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A. Metrikine
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Journal article
(2026)
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Ponni Maya, José A.A. Antolínez, Kai Parker, Laura Cagigal, Andrei V. Metrikine
This study presents a multivariate spatio-temporal clustering framework to characterise joint wind–wave regimes across European seas using the fifth-generation atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ERA5; 1979–2014). Seasonal and annual statistics of significant wave height, mean wave period, wind speed, and wave/wind direction were computed at 0.5° resolution. Principal component analysis was used to reduce dimensionality, retaining 30 components that captured 99% of the variance. K-means clustering was then used to identify nine coherent dynamical regimes with persistent spatio-temporal signatures. These regimes were grouped into open-ocean, transitional, and enclosed/semi-enclosed categories based on internal variability, directional spread, and geographic exposure. Open-Atlantic regimes are found to be energy-rich, exhibiting clear December–February maxima in significant wave height ((Formula presented.)), mean wave period ((Formula presented.)), and 10 m wind speed ((Formula presented.)); enclosed and semi-enclosed basins show lower amplitudes and reduced variability, while transitional shelves and the southern Mediterranean display intermediate conditions, characterised by moderate (Formula presented.) levels and seasonal rotation of wave and wind directions, reflecting a mixed influence of locally generated seas and remotely forced swell. Dispersion analysis highlights a clear Atlantic–Mediterranean partition, with transitional shelves forming a dynamical bridge between open-ocean and enclosed basins. Teleconnection analysis shows that the North Atlantic Oscillation and Arctic Oscillation dominate Atlantic regimes, while the Scandinavia, East Atlantic, and Polar/Eurasia patterns modulate variability and directional persistence in transitional and enclosed seas. The classification defines a climatological framework of European wind–wave conditions and establishes a practical basis for renewable energy assessment, engineering design, and long-term change analysis, with methods transferable to other basins.
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This study presents a multivariate spatio-temporal clustering framework to characterise joint wind–wave regimes across European seas using the fifth-generation atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ERA5; 1979–2014). Seasonal and annual statistics of significant wave height, mean wave period, wind speed, and wave/wind direction were computed at 0.5° resolution. Principal component analysis was used to reduce dimensionality, retaining 30 components that captured 99% of the variance. K-means clustering was then used to identify nine coherent dynamical regimes with persistent spatio-temporal signatures. These regimes were grouped into open-ocean, transitional, and enclosed/semi-enclosed categories based on internal variability, directional spread, and geographic exposure. Open-Atlantic regimes are found to be energy-rich, exhibiting clear December–February maxima in significant wave height ((Formula presented.)), mean wave period ((Formula presented.)), and 10 m wind speed ((Formula presented.)); enclosed and semi-enclosed basins show lower amplitudes and reduced variability, while transitional shelves and the southern Mediterranean display intermediate conditions, characterised by moderate (Formula presented.) levels and seasonal rotation of wave and wind directions, reflecting a mixed influence of locally generated seas and remotely forced swell. Dispersion analysis highlights a clear Atlantic–Mediterranean partition, with transitional shelves forming a dynamical bridge between open-ocean and enclosed basins. Teleconnection analysis shows that the North Atlantic Oscillation and Arctic Oscillation dominate Atlantic regimes, while the Scandinavia, East Atlantic, and Polar/Eurasia patterns modulate variability and directional persistence in transitional and enclosed seas. The classification defines a climatological framework of European wind–wave conditions and establishes a practical basis for renewable energy assessment, engineering design, and long-term change analysis, with methods transferable to other basins.
Wave energy arrays are essential for reducing the Levelised Cost of Energy, yet the performance of traditional mono-device arrays is often limited by destructive hydrodynamic interactions and directional sensitivity. This work focuses on ”mixed arrays,” wherein different types and geometries of wave energy converters operating in different degrees of freedom (point Absorber and a flap) are deployed within the same array to exploit complementary device dynamics, whilst reducing spatial requirements. Using a weakly non-linear frequency-domain model utilising the solver HAMS-MREL, a systematic comparison is performed across 3360 cases considering varying array sizes, spacings, wave directions, and control strategies (active and passive). Comparison of array performance is based on the well known q-factor and a new geometry dependent metric (M-factor). The results demonstrate that mixed arrays can outperform mono-device arrays by leveraging favourable hydrodynamic cross-coupling and radiated wave-field alignment. For a 10-device staggered configuration, mixed arrays achieved a peak q-factor of 1.6 and an M-factor of 2.25 under regular waves, showing a 175% increase in point absorber heave response under displacement constraints and 34% increase in flap excitation forces. Performance is sensitive to the spacing-to-wavelength ratio, mixed arrays exhibit superior directional robustness, and reduced efficiency collapse compared to mono-flap arrays. The findings suggest that mixed-device configurations can provide a robust alternative for optimising energy capture, reducing spatial requirements, offering new collaboration opportunities and contributing to the viability of wave energy arrays.
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Wave energy arrays are essential for reducing the Levelised Cost of Energy, yet the performance of traditional mono-device arrays is often limited by destructive hydrodynamic interactions and directional sensitivity. This work focuses on ”mixed arrays,” wherein different types and geometries of wave energy converters operating in different degrees of freedom (point Absorber and a flap) are deployed within the same array to exploit complementary device dynamics, whilst reducing spatial requirements. Using a weakly non-linear frequency-domain model utilising the solver HAMS-MREL, a systematic comparison is performed across 3360 cases considering varying array sizes, spacings, wave directions, and control strategies (active and passive). Comparison of array performance is based on the well known q-factor and a new geometry dependent metric (M-factor). The results demonstrate that mixed arrays can outperform mono-device arrays by leveraging favourable hydrodynamic cross-coupling and radiated wave-field alignment. For a 10-device staggered configuration, mixed arrays achieved a peak q-factor of 1.6 and an M-factor of 2.25 under regular waves, showing a 175% increase in point absorber heave response under displacement constraints and 34% increase in flap excitation forces. Performance is sensitive to the spacing-to-wavelength ratio, mixed arrays exhibit superior directional robustness, and reduced efficiency collapse compared to mono-flap arrays. The findings suggest that mixed-device configurations can provide a robust alternative for optimising energy capture, reducing spatial requirements, offering new collaboration opportunities and contributing to the viability of wave energy arrays.
A novel boundary formulation is presented by applying the Boundary Element Method (BEM) to a dynamically loaded medium modelled as a discrete system. The two-dimensional medium is divided into a nonlinear discrete lattice in the near field, and a corresponding linear viscoelastic far field. The resulting boundary formulation is derived from the dynamic reciprocal work theorem and describes the far-field response through a Laplace domain force–displacement relation. The involved dynamic compliance matrix is composed of newly derived expressions for the Green’s functions of a viscoelastic half-plane of particles. It is demonstrated that the presented method yields a perfectly non-reflective boundary in the Laplace domain, without the need for artificial absorbing boundaries. Additionally, this contribution shows the successful time-domain application of the boundary method to a medium that exhibits non-smooth behaviour in the vicinity of a load source. In the time domain, the boundary equations are obtained by numerical application of the inverse Laplace transform, and the non-reflectiveness of the boundary is sensitive to the size of the time step. The presented method provides a consistent boundary approach for discrete lattices, and provides an alternative to continuum-based boundary methods for the dynamic response of solid media.
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A novel boundary formulation is presented by applying the Boundary Element Method (BEM) to a dynamically loaded medium modelled as a discrete system. The two-dimensional medium is divided into a nonlinear discrete lattice in the near field, and a corresponding linear viscoelastic far field. The resulting boundary formulation is derived from the dynamic reciprocal work theorem and describes the far-field response through a Laplace domain force–displacement relation. The involved dynamic compliance matrix is composed of newly derived expressions for the Green’s functions of a viscoelastic half-plane of particles. It is demonstrated that the presented method yields a perfectly non-reflective boundary in the Laplace domain, without the need for artificial absorbing boundaries. Additionally, this contribution shows the successful time-domain application of the boundary method to a medium that exhibits non-smooth behaviour in the vicinity of a load source. In the time domain, the boundary equations are obtained by numerical application of the inverse Laplace transform, and the non-reflectiveness of the boundary is sensitive to the size of the time step. The presented method provides a consistent boundary approach for discrete lattices, and provides an alternative to continuum-based boundary methods for the dynamic response of solid media.
Ocean renewable energy is a key enabler of the global transition toward a decarbonised and resilient energy system. Among marine resources, wave energy offers high energy density, predictability, and strong complementarity with offshore wind, making it a promising candidate for reliable power generation. Despite this potential, commercial deployment remains limited due to challenges related to efficiency, survivability, and cost. As a result, research has increasingly shifted from individual devices to wave energy arrays, where hydrodynamic interactions can play a critical role in enhancing overall performance.
Two-body raft-type attenuators, such as the designs of the wave energy converters of Mocean Energy, have emerged as a promising configuration for intermediate to deep waters. These devices consist of two floating sections connected by a hinge joint, with energy extracted from their relative rotation through a power take-off (PTO) system. While the hydrodynamics and control of single raft devices have been studied, array-scale analyses of such hinged attenuators remain scarce, particularly those incorporating explicit PTO modelling. This gap limits current understanding of how inter-device hydrodynamic coupling influences array performance. This study presents a systematic assessment of arrays of two-body hinged raft attenuators using a weakly nonlinear frequency-domain model implemented in the open-source BIEM solver HAMS-MREL. The solver resolves multi-body diffraction and radiation interactions while explicitly representing hinge dynamics through frequency-dependent PTO damping and stiffness. A range of array configurations is analysed, varying the number of devices, spacing, and layout. Array performance is quantified solely using the array interaction factor (q-factor), enabling direct assessment of constructive and destructive hydrodynamic interactions. The results provide new insight into the role of array configuration and PTO characteristics in governing performance and highlight the potential for power amplification through favourable wave–device interactions. ...
Two-body raft-type attenuators, such as the designs of the wave energy converters of Mocean Energy, have emerged as a promising configuration for intermediate to deep waters. These devices consist of two floating sections connected by a hinge joint, with energy extracted from their relative rotation through a power take-off (PTO) system. While the hydrodynamics and control of single raft devices have been studied, array-scale analyses of such hinged attenuators remain scarce, particularly those incorporating explicit PTO modelling. This gap limits current understanding of how inter-device hydrodynamic coupling influences array performance. This study presents a systematic assessment of arrays of two-body hinged raft attenuators using a weakly nonlinear frequency-domain model implemented in the open-source BIEM solver HAMS-MREL. The solver resolves multi-body diffraction and radiation interactions while explicitly representing hinge dynamics through frequency-dependent PTO damping and stiffness. A range of array configurations is analysed, varying the number of devices, spacing, and layout. Array performance is quantified solely using the array interaction factor (q-factor), enabling direct assessment of constructive and destructive hydrodynamic interactions. The results provide new insight into the role of array configuration and PTO characteristics in governing performance and highlight the potential for power amplification through favourable wave–device interactions. ...
Ocean renewable energy is a key enabler of the global transition toward a decarbonised and resilient energy system. Among marine resources, wave energy offers high energy density, predictability, and strong complementarity with offshore wind, making it a promising candidate for reliable power generation. Despite this potential, commercial deployment remains limited due to challenges related to efficiency, survivability, and cost. As a result, research has increasingly shifted from individual devices to wave energy arrays, where hydrodynamic interactions can play a critical role in enhancing overall performance.
Two-body raft-type attenuators, such as the designs of the wave energy converters of Mocean Energy, have emerged as a promising configuration for intermediate to deep waters. These devices consist of two floating sections connected by a hinge joint, with energy extracted from their relative rotation through a power take-off (PTO) system. While the hydrodynamics and control of single raft devices have been studied, array-scale analyses of such hinged attenuators remain scarce, particularly those incorporating explicit PTO modelling. This gap limits current understanding of how inter-device hydrodynamic coupling influences array performance. This study presents a systematic assessment of arrays of two-body hinged raft attenuators using a weakly nonlinear frequency-domain model implemented in the open-source BIEM solver HAMS-MREL. The solver resolves multi-body diffraction and radiation interactions while explicitly representing hinge dynamics through frequency-dependent PTO damping and stiffness. A range of array configurations is analysed, varying the number of devices, spacing, and layout. Array performance is quantified solely using the array interaction factor (q-factor), enabling direct assessment of constructive and destructive hydrodynamic interactions. The results provide new insight into the role of array configuration and PTO characteristics in governing performance and highlight the potential for power amplification through favourable wave–device interactions.
Two-body raft-type attenuators, such as the designs of the wave energy converters of Mocean Energy, have emerged as a promising configuration for intermediate to deep waters. These devices consist of two floating sections connected by a hinge joint, with energy extracted from their relative rotation through a power take-off (PTO) system. While the hydrodynamics and control of single raft devices have been studied, array-scale analyses of such hinged attenuators remain scarce, particularly those incorporating explicit PTO modelling. This gap limits current understanding of how inter-device hydrodynamic coupling influences array performance. This study presents a systematic assessment of arrays of two-body hinged raft attenuators using a weakly nonlinear frequency-domain model implemented in the open-source BIEM solver HAMS-MREL. The solver resolves multi-body diffraction and radiation interactions while explicitly representing hinge dynamics through frequency-dependent PTO damping and stiffness. A range of array configurations is analysed, varying the number of devices, spacing, and layout. Array performance is quantified solely using the array interaction factor (q-factor), enabling direct assessment of constructive and destructive hydrodynamic interactions. The results provide new insight into the role of array configuration and PTO characteristics in governing performance and highlight the potential for power amplification through favourable wave–device interactions.
Wave energy arrays are essential for reducing the Levelised Cost of Energy, yet the performance of traditional mono-device arrays is often limited by destructive hydrodynamic interactions and directional sensitivity. This work focuses on ”mixed arrays,” wherein different types and geometries of wave energy converters operating in different degrees of freedom (point Absorber and a flap) are deployed within the same array to exploit complementary device dynamics, whilst reducing spatial requirements. Using a weakly non-linear frequency-domain model utilising the solver HAMS-MREL, a systematic comparison is performed across 3360 cases considering varying array sizes, spacings, wave directions, and control strategies (active and passive). Comparison of array performance is based on the well known q-factor and a new geometry dependent metric (M-factor). The results demonstrate that mixed arrays can outperform mono-device arrays by leveraging favourable hydrodynamic cross-coupling and radiated wave-field alignment. For a 10-device staggered configuration, mixed arrays achieved a peak q-factor of 1.6 and an M-factor of 2.25 under regular waves, showing a 175% increase in point absorber heave response under displacement constraints and 34% increase in flap excitation forces. Performance is sensitive to the spacing-to-wavelength ratio, mixed arrays exhibit superior directional robustness, and reduced efficiency collapse compared to mono-flap arrays. The findings suggest that mixed-device configurations can provide a robust alternative for optimising energy capture, reducing spatial requirements, offering new collaboration opportunities and contributing to the viability of wave energy arrays.
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Wave energy arrays are essential for reducing the Levelised Cost of Energy, yet the performance of traditional mono-device arrays is often limited by destructive hydrodynamic interactions and directional sensitivity. This work focuses on ”mixed arrays,” wherein different types and geometries of wave energy converters operating in different degrees of freedom (point Absorber and a flap) are deployed within the same array to exploit complementary device dynamics, whilst reducing spatial requirements. Using a weakly non-linear frequency-domain model utilising the solver HAMS-MREL, a systematic comparison is performed across 3360 cases considering varying array sizes, spacings, wave directions, and control strategies (active and passive). Comparison of array performance is based on the well known q-factor and a new geometry dependent metric (M-factor). The results demonstrate that mixed arrays can outperform mono-device arrays by leveraging favourable hydrodynamic cross-coupling and radiated wave-field alignment. For a 10-device staggered configuration, mixed arrays achieved a peak q-factor of 1.6 and an M-factor of 2.25 under regular waves, showing a 175% increase in point absorber heave response under displacement constraints and 34% increase in flap excitation forces. Performance is sensitive to the spacing-to-wavelength ratio, mixed arrays exhibit superior directional robustness, and reduced efficiency collapse compared to mono-flap arrays. The findings suggest that mixed-device configurations can provide a robust alternative for optimising energy capture, reducing spatial requirements, offering new collaboration opportunities and contributing to the viability of wave energy arrays.
Journal article
(2026)
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Jithu Paul, Karel N. van Dalen, Andrei B. Fărăgău, Rens J. van Leijden, Biagio Carboni, Andrei V. Metrikine
This paper investigates the dynamic stability of an electromagnetically suspended vehicle, encountered in Hyperloop and Maglev systems, subject to purely sinusoidal base excitation caused by surface irregularities or vibration of the support induced by external noise. The narrow airgap between the vehicle and the support makes the system sensitive to the motion of the support, as small amplitudes of the latter create significant excitation. The vehicle is modelled as a three-degree-of-freedom model where the vehicle is suspended via two identical electromagnetic actuators from rigid supports that oscillate. The governing equations are derived using force and torque balances, incorporating nonlinear electromagnetic forces, and Kirchhoff’s law for the electromagnets with PD control strategy on the airgap. The equations of motion are linearized around the steady state induced by the surface oscillation, yielding a system with time-periodic coefficients. We analytically explore both simple and combination parametric resonances using an extended Hill’s method, and Floquet theory is used for numerical validation. The stability boundaries are obtained as ellipses in the PD control parameter space, and the influence of system parameters on these boundaries is characterized. For a mean phase shift between the base excitations, the ratio of the sizes of the two simple-parametric resonance ellipses is three to one, whereas for the combination parametric resonance ellipses, the ratio is fourteen to one. One of the ellipses associated with the combination parametric resonance is the largest in that situation. Moreover, we found that in all cases, the relative sizes of the ellipses are independent of the excitation frequency, when normalized by the local width of the stable domain. Additionally, the impact of using hybrid magnets in the supports—combining electromagnets with permanent magnets—on the parametric resonances is analysed, showing that they are equivalent to those of the electromagnet-only case; the ellipses only shift in accordance with an overall widening of the stable domain. Results reveal critical conditions under which each type of resonance dominates, offering key insights for safe design and operation of magnetically suspended vehicles.
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This paper investigates the dynamic stability of an electromagnetically suspended vehicle, encountered in Hyperloop and Maglev systems, subject to purely sinusoidal base excitation caused by surface irregularities or vibration of the support induced by external noise. The narrow airgap between the vehicle and the support makes the system sensitive to the motion of the support, as small amplitudes of the latter create significant excitation. The vehicle is modelled as a three-degree-of-freedom model where the vehicle is suspended via two identical electromagnetic actuators from rigid supports that oscillate. The governing equations are derived using force and torque balances, incorporating nonlinear electromagnetic forces, and Kirchhoff’s law for the electromagnets with PD control strategy on the airgap. The equations of motion are linearized around the steady state induced by the surface oscillation, yielding a system with time-periodic coefficients. We analytically explore both simple and combination parametric resonances using an extended Hill’s method, and Floquet theory is used for numerical validation. The stability boundaries are obtained as ellipses in the PD control parameter space, and the influence of system parameters on these boundaries is characterized. For a mean phase shift between the base excitations, the ratio of the sizes of the two simple-parametric resonance ellipses is three to one, whereas for the combination parametric resonance ellipses, the ratio is fourteen to one. One of the ellipses associated with the combination parametric resonance is the largest in that situation. Moreover, we found that in all cases, the relative sizes of the ellipses are independent of the excitation frequency, when normalized by the local width of the stable domain. Additionally, the impact of using hybrid magnets in the supports—combining electromagnets with permanent magnets—on the parametric resonances is analysed, showing that they are equivalent to those of the electromagnet-only case; the ellipses only shift in accordance with an overall widening of the stable domain. Results reveal critical conditions under which each type of resonance dominates, offering key insights for safe design and operation of magnetically suspended vehicles.
Journal article
(2026)
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Rens J. van Leijden, Karel N. van Dalen, Andrei B. Fărăgău, Jithu Paul, Andrei V. Metrikine
This study addresses the dynamic stability of a moving mass suspended electromagnetically from a flexible beam that is supported periodically by discrete elastic springs. The stability is generally determined by the interaction of the wave-induced and electromagnetic instability mechanisms. Both are related to a potentially destabilizing force: the controlled electromagnetic force and the reaction force of the guideway (beam-foundation system). The former is destabilizing if the control is inappropriate, and the latter when sufficiently energetic anomalous Doppler waves are excited in the guideway that feedback energy into the vehicle vibration. Using a generalization of Hill’s method, the stability boundary is determined in the plane of electromagnetic-control parameters. The obtained boundary is roughly triangular, like for the equivalent non-periodic system. The left, straight boundary marks the emergence of a divergence instability. The right boundary generally marks the emergence of an oscillatory (flutter-type) instability, but specific, elliptical indentations are related to parametric resonances. The divergence instability is always electromagnetics induced, but the oscillatory instability and parametric resonances can be either wave or electromagnetics induced, although the latter are often electromagnetics induced. Wave-induced instability takes place mostly for large speeds and only for small values of the control parameters. The stability boundary locally bends back there, reducing the size of the stable zone considerably. Next to the T and 2T parametric-resonance indentations, the right boundary has a significant amorphous indentation compared to that of the non-periodic system. Furthermore, the 2T parametric resonance ellipse is very significant in size when the inhomogeneity of the periodic guideway is relatively strong. Interestingly, the amorphous indentation is related to the occurrence of an evanescent wave in the periodic guideway, but parametric resonance appears to be not uniquely related to a single wave type. Although the current study is fundamental in nature, the findings do pave the way towards the design of safe and cost-effective Maglev and Hyperloop infrastructure as well as of electromagnetic-suspension controllers. We emphasize that the wave-induced instability mechanism, and more generally speaking the influence of the periodic guideway, is also relevant in the context of other (than the simple PD) control strategies as well as for different Maglev and Hyperloop suspension/levitation systems such as the electrodynamic, the hybrid and the superconducting magnet suspensions.
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This study addresses the dynamic stability of a moving mass suspended electromagnetically from a flexible beam that is supported periodically by discrete elastic springs. The stability is generally determined by the interaction of the wave-induced and electromagnetic instability mechanisms. Both are related to a potentially destabilizing force: the controlled electromagnetic force and the reaction force of the guideway (beam-foundation system). The former is destabilizing if the control is inappropriate, and the latter when sufficiently energetic anomalous Doppler waves are excited in the guideway that feedback energy into the vehicle vibration. Using a generalization of Hill’s method, the stability boundary is determined in the plane of electromagnetic-control parameters. The obtained boundary is roughly triangular, like for the equivalent non-periodic system. The left, straight boundary marks the emergence of a divergence instability. The right boundary generally marks the emergence of an oscillatory (flutter-type) instability, but specific, elliptical indentations are related to parametric resonances. The divergence instability is always electromagnetics induced, but the oscillatory instability and parametric resonances can be either wave or electromagnetics induced, although the latter are often electromagnetics induced. Wave-induced instability takes place mostly for large speeds and only for small values of the control parameters. The stability boundary locally bends back there, reducing the size of the stable zone considerably. Next to the T and 2T parametric-resonance indentations, the right boundary has a significant amorphous indentation compared to that of the non-periodic system. Furthermore, the 2T parametric resonance ellipse is very significant in size when the inhomogeneity of the periodic guideway is relatively strong. Interestingly, the amorphous indentation is related to the occurrence of an evanescent wave in the periodic guideway, but parametric resonance appears to be not uniquely related to a single wave type. Although the current study is fundamental in nature, the findings do pave the way towards the design of safe and cost-effective Maglev and Hyperloop infrastructure as well as of electromagnetic-suspension controllers. We emphasize that the wave-induced instability mechanism, and more generally speaking the influence of the periodic guideway, is also relevant in the context of other (than the simple PD) control strategies as well as for different Maglev and Hyperloop suspension/levitation systems such as the electrodynamic, the hybrid and the superconducting magnet suspensions.
Conference paper
(2026)
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Sijia Zhou, Janno de Bruijn, Floris Besseling, Andrei Metrikine, Karel van Dalen, Michaël Steenbergen
The study of train-track interaction and resulting ground vibrations generally (and often exclusively) focuses on the vertical direction. This study explores the directional characteristics of train-induced ground vibration, based on in-situ measurements conducted at different locations in the Netherlands with two subsoil types-sand and clay, and different substructures, for a set of operational parameters. Triaxial accelerometers were installed at the ground surface along the track, in a spatial configuration capturing both near-field (or non-radiating) and far-field (or radiating) contributions of the ground response in terms of particle motion. Through statistical and comparative analyses of field-measured data, the results show a strong dependence of the dominating directions of particle motion on the ground composition (soft or still soils) and therefore also on the cross-sectional track geometry in terms of substructure and embankment. These findings highlight the relevance of paying due attention to both normal and in-plane (longitudinal and lateral) components of train-track interaction and ground particle motion in the modeling, mitigation and prediction of train-induced vibration hindrance.
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The study of train-track interaction and resulting ground vibrations generally (and often exclusively) focuses on the vertical direction. This study explores the directional characteristics of train-induced ground vibration, based on in-situ measurements conducted at different locations in the Netherlands with two subsoil types-sand and clay, and different substructures, for a set of operational parameters. Triaxial accelerometers were installed at the ground surface along the track, in a spatial configuration capturing both near-field (or non-radiating) and far-field (or radiating) contributions of the ground response in terms of particle motion. Through statistical and comparative analyses of field-measured data, the results show a strong dependence of the dominating directions of particle motion on the ground composition (soft or still soils) and therefore also on the cross-sectional track geometry in terms of substructure and embankment. These findings highlight the relevance of paying due attention to both normal and in-plane (longitudinal and lateral) components of train-track interaction and ground particle motion in the modeling, mitigation and prediction of train-induced vibration hindrance.
Viscoelastic floating membranes can be used as flexible wave breakers to protect coastal and offshore structures or as flexible wave energy converters. Despite their potential, the role of viscoelastic floating membranes in optimally harvesting or dissipating wave energy remains largely unexplored, particularly regarding how spatially varying material properties influence their performance. To address this gap, we develop an adjoint-based PDE-constrained optimization framework, built on a monolithic finite element formulation of the coupled fluid–structure interaction problem, to investigate and optimize the viscoelastic properties of floating membranes. This methodology enables a systematic optimization of design parameters such as the mass, tension, and damping, which govern the response of the membrane at different wave conditions. In this study we demonstrate that the proposed methodology allows for the optimization of homogeneous and inhomogeneous properties of membranes for different wave excitation frequencies, leading to significant improvements in energy absorption. The framework is implemented in Julia using the Gridap package ecosystem, which enables automatic differentiation of adjoints and avoids the need to derive complex adjoint formulations.
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Viscoelastic floating membranes can be used as flexible wave breakers to protect coastal and offshore structures or as flexible wave energy converters. Despite their potential, the role of viscoelastic floating membranes in optimally harvesting or dissipating wave energy remains largely unexplored, particularly regarding how spatially varying material properties influence their performance. To address this gap, we develop an adjoint-based PDE-constrained optimization framework, built on a monolithic finite element formulation of the coupled fluid–structure interaction problem, to investigate and optimize the viscoelastic properties of floating membranes. This methodology enables a systematic optimization of design parameters such as the mass, tension, and damping, which govern the response of the membrane at different wave conditions. In this study we demonstrate that the proposed methodology allows for the optimization of homogeneous and inhomogeneous properties of membranes for different wave excitation frequencies, leading to significant improvements in energy absorption. The framework is implemented in Julia using the Gridap package ecosystem, which enables automatic differentiation of adjoints and avoids the need to derive complex adjoint formulations.
Journal article
(2025)
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Mingjuan Zhao, João Manuel de Oliveira Barbosa, Andrei V. Metrikine, Karel N. van Dalen
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.
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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.
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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.
Additional features in HAMS-MREL
A new open-source BIEM solver for offshore energy applications
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.
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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.
Soil resistance during vibratory pile installation
Experimental findings from lab-scale tests
Journal article
(2025)
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Mario Martinelli, Athanasios Tsetas, Andrei B. Fărăgău, Andrei Metrikine, Apostolos Tsouvalas
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.
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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.
Journal article
(2025)
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Jithu Paul, Karel N. van Dalen, Andrei B. Fărăgău, Rens J. van Leijden, Mouad Ouggaâli, Andrei V. Metrikine
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.
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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.
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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 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.
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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.
The present study introduces a coupled contactless control approach for managing both translational and torsional motions of a suspended load. This method utilizes magnet-to-magnet interactions between two pairs of magnetic dipoles, with translational motion controlled by adjusting the polarity and intensity of the electromagnetic actuator, and torsional motion regulated through the orientation of the external magnetic field. The results demonstrate effective motion dissipation in response to external excitations and non-trivial initial conditions. Key control parameters include the initial distance between interacting magnets and the ability of translational control to counteract the attractive forces generated by torsional torque. The proposed magnetic control method presents a promising foundation for non-contact position control in offshore wind turbine installations.
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The present study introduces a coupled contactless control approach for managing both translational and torsional motions of a suspended load. This method utilizes magnet-to-magnet interactions between two pairs of magnetic dipoles, with translational motion controlled by adjusting the polarity and intensity of the electromagnetic actuator, and torsional motion regulated through the orientation of the external magnetic field. The results demonstrate effective motion dissipation in response to external excitations and non-trivial initial conditions. Key control parameters include the initial distance between interacting magnets and the ability of translational control to counteract the attractive forces generated by torsional torque. The proposed magnetic control method presents a promising foundation for non-contact position control in offshore wind turbine installations.
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.
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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.
Journal article
(2025)
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Andreas T. Asiikkis, Vaibhav Raghavan, Dimokratis G.E. Grigoriadis, Andrei V. Metrikine, George Lavidas, Antonis I. Vakis
The accurate modelling of hydrodynamic interactions in dense arrays of Wave Energy Converters (WECs) is critical for optimizing design and predicting energy capture efficiency. This study presents the first time-domain experimental validation of the Boundary Element Method (BEM) multi body solver HAMS-MREL, for WEC arrays. The validation involves a comparative assessment of wave excitation forces from numerical predictions and physical measurements for an array of 5 floaters. Results exhibit good overall agreement, with Normalized Root Mean Square Error (NRMSE) values typically below 10 %, though with some exceptions. The results highlight solver limitations that vary with wave steepness and floater positioning within the array. Additionally, this study presents the first integration of HAMS-MREL with WEC-Sim for time-domain simulations, evaluating the linear HAMS-MREL and the weakly nonlinear WEC-Sim hydrodynamic models across various wave conditions. The comparative study conducted with the Ocean Grazer 4.0 case, a dense array of 18 floaters around a monopile, reveals the conditions under which linear modelling remains valid and when nonlinear approaches become necessary. Despite significant wave excitation force differences at wave steepness above 2 %, power output estimates remain within acceptable limits (∼10 %). These findings offer critical insights into appropriate model selection for different wave conditions.
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The accurate modelling of hydrodynamic interactions in dense arrays of Wave Energy Converters (WECs) is critical for optimizing design and predicting energy capture efficiency. This study presents the first time-domain experimental validation of the Boundary Element Method (BEM) multi body solver HAMS-MREL, for WEC arrays. The validation involves a comparative assessment of wave excitation forces from numerical predictions and physical measurements for an array of 5 floaters. Results exhibit good overall agreement, with Normalized Root Mean Square Error (NRMSE) values typically below 10 %, though with some exceptions. The results highlight solver limitations that vary with wave steepness and floater positioning within the array. Additionally, this study presents the first integration of HAMS-MREL with WEC-Sim for time-domain simulations, evaluating the linear HAMS-MREL and the weakly nonlinear WEC-Sim hydrodynamic models across various wave conditions. The comparative study conducted with the Ocean Grazer 4.0 case, a dense array of 18 floaters around a monopile, reveals the conditions under which linear modelling remains valid and when nonlinear approaches become necessary. Despite significant wave excitation force differences at wave steepness above 2 %, power output estimates remain within acceptable limits (∼10 %). These findings offer critical insights into appropriate model selection for different wave conditions.
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.
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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.