Wave Loading Research Articles

Analysis of Wave Load Characteristics of Hovercraft Based on Model Test

The prediction of the wave load on a hovercraft is essential for the design of the hull structure and safety. However, theoretical methods for the prediction of wave loads are still not mature enough due to the unique and complex nature of the air cushion structure, and numerical modeling and simulation are challenging due to the complexity of the gas-solid-liquid three-phase coupling, so the study of wave loads on hovercrafts still relies on experimentation. In this study, we aim to analyze the wave load response characteristics of a four-chamber hovercraft by conducting a wave load model test under medium/low sea states. The load components and amplitude-frequency response characteristics were thoroughly analyzed based on the acquired data of the cushion pressure, acceleration, and bending moment. The main characteristics of the wave-induced response of the hovercraft were described in detail, and an analytical relationship between the cushion pressure and hull acceleration was derived. The reliability of the experimental results was confirmed through a comparison with the derived results. The relationship between the cushion pressure and cushion volume was investigated in terms of the observed geometric volume of the air chamber, and the relationship between the cushion pressure and flow rate was analyzed to validate the derivation of the theory of wave loads on hovercrafts.

Optimization and evaluation of tuned inerter-based dampers for mitigating coupled responses of offshore wind turbines

To achieve lightweight vibration control in offshore wind turbines (OWTs), this study proposes the utilization of two types of tuned inerter-based dampers (TIBDs), namely, the tuned viscous mass damper (TVMD) and tuned inerter damper (TID), to mitigate the coupled responses of an OWT induced by wind and wave loads. First, a multi-degree-of-freedom (MDOF) lumped mass model is established to represent an OWT equipped with a TIBD. Then, a novel structural control module for TIBDs is developed and seamlessly integrated into the modular numerical analysis code OpenFAST. This enables fully coupled aero-hydro-servo-elastic simulations of the OWT-TIBD system. Using the established MDOF model, a TIBD parameter optimization design method is proposed to minimize the peak of the non-dimensional displacement frequency response function. Additionally, a parametric study is performed to investigate the effect of inertance and span height on the control performance. Finally, the performance of the TIBD in attenuating both fatigue and extreme loads is evaluated through nonlinear fully coupled time-domain simulations using OpenFAST and compared to traditional tuned mass dampers (TMDs). The results showed that a lightweight and small damper displacement TIBD is capable of effectively dampening OWT vibrations, yielding a better mitigation effect than that provided by a bulky TMD. Overall, the reduced installation requirements and the commendable control efficiency of a TIBD highlight its potential as a promising candidate for passive control devices in OWT applications.

Motion and Mooring Load Responses of a Novel 12-MW Semi-Submersible Floating Wind Turbine: An Experimental Study

Abstract Due to the complexity of the integrated Floating Wind Turbine (FWT) system, obtaining reliable results necessitates extensive experiments. This paper conducts a comprehensive study on the motion performance and mooring load responses of a novel 12-MW semi-submersible FWT through model tests carried out in a wave basin. A multi-blade large-scale wind-generation system, equipped with a rectifier network, was enhanced and constructed to provide a dependable wind field. And a flexible tower was designed and fabricated, achieving an accurate simulation of the tower's stiffness characteristic and its impact on the overall dynamic response. The marine environmental conditions encompass various combinations of wind, waves, and currents. Rigorous calibration and identification tests were undertaken to validate the environmental conditions and the model system. The findings reveal that, under mild wave parameters, the mooring load is primarily influenced by the resonance response with platform motions, particularly surge resonance. The load effect of wind and current induces mean surge and pitch motions, while their damping effect reduces the standard deviation of responses, notably suppressing the pitch response peak at its natural motion frequency. Wave loads predominantly dictate the vibration range of motion responses. When the current velocity reaches a sufficient magnitude, the coupling effect between current and wave in the wave–frequency region significantly amplifies the mooring response. Notably, motions and mooring loads in the 60-deg and 90-deg directions surpass those in the 0-deg direction, with the maximum responses occurring at 60 deg.

Mixed-mode crack-tip stress intensity factors measurements by caustics method: A comparison between low and high loading rate conditions

Mixed-mode crack-tip stress field is different in low and high loading rate conditions, resulting in different mixed-mode stress intensity factors (SIFs) measurements. How to correctly measure mixed-mode SIFs in different loading rate conditions is of critical importance. To this end, mixed-mode SIFs are measured and compared by optical caustics method with high-speed photography, specifically by the interpretation of crack-tip optical image, i.e., caustics pattern which reflects crack-tip stress field. Different mixed-mode caustics patterns in shape are observed in drop weight and blast loading conditions, indicating that corresponding crack-tip stress field and mixed-mode SIFs measurements are different. Under drop weight loading, mixed-mode caustics patterns are consistent with the classical caustics interpretation for SIFs measurements, while those under reflected P wave loading in blasts are not consistent. Therefore, a modified mixed-mode caustics interpretation is proposed and verified to be available for SIFs measurements in blast loading condition. Finally, underlying reasons for different mixed-mode SIFs measurements in low and high loading rate conditions are discussed, and it is concluded that in low loading rate condition, a longer loading time results in crack-tip K-dominated stress field which is suitable for the classical caustics interpretation, while in high loading rate condition, the loading time is too short to form K-dominated stress field in the crack tip, hence a modified caustics interpretation is necessary. This paper benefits correct applications of caustics method to mixed-mode SIFs measurements in different loading rate conditions.

Numerical simulation and experimental study of the dynamic characteristics of a gas turbine rotor system with beam sea and head sea excitation

Vibration analysis is crucial for studying rotor dynamics. The gas turbine rotor system is subjected to complex alternating loads during navigation, resulting in vibrations transmitted to the bearings that alter the system’s dynamic characteristics. Based on the similarity law of the wave resistance test, a hull model was established. Beam sea and head sea tests were conducted in the towing pool to measure the acceleration response at the key positions. A finite element model of the turbine rotor system was established, and the test data were imported into the model after wavelet noise reduction and resampling to calculate the vibration response at the front and rear bearing points. The vibration responses transmitted to different locations and directions caused by beam sea and head sea conditions were analyzed. A comparison and analysis were conducted on the acceleration responses in various locations and directions under beam sea or head sea conditions. The equivalent von Mises stress distribution of the gas turbine rotor system under beam sea and head sea loads was obtained. The vibration transfer model was verified for accuracy and can be used to quickly analyze the vibration response of bearings under wave load transfer. This study provides a theoretical basis and reference for enhancing the stability of the gas turbine rotor system.

Analysis of edge stress of combined shell under internal waves

Internal wave is essentially a gravity wave induced by the layered structure of water (e.g., density stable layering), with its maximum amplitude occurring within the ocean. Similar to surface waves, internal waves have significant influence on the strength and stability of a submerged body as an external factor. Meanwhile, combined shells are exposed to complicated loads under internal waves, and edge stress is dominant. In this study, the edge stresses of combined shell (typical hemisphere–cylinder combined shell and unfolded sphere–cylinder combined shell) under internal waves were analyzed. Indeed, a semi-empirical, semi-theoretical formula for the edge stress of combined shells (typical hemisphere–cylinder combined shell and unfolded sphere–cylinder combined shell) has been proposed. In this study, the semi-empirical, semi-theoretical formula was corrected by introducing internal wave loads, with the depth of the internal wave taken into consideration. In addition, the corrected formula was verified by finite element analysis, and a simplified equation for the calculation of edge stress of the combined shell under internal waves was developed, with errors in a rational range.

Modelling the Blast Cracking Processes of Rock Masses Using a Total Lagrange Meshless Method

The dynamic damage of surrounding rock masses has a great impact on the tunnel stability during the drilling and blasting construction processes. However, traditional FEM has some difficulties in simulating the blast damage processes of rock masses during mesh re-divisions. In our work, the smoothing kernel function in traditional SPH method has been improved, and the momentum equation considering the blasting load is derived, which realizes the modeling of the dynamic damage evolution processes under the SPH framework. Firstly, two typical examples are numerically simulated: 1) Upper slow and lower steep “Y” shaped fissure and 2) Upper short and lower long “Y” shaped fissure. The simulation results are compared with previous experimental results to verify the correctness of the SPH method. Then, the progressive blast damage processes are simulated, and the effects of different stress wave loading modes, different pre-existing fissure distances, different fissure dip angles as well as different ground stress levels on the blast cracking morphologies are investigated. Results show that: The blast cracks first appear around the blast hole, then the radial cracks propagate to the model boundary; The radial crack length increases with the increase of peak blast stress wave; The length of the horizontal radial crack decreases and the length of the vertical radial crack increases with the increase of the horizontal ground stress; The existence of pre-existing fissure prevents the further extension of the blasting cracks, and the increase of the fissure dip angle leads to the crack propagation at the fissure tips; The increase of fissure distance leads to the larger crack propagation in the around the fissure; The damage count increases with the increase of peak blast stress wave; The increase of the ratio of horizontal stress to vertical stress decreases the damage count; The damage counts increase with the increase of fissure dip angles; The damage degree of the model increases with the increase of the fissure distance.

Joint input-state estimation of structures subjected to complex loads via augmented Kalman Filter with physics informed latent force models

Joint input-state estimation algorithms such as the Augmented Kalman Filter (AKF) rely on the assumption that the distribution of the input loads follows simple spatial patterns, which are either spatially distributed or sparse. However, in many real situations the spatial distribution of the loads is complex and time-varying, which poses a significant challenge. To tackle this issue, this paper introduces a novel method named the Augmented Kalman Filter with Physics Informed Latent Force Models (AKF-PILFM), which incorporates knowledge about the physics underlying the dynamics of the input loads in the estimation based on training data. In the paper, the general formulation of the AKF-PILFM is described, followed by its tailored application to structures subjected to loads with a complex spatiotemporal behavior such as wave loads. The dominant characteristics of the wave loads are identified from training data via the Dynamic Mode Decomposition, enabling the development of a state space model of the loads that can be integrated with the AKF-PILFM. To demonstrate the effectiveness of the proposed methodology, a numerical example is provided consisting of a 3D steel jacket structure subjected to nonlinear irregular waves. The AKF-PILFM shows accurate estimation results and, in the example, outperforms an existing method based on the Gaussian Process Latent Force Models and equivalent modal loads, signifying that the load’s spatiotemporal behavior substantially influences the structural response.

Insights into the scale effects on ship motions and wave loads considering hydroelasticity

To investigate the scale effects on ship seakeeping and wave loads, ship motions and wave loads considering hydroelasticity responses of a 310-m-long ship are calculated in four different scales, i.e., model scale 1:100, 1:50, 1:25 and full-scale 1:1 by using a partitioned CFD-FEM two-way coupled method. The simulation results of the 1:50 scaled model are also compared with tank experimental data of a segmented model with a same scale and configuration for validation. Then the hydrodynamic coefficients, incident waves, heave and pitch motions, vertical bending moment, vertical shearing force and whipping loads obtained by different scaled simulations are compared and the associated scale effects are systematically analyzed. This paper also investigates the influence of segment scheme and backbone configuration on ship modal characteristics, which sheds some light on the design of segmented models with backbone for hydroelasticity experiments.

Model test on dynamic response of coral sand in island dredging airport under wave, tidal and aircraft landing load

The construction of an island airport on a coral reef will inevitably encounter wave, tidal and aircraft takeoff and landing loads. To study the dynamic response of the coral sand island airport under these loads, a 1:50 laboratory model test was conducted with Meiji Reef Airport as the engineering background. The model test studied the pore water pressure characteristics of the coral sand strata beneath the airport runway under wave loads with different wave heights, tidal loads with different tidal heights, and aircraft impact loads with different cyclic loading times. Additionally, the displacement characteristics of the coral sand strata beneath the airport runway under the aircraft impact loads with different cyclic loading times were also studied. The results show that the pore water pressure of coral sand strata under the airport runway decreases with the increasing offshore distance under the wave and tidal loads. The change of wave height has little influence on the pore water pressure of coral sand strata, while the change of tidal water level has a significant effect on it. As the number of aircraft impact load cycles increases, the cumulative excess pore pressure in the coral sand strata under the airport runway no longer increases and plastic deformation occurs. The research can provide a reference for the runway foundation treatment of the island airport under construction and planning.

Using the polynomial chaos expansion and bias-variance tradeoff to analyse the statistical characteristics of a trimaran cross-deck structure

The tendency to design high-performance ships demonstrates the importance of the trimaran and the cross-deck is of particular interest due to its exclusive structures and wave loads. Limited by the high cost of structural numerical simulation, relevant studies emphasize the effectiveness of a specific design scheme. This paper introduces the polynomial chaos expansion (PCE) and the bias-variance tradeoff to explore the statistical characteristics of the cross-deck's strength. The geometric model of a high-speed trimaran is built and the load case is designed. Samples are obtained using the Latin hypercube sampling technique and the corresponding stress response of the cross-deck is extracted by the finite element method. To overcome the limitation of sample size, the PCE is applied as a surrogate model to compute the statistical indicators of the stresses and the bias-variance tradeoff is introduced to select the hyperparameter of the PCE. The results show that the stresses at the cross-deck's corner are much higher and more sensitive to the plate thickness than those at other locations. Furthermore, the PCE is also compared with the Monte Carlo simulation to demonstrate its advantages, and it is shown that the PCE performs better under the limitation of sample size considering accuracy and convergence. The feasibility and efficiency of the PCE and bias-variance tradeoff in the statistical analysis of trimaran cross-deck structure is proved. The insights and recommendations summarized will be a useful aid for the design and optimization of the trimaran.

Novel multivariate design concept for floating wind turbines by Gaidai multivariate reliability method and deconvolution scheme

Development of novel risk and reliability assessment methods is intended to support safer construction of offshore structures, subjected to environmental wave loads. Current study investigated 10-MW FWT (i.e., Floating Wind Turbine), operating under realistic environmental conditions. While increasing operating safety, enhanced risk and reliability assessment methods may eventually help reduce manufacturing and maintenance costs. Excessive structural dynamics being usually caused by environmental stressors, acting on structural system. Environmental loads resulting from ambient wind and wave motions are typical for offshore structures. Current work advocates a novel risk and reliability assessment methodology that allows for reliable forecasting of failure/damage risks, arising from excessive FWT structural dynamics. Recently developed Gaidai multivariate reliability methodology along with state-of-the-art deconvolution method had been employed. Unlike existing reliability approaches such as Weibull-type, GP (i.e., Generalized Pareto), POT (i.e., Peaks Over the Threshold), etc., the recommended methodology does not rely on any pre-assumed functional class, when extrapolating failure probability functional tail. Practical advantages of the suggested multivariate reliability methodology combined with deconvolution scheme over, that is, 4-parameter Weibull’s extrapolation method had been demonstrated. Suggested methodology makes effective use of even limited underlying datasets, enabling robust and accurate projections of multidimensional structural system failure/damage risks. Overall methodological performance suggests that numerically stable and accurate extreme dynamics forecasts for FWT structural bending moments might be obtained, utilizing suggested multivariate reliability methodology. Deconvolution extrapolation approach being more numerically stable than parametric extrapolation techniques, due to its non-parametric nature.

Research on simulating coal crack development under high voltage electric pulse stress waves using zero thickness cohesive elements

High voltage electric pulse (HVEP) technology has demonstrated significant potential in enhancing coal seam permeability. However, there is a notable gap in numerical simulation studies that investigate the cracks development patterns in coal under the influence of this technology. In this study, a HVEP coal rock fracturing system was utilized to conduct a physical simulation experiment of coal sample electrical fragmentation. A finite-discrete element method (FDEM) model, incorporating zero-thickness cohesive elements, was developed to simulate the process of stress wave-induced crack propagation in coal, triggered by the plasma channel. The results indicate that over time, the stress wave typically exhibits an initial rapid rise followed by an oscillatory decline. The peak value of the stress wave decreases significantly with distance, stabilizing beyond a propagation distance of 10 mm. Furthermore, the fracturing efficacy of coal by HVEP stress waves is closely linked to specific characteristic parameters: within the range of 75–125 MPa, a positive correlation exists between the stress wave peak and the complexity of the coal crack network. Reducing the stress wave loading rate can increase the crack area to some extent, although excessively slow loading rates may lead to excessive energy dissipation during propagation, which is detrimental to crack expansion. Conversely, when the ratio of β to α ranges from 1 to 100, decelerating the attenuation rate of the stress wave aids in generating stress concentration within the crack zone, thereby facilitating crack propagation. The established numerical model aims to advance understanding of HVEP’s fracturing mechanisms and enhance its application in coalbed methane extraction.

Characteristics of wave loading and viscous energy loss of a bottom-sitting U-OWC wave energy device: A validated numerical perspective

This study involves numerical simulations of regular waves interacting with a bottom-sitting circular OWC wave energy converter with a U-shaped duct (circular U-OWC). A numerical wave tank is built based on the RANS equation and is validated against experiments. The effect of water depth and the height of the outer tube of the U-shaped duct on capture efficiency, wave loading, and viscous energy loss is investigated numerically. Results show that the height of the outer tube of the U-shaped duct has a significant effect on the capture efficiency of the device. Wave loading analysis reveals a critical mode of stability that may threaten the operation safety of the device. It is found that increasing the height of the U-shaped duct opening increases the viscous energy loss inside the U-shaped duct. A semi-theoretical model between work done by waves to the device and the viscous energy loss in the U-shaped duct is established, numerical data indicates that a significant amount of work done by waves to the device is lost in viscous effects. This suggests that certain optimization for reducing wave loading could possibly also reduce viscous energy loss, thus improving the overall efficiency of the device.

Investigation of mooring breakage impact on dynamic responses of a 15 MW floating offshore wind turbine

The stability and integrity of the mooring system are some of critical factors affecting the safety and performance of floating offshore wind turbines (FOWTs). For this reason, it is necessary to investigate the dynamic responses of the rotor, platform, and the remaining cables of the FOWT subjected to mooring breakages. This is because a mooring breakage significantly increases the risk of damage to the FOWT, especially for a nonredundant mooring system. This study has analyzed the platform motions and mooring tension of a 15 MW FOWT, where each offset column connects to two and three mooring lines to enhance the redundancy of the mooring system. The fully coupled simulations of the FOWTs under mooring breakage scenarios are examined using the well-validated numerical framework, OpenF2A, to consider wind, wave and current loading combinations. The result reveals that the breakage of a single mooring has a minor impact on the aerodynamic performance and aeroelastic response of the FOWT for both mooring system configurations. Notably, the platform experiences significant surge and sway when the upwind mooring breaks, leading to a sharp increase in tension of the remaining mooring lines positioned in the same direction. Moreover, the occurrence of snap load events is another factor resulting in the abrupt increase in the mooring tension. However, the maximum tension in the remaining mooring lines has not exceeded the threshold of breaking stress for both redundant mooring systems. The mooring configuration with two catenary cables connected to each column is suggested for the station-keeping system of the 15 MW FOWT considering the dynamic behavior and manufacture cost.

Investigation of the Overall Damage Assessment Method Used for Unmanned Aerial Vehicles Subjected to Blast Waves

With the aim of investigating the assessment methodology for the overall damage effects on an unmanned aerial vehicle (UAV) subjected to a blast wave, the failure criteria for the typical UAV was formulated through an analysis of the structural strength design standards. Specifically, the shear force associated with wing failure can serve as a critical parameter for assessing the overall damage inflicted on the UAV by blast waves. According to the design load criterion of the aircraft, the shear force value corresponding to the overall failure of the typical UAV was calculated. Numerical simulations were conducted to investigate the mechanical response of UAV structures under blast wave loading generated by a 500 g explosive. Combining the critical shear force values obtained from theoretical calculations with the numerical simulation results, two distances between the explosives and the UAV that could produce different damage effects were estimated, namely 1 m and 2.5 m. Subsequently, static explosion experiments with equivalent explosive charges were performed, revealing different damage effects on a typical UAV at two specific distances. The numerical simulation results were highly consistent with the experimental observations, further validating the scientific and rational basis for using shear force as a primary parameter in assessing overall structural damage to fixed-wing UAVs.

A frequency-domain hydroelastic approach for modeling and stochastic dynamic analysis of pontoon-type floating bridges

In recent years floating bridges have been extensively studied owing to their potential application for crossing wide and deep fjords. An efficient approach for analyzing stochastic hydroelastic responses of floating bridges is valuable for fast assessment of various load effects for preliminary design. This study develops a frequency-domain approach for hydroelastic analysis of pontoon-type floating bridges subjected to wave loads. The frequency-dependent motion equation of the multi-pontoons is established based on the potential flow theory and linearized Morison’s equation for viscous damping. The structural dynamics of the elastic bridge girder are represented utilizing a beam model with excitations transferred from each pontoon. The proposed method is applied to an end-anchored curved floating bridge, with highlights on the verification against a validated time-domain simulation tool. Convincing agreements are found in terms of the eigenvalues, wave excitation loads, and response statistics. The method shows high fidelity with an accurate capture of the linear wave-frequency responses as well as the low-frequency resonances. A further discussion demonstrates that the wave viscous damping restrains low-frequency resonant responses, whereas the hydrodynamic interactions of pontoons induce more resonant peaks in the wave frequency.

Experimental and numerical study on dynamic response of a photovoltaic support structural platform with a U-shaped tuned liquid column damper

A tuned liquid column damper (TLCD) is widely used in offshore structures as a passive energy dissipation device to reduce the harm of wind, wave, and current loads to the safety of offshore platforms. This investigation explores the dynamic response and interaction mechanism of a photovoltaic support structural platform (SSP) equipped with a TLCD by experimental and numerical analysis. The vibration mitigation performance of the TLCD under varying liquid depth ratios, external excitation frequencies, and amplitudes is systematically evaluated. The experiments focus on assessing the structural dynamic response and wall pressure to determine the vibration reduction efficiency of the TLCD for structures with fundamental frequencies more than 2 Hz. The experimental results indicate that the TLCD can reduce the structural response maximally near the natural frequency (2.52 Hz) of the structure, with vibration reduction effectiveness ranging from 42.0% to 85.1%. Additionally, one develops a two-way fluid-structure interaction (FSI) model to investigate further the impact of hydrodynamic pressure caused by sloshing inside the TLCD on the SSP motion response, which providing a more detailed explanation for the different phenomena observed in the experimental results.

Dynamic response of OWT tripod pile foundation in clay considering scour

Tripod-supported offshore wind turbine (OWT) foundation must withstand wind, wave, and seismic loads. In addition, it may be threatened by scouring during its service life, which could affect its bearing capacity and the overall OWT dynamic response. This study develops a three-dimensional numerical model of OWT tripod pile foundation to investigate scour effects. The numerical model incorporates a simplified single bounding surface model to simulate the dynamic stress–strain response of clay soil. The results revealed that scouring can reduce the first-order natural frequency of tripod pile-OWT system; however, the reduction usually does not lead to resonance within the 1P frequency range. Nonetheless, as the scour depth increases under wind and wave loads, the horizontal displacement of the wind turbine structure increases monotonously; however, its peak acceleration increases initially then decreases slightly as the scour depth continues to increase. Under seismic loading only, the OWT response exhibits complex evolution pattern as the scour depth increases. On the other hand, the foundation horizontal displacement and rotation angle increase significantly under combined wind-wave-seismic loads when the scouring depth reaches three times the pile diameter. Finally, the scouring depth has a relatively small impact on the foundation vertical displacement.

Active pendulation control of hoisting systems of ship-mounted cranes under ocean wave excitations: Principle and experimental study

Large-scale ship-mounted cranes are important facilities for marine construction. However, under harsh sea conditions, the hoisting system of a ship-mounted crane is often subjected to wave loadings, leading to frequent occurrences of large-amplitude resonance. This paper proposes an active control method, termed the active displacement compensation (ADC) approach, designed for suppressing the large-amplitude pendulation of the hoisting system of ship-mounted cranes. By controlling the position of the suspension point of the hoisting system using linear-motion actuators, the input excitations of the hoisting system induced by the ship motions can be partially or fully compensated in real-time. Therefore, the proposed ADC approach can significantly suppress the large-amplitude pendulation of the hoisting system. The optimal feedback gain and time delay of the ADC approach are theoretically obtained. The ADC approach has been validated by using a six-degree-of-freedoms shaking table test and numerical simulation on the in-plane pendulation suppression of a small-scale hoisting system. Experimental results indicate that the ADC approach achieves a pendulation reduction ratio between 85 % and 89 % for the hoisting system subjected to scaled ship motion records. This study may help develop efficient active control techniques for hoisting systems of ship-mounted cranes under harsh sea conditions.