for non-local continuum theories, as well as unveiling desirable dispersion characteristics for the design of metamaterials.

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.