Nonlinear Wave Loads Research Articles

Directional effects on the nonlinear response of vehicle-bridge system under correlated wind and waves

Long-span railway sea-crossing bridges are subjected to strong winds and high waves. Due to variations in structural features, including stiffness and size across diverse orientations, the dynamic response of vehicles and bridges can exhibit significant differences under distinct wind and wave directions. Consequently, a novel approach for analyzing bridge and vehicle dynamic performance called the directional wind-wave-vehicle-bridge (DWWVB) model has been developed. To acquire the statistical characterization of the correlation between wind and wave conditions, a three-dimensional joint probability distribution of wind and wave characteristics derived from collected data at the bridge site is established. The wind loads are derived from wind tunnel tests and computational fluid dynamics simulations. The nonlinear wave loads are solved utilizing the hydrodynamic solver ANSYS-AQWA. Based on the finite element bridge model and a 23-degree-of-freedom mass-spring-damper vehicle model, the aerodynamic nonlinearity and initial geometric nonlinearity are considered during the iteration process. The Newmark-β method is employed to solve the dynamic response of bridges and vehicles. The calculation results reveal that the most unfavorable response occurs when the wind direction is 45° and the wave direction is 90°. The directional analysis provides valuable insights for selecting optimal bridge locations and reasonable design environmental parameters.

Intelligent prediction of wave loads based on multi-source data-driven methods

ABSTRACT High-fidelity wave-load tests is pivotal in the design and development of modern ship structures. Nonetheless, the prohibitive cost of conducting such tests limits their applicability. A wave-load data fusion method was implemented using the model test data from a typical displacement-type ship to generalise the small sample test, and a multi-source data characterisation and model parameter optimisation method were established to achieve efficient wave-load (wave frequency and slamming superposition) prediction. Using multi-source data, a multi-fidelity wave-load prediction (MFWLP) model was constructed by combining numerical computation, regular wave tests (RWT), and irregular wave test (IWT) data based on transfer learning with a secondary correction wave load prediction under irregular wave conditions. The model was effectively employed in a ship wave-load engineering case. This study reveals that the adopted MFWLP model demonstrates adequate extrapolation and prediction capabilities, even with limited high-fidelity test samples. The discrepancy between the nonlinear wave load prediction and model test was found to be within 15%. Therefore, the proposed method can serve as a foundation for rapidly assessing ship wave loads across various sea conditions, especially under high sea states.

Nonlinear buffeting responses of a coastal long-span bridge under the coupled wind, wave and current loads

The buffeting responses of sea-crossing bridges pose significant challenges due to the diverse terrain in the bridge region and intricate coupling effects between the environmental variables and structures. A novel Wind-Wave-Current-Bridge (WWCB) framework is proposed to assess the buffeting responses of coastal long-span bridges under coupled wind, wave, and current loads. By employing measured wind and wave data, the optimized C-vine copula and Ekman drift current theory are utilized to establish correlations among four environmental variables, namely wind speed, wave height, wave period, and current velocity. The nonlinear wave loads acting on the pile-cap foundations are computed using the potential flow theory and boundary element method (BEM). The interactions among wind, wave, current, and bridge involve both aerodynamic and geometric nonlinearity. The dynamic responses of the full bridge finite element model are iteratively solved until structural convergence is achieved using the Newmark-β method. Subsequently, the buffeting responses and the vibration mechanism of bridges are discussed in both the time and frequency domains. The results indicate that the nonlinear and correlation effects of wind, waves, and currents significantly affect the buffeting responses of the example bridge. Furthermore, the influence mechanism of wind and waves on the sea-crossing bridge is also discussed.

A new Gaussian Process based model for non-linear wave loading on vertical cylinders

We aim to establish a fast and accurate model for fast prediction of nonlinear loading on vertical cylinders such as are typically used for fixed offshore wind turbines. We follow a ‘Stokes-type’ force model and approximate the amplitude of the higher harmonics of force by relating these to the linear force time series raised to appropriate power through amplitude and phase coefficients. We reanalyse previous experimental data and perform new experiments to expand the parameter space and establish a force coefficients database for engineering applications. A machine learning model is used to interpolate the database and make predictions on the higher order force coefficients. The machine learning model also provides a cross-validated confidence interval to indicate the prediction uncertainty and reflect model reliability. We further extend the prediction capability to unidirectional random waves with a novel force segmentation method, which localised wave groups from the random background. The new Stokes-Gaussian Process (Stokes-GP) model developed can provide engineering predictions of nonlinear wave loading on a cylinder for individual wave groups and random seas, which are straightforward to apply and fast to compute and the important higher-order loading components are considered. This will significantly improve the accuracy of the loading prediction and the ease of application for force predictions.

Data Informed Model Test Design With Machine Learning – an Example in Nonlinear Wave Load on a Vertical Cylinder

Abstract Model testing is common in coastal and offshore engineering. The design of such model tests is important such that the maximal information of the underlying physics can be extrapolated with a limited amount of test cases. The optimal design of experiments also requires considering the previous similar experimental results and the typical sea-states of the ocean environments. In this study, we develop a model test design strategy based on Bayesian sampling for a classic problem in ocean engineering -- nonlinear wave loading on a vertical cylinder. The new experimental design strategy is achieved through a GP-based surrogate model, which considers the previous experimental data as the prior information. The metocean data are further incorporated into the experimental design through a modified acquisition function. We perform a new experiment, which is mainly designed by data-driven methods including several critical parameters such as the size of the cylinder and all the wave conditions. We examine the performance of such a method when compared to traditional experimental design based on manual decisions. This method is a step forward to a more systematic way of approaching test designs with marginally better performance in capturing the higher-order force coefficients. The current surrogate model also made several ‘interpretable’ decisions which can be explained with physical insights.

Hurricane Wave Loads on Spar-Type Floating Wind Turbines: A Comparison of Simulation Schemes

Floating wind turbines are sensitive to hurricane events. Since the turbine rotors are parked and the blades are feathered during hurricanes, the aerodynamic loads due to boundary-layer winds are relatively small compared to the hydrodynamic loads due to sea surface elevations. Hence, accurate modeling of the hurricane wave loads is crucial to ensure the safety of floating wind turbines. During a hurricane, large wave heights with severe flow separation make it inaccurate to use either linear panel method-based models (without nonlinear consideration associated with fluid viscosity) or Morison equation-based models (without unsteady consideration associated with fluid memory). Efforts have been made to advance simulation schemes of hurricane wave loads on spar-type floating wind turbines. This study systematically compares and assesses the efficacy of six hydrodynamic models available in the literature along with a newly proposed model. The ability of these seven hydrodynamic models to capture nonlinear and/or unsteady effects is investigated. As a demonstration example, the wave loads on a spar-type wind turbine are calculated using these seven models to highlight the underlying role of each simulation scheme in accurately acquiring the dynamic responses of this type of offshore floating structure in severe hurricane seas. It is found that the nonlinear viscous term in the Morison equation and hybrid model serves as an important nonlinear damping mechanism. The reduction of the low-frequency wave load and added mass in the modified hybrid model collectively leads to larger displacements compared to those based on the hybrid model. While the displacements based on the stretching method and Rainey’s equation are similarly larger than those based on the Morison equation, their nonlinear wave loads are much smaller than those in FNV theory.

Comparative Study of Numerical Methods for Predicting Wave-Induced Motions and Loads on a Semisubmersible

Numerical simulation tools based on potential-flow theory and/or Morison’s equation are widely used for predicting the hydrodynamic responses of floating offshore wind platforms. In general, these simplified approaches are used for the analysis under operational conditions, albeit with a carefully selected approach to account for viscous effects. Nevertheless, due to the limit hydrodynamic modelling to linear and weakly nonlinear models, these approaches severely underpredict the low-frequency nonlinear wave loads and dynamic responses of a semisubmersible. They may not capture important nonlinearities in severe sea states. For the prediction of wave-induced motions and loads on a semisubmersible, this work systematically compares a fully nonlinear viscous-flow solver and a hybrid model combining the potential-flow theory with Morison-drag loads in steep waves. Results show that when nonlinear phenomena are not dominant, the results obtained by the hybrid model and the high-fidelity method show reasonable agreement, while larger discrepancies occur for highly nonlinear regular waves. Specifically, regular waves with various steepness over different frequencies are focused in the present study, which supplements the understanding in applicability of these two groups of method.

Numerical and Experimental Investigations on Non-Linear Wave Action on Offshore Wind Turbine Monopile Foundation

Monopiles are commonly utilized in offshore wind farms but are prone to non-linear wave loads and run-ups, significantly affecting their engineering design. Therefore, it is crucial to pursue a complete understanding of the non-linear wave action on monopile foundations. Both numerical and experimental investigations on the non-linear wave loads and run-ups on an offshore wind turbine monopile foundation are performed in this paper. The experiment is carried out at a scale of 1/30 in a wave flume at the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, in which the wave loads and run-ups along the monopile are measured. Based on the second-order potential flow model and time-domain higher-order boundary element method (HOBEM), the related numerical tests are conducted to study the non-linear effects further. It is found that the present non-linear potential theory is sufficient for the simulation of wave force and run-ups on the monopile in the range of wave slope kA < 0.15 before wave breaking. “W” type distribution of wave run-up along the monopile is found, in which the peak value occurs at the frontward side (i.e., θ =180°) and is the maximum due to full reflection; the two symmetrical minimum amplitudes lie in the zones of (45° ≤ θ ≤ 90°) and (270° ≤ θ ≤ 315°), whose positions shift downward with the increase of wave non-linearity. Energy transfer among the fundamental wave component and higher-order components is also found, which is most apparent on the backward side. Besides, the transverse resonance occurs in the wave flume due to the wavelength being near the flume width, which induces the wave run-up at the backward position larger than that at the frontward position.

A high-order finite difference method with immersed-boundary treatment for fully-nonlinear wave–structure interaction

In order to predict nonlinear wave loading on marine structures, a fully nonlinear higher-order finite difference based potential flow solver with all boundary conditions treated by an immersed boundary method has been developed in this paper. The solver adopts high-order finite difference schemes for the spatial derivatives and a 4th order Runge–Kutta method for time stepping. Test cases of forced oscillation of a cylinder in an infinite fluid domain are first studied, which reveal the advantage of the acceleration potential method in terms of wave load computation. Then a wave generation problem using a piston type wave maker is tested. Special attention is paid to the intersection point between the free surface and the body surface, and a scheme which best meets the accuracy and stability requirements is suggested from several proposals. A novel hyperviscosity filter, which works for both uniform and non-uniform grids, is introduced to stabilize the time-domain solution of the wave maker problem. Finally, a forced heaving cylinder on the free surface is considered, and the nonlinear wave loads on the cylinder are analyzed and compared to benchmark results.

Harmonic structure of wave loads on a surface piercing column in directionally spread and unidirectional random seas

We investigate the harmonic structure of wave-induced loads on vertical cylinders with dimensions comparable to those used to support offshore wind turbines. Many offshore wind turbines are designed, so the structural resonance is two or three times the fundamental wave loading period, which may be excited by higher harmonics of wave loading. The suitability of a ‘Stokes-type’ model for force is examined. We analyse experimental data for unidirectional and directionally spread sea-states. We demonstrate that approximate harmonic components may be extracted from a random time series, using a novel signal processing method. The extracted harmonics are shown to follow a ‘Stokes-like’ model, where the higher harmonics in frequency are proportional to the n-th power of the linear inline force component and its Hilbert transform. Results show that the third harmonic component of force is fitted less well by this model, which is consistent with the literature. A key new result is that the harmonic coefficients for spread and unidirectional seas are nearly identical when fitted as powers of the linear inline force and its Hilbert transform. This finding has the potential to greatly simplify the process of generating harmonic data for new wavelength to cylinder and wavelength to depth ratios. This also implies that the size of the inline component of the ntextrm{th} harmonic for force in a directional sea relative to the same component in a unidirectional sea scales as cos ^n sigma _theta , where sigma _theta is the rms directional spreading angle of the incident wave field. Hence, higher harmonics will be of less importance in directionally spread seas than unidirectional ones. We show that the computationally fast harmonic decomposition approach taken here can reproduce the shape and magnitude of the loading from non-breaking waves waves in a wide range of realistic unidirectional and directionally spread sea-states. The proposed force model has potential as an engineering tool for computationally fast prediction of nonlinear wave loads.

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Calculation of slamming wave loads on monopiles using fully nonlinear kinematics and a pressure impulse model

The design methods for highly nonlinear wave loads on monopile structures has over the past years been extended with methods based on pre-computed fully nonlinear wave kinematics. Yet, the slamming events of the strong sea states cannot currently be predicted with these methods. We here present a simple recipe for the application of a recent pressure impulse based slamming load model in combination with fully nonlinear wave kinematics and validate the results against lab measurements of uni- and multi-directional storm sea states. The experimental slamming loads are extracted from lab measurements equivalent to 954 full scale hours. Six methods for the extraction of the slamming force are developed and analysed in detail, with a final selection of two for the further analysis. The experimental analysis shows that the frequency of slamming is larger in uni-directional sea states relative to sea states with directional spreading, and with slightly smaller force impulses. The calculated slamming frequencies from the measurements are used in the application of the numerical slamming model. It is shown that the application is straightforward and robust and involves an intuitive selection of the model inputs from the incident wave kinematics. A generally good agreement between the model and measurement distributions of the force impulse is observed. The difference between 3D and 2D slamming impulses, though, is found to be larger in the numerical model. This is traced to the numerical particle velocities in the wave crests. The pressure impulse model is next extended by assuming a predefined generic slamming force time variation and through calibration of the peak slamming force, a generally good agreement between the model and ensemble-averaged measured slamming force time series is obtained, given the uncertainty in the slamming load extraction. It is also observed that the commonly used non-dimensional slamming force peak of 2π is unrealistically large in the irregular slamming waves because of the 3D effects of small curling factors.

Failure mechanism and vulnerability assessment of coastal box-girder bridge with laminated rubber bearings under extreme waves

Coastal box-girder bridges have wide applications in the near-shore transportation systems and many low-lying bridges are under serious threats from extreme waves. However, few researchers paid attention to the dynamic structural behaviors of coastal low-lying bridges under extreme wave conditions, which is crucial to the rational design of these bridges. In this study, a three-dimensional finite element model, including the local nonlinear bearing material model and wave loading importation from the computational fluid dynamics (CFD) simulations, is established to investigate the dynamic behavior of the bridge structure. Specifically, to provide a more scientific and precise evaluation for the dynamic behavior of coastal bridges, the laminated rubber bearing model is established at joints between the superstructure/box-girder and bent cap using solid elements. Three common failure modes, including the large lateral shear deformation of the rubber bearing, sliding between the girder and bearings, and overturning of the superstructure, are investigated in detail. To consider the uncertainty under different loading conditions, one surrogate model based on the support vector machine (SVM) is adopted to enhance the calculation efficiency of the vulnerability assessment for the coastal box-girder bridge. It is revealed that (a) The overturning and sliding failures are more likely to occur for the box-girder in submerged states, while the large lateral shear deformation for the bearing is prone to arise when the girder is elevated; (b) The wave height to water depth ratio has a significant influence on the safety of the bridge; and (c) The high failure probability indicates that appropriate countermeasures are necessary to improve the safety margin of the bridge.

Dynamic analysis of bridge structures under combined earthquakes and wave loadings based on a simplified nonlinear Morison equation considering limit wave steepness

Utilizing the traditional Morison equation to calculate wave forces in cylindrical structures is cumbersome, and there are currently few studies regarding the high-order nonlinear Morison equation. In this study, the traditional Morison equation is simplified, and the simplified second-order nonlinear Morison equation based on the Stokes second-order wave is derived. The correctness of the simplified Morison equation is verified, and the use of the stability point method to solve the second-order nonlinear wave force is proposed. Based on the simplified second-order nonlinear Morison equation, the nonlinear dynamics of bridge structures under the combined loadings of earthquakes and second-order nonlinear waves are investigated. The results indicate that the displacement and stress responses of the second-order nonlinear wave to the bridge structure are significantly greater than those of the linear wave. When under second-order nonlinear waves and earthquake loadings combined within bridge structures, earthquakes will significantly affect these bridge structures. The formula for the breaking wave force based on second-order nonlinear waves is proposed. The breaking wave force based on second-order nonlinear waves has a large load on the bridge structures, and it will induce a weak high-frequency effect. When under combined the second-order nonlinear breaking wave and earthquake loadings on the bridge structure, earthquakes will still play a major role.

A GPU-accelerated domain decomposition method for numerical analysis of nonlinear waves-current-structure interactions

A fully nonlinear near-far fields coupling solver is proposed in this work. The target is to provide an efficient numerical tool for wave-current-structure interaction simulations. A GPU-accelerated high-order spectral (HOS) solver is developed to simulate the wave propagation and interaction with current in large far field and an incompressible flow solver with free surface capture scheme from the OpenFOAM library is adopted in the near field to solve the nonlinear wave loads and seakeeping response of the ship hull. The newly developed HOS solver is firstly validated by two wave-current interaction test cases, including a regular wave train travelling on collinear following and opposing current, and regular waves blocked by strong opposing current. Then, the near and far field coupling solver is applied to a simulation of the seakeeping response of a cruising ship hull in head wave condition. Lastly, The proposed method is applied to a more practical application, i.e. the self-propulsion of a hull in short crested spreading irregular waves. The numerical results are compared to the lab measurement data or numerical results, good agreements have been obtained.

Numerical investigation of nonlinear wave loads on a trestle-netting enclosure aquaculture facility

The rapid development of the marine industry offers more opportunities to combine aquaculture with other marine uses. This study reports a trestle-netting enclosure aquaculture facility that combines an offshore steel trestle with a marine aquaculture facility in which the trestle acts as a supporting substructure. In this study, the numerical models include one configuration without netting and three configurations with netting in different regular waves, which are generated based on stream function theory owing to nonlinear wave problems. The time series of the horizontal wave forces were obtained and analyzed in the four models. Numerical results showed that netting can significantly increase the positive amplitudes of horizontal wave forces, and the wave forces of trestle with the lee-side netting were almost smaller than those of the wave-side netting. Moreover, we investigated the nonlinear features of the wave forces and profiles. The horizontal asymmetry factors of the wave forces are affected by those of the wave profiles, while the vertical asymmetry factors of the wave forces are affected by those of the wave slope profiles. The effects of the netting on the force-positive amplitudes agree with the horizontal asymmetry factors of the wave forces but not with the vertical asymmetry factors.

Frequency domain modeling of long-span sea-crossing bridge under stochastic wind and waves

In this study, a frequency domain modeling framework that assembles aero- and hydro-dynamic approaches to characterize the structural motions of a long-span sea-crossing bridge under stochastic wind and waves is proposed as an efficient alternative for the conventional time-consuming time domain analysis. The improved quasi-steady buffeting model is employed to investigate the fluctuating wind actions on structural components and the aero-elastic effect of bridge decks. Potential flow theory associated with constant boundary element method is applied to calculate the linear as well as quadratic hydrodynamic transfer functions and both first- and second-order wave loads are considered and coupled in the modeling framework. The proposed methodology is well validated using a benchwork experiment of a flexible cylinder subjected to wind and waves. The dynamic performance of a long-span sea-crossing bridge under extreme wind and wave conditions is modeled using the proposed framework. The effects of wind and waves, different mode combinations, directionality and nonlinear wave loads on global responses are discussed. In the proposed approach, a combination of only a few main modes is necessary to yield plausible displacement responses of bridge deck, while more modes are required to obtain converged internal force responses.

Experimental investigation of hydrodynamic loading induced by regular, steep non-breaking and breaking focused waves on a fixed and moving cylinder

Monopiles are commonly adopted in marine structures and subject to combined loading from waves and currents. The nature of superposition of wave and current loads needs to be known during the design stage. In the present paper, combined hydrodynamic loading induced by nonlinear waves and uniform currents on a cylinder is experimentally investigated. The current is represented by towing the cylinder along the flume. By this, nonlinear wave–current interactions are excluded physically, but the loading of a proportional current following or opposing a wave group is captured and analyzed. It is argued that towing makes provision for analyzing the nature of superposition of wave and current loads using Morison theory (which is not applicable to true combined wave–current fields) and also facilitates experimentation of a wide range of nonlinear wave and uniform current loading combinations onto the structure. Accordingly, regular, steep non-breaking and breaking focused waves interacting with the cylinder towed along and in opposition to the wave-field at different speeds have been investigated. The non-breaking wave–structure interactions have been analyzed within the framework of Morison theory using Fully Nonlinear Potential Theory (FNPT) based kinematics. Breaking wave–cylinder interactions have been analyzed through a spectral approach. The experiments demonstrate that wave and locally-acting current loads on the structure can be linearly superimposed, irrespective of the nature of waves and towing speed. Hence, provided wave–current interactions are excluded, steep breaking wave and uniform current loads can be linearly superimposed, despite focused wave generation itself being inherently nonlinear.