Hydroelasticity Analysis in Frequency Domain and Time Domain

Hydroelasticity has been introduced in ship seakeeping assessment for more than three decades, and it finally becomes an essential tool in marine industry for design of some types of ship. In the 35 years of evolution, hydroelasticity methods applied in industry of marine and offshore energy grown up from two dimensional to three dimensional and now has analysis models of linear model in frequency domain and nonlinear model in time domain. In this paper, we present the three dimensional hydroelasticity theory model in frequency domain and time domain, show the difference in the approach, and discuss their applications in wave-structure interaction.

Hydroelasticity analysis of a vessel-shaped fish cage under incident,diffraction and radiation wave fields

Vessel-shaped fish cages are promising large aquaculture structures developed in recent years,with an overall length of nearly 400 m.In this paper,a coupled hydroelasticity model of a vessel-shaped fish cage is used to calculate the motion and structural response in the time domain.First,the floating body of the cage is discretized into a multimodule system to calculate the frequency-domain hydrodynamic loads.Then,the multimodule system is connected by equivalent elastic beams to consider the hydroelastic be-havior in the time domain.The hydrodynamic loads of the multimodule system are transformed from the frequency-domain loads.Moreover,based on the velocity field transfer functions and the motion of the multimodule system,coupling wave fields considering incident,diffraction and radiation waves are built and used to calculate the loads on the net and steel frame.By iterating the motion response of the multi-module system and the hydrodynamic loads on the net and steel frame in the time domain,the balanced hydroelasticity response of the whole cage is finally obtained.The results show that the hydroelasticity effects have a significant influence on the vertical displacement and cross-sectional load effects of the vessel-shaped fish cage.

A three-dimensional hydroelasticity theory for ship structures in acoustic field of shallow sea

Nowadays the development of green ship technology requires the vibration and noise control of oceangoing ships. The three-dimensional hydroelasticity theory of ships was previously extended to include the effect of fluid compressibility. This enables the dynamic responses and the acoustic radiations of a ship excited by onboard machineries or fluid fluctuation loads to be predicted. In this paper the hydroelastic analysis and sonoelastic analysis methods are fixrther incorporated with the Green＇s function in the Pekeris ocean hydro-acoustic waveguide model to work out a three-dimensional sonoelastic analysis method for ships in the ocean hydro-acoustic environment. As examples, the sound radiations of a floating elastic spherical shell excited by a concentrated force and a traveling LNG ship excited by the propeller induced pulsating forces acting on the wetted bottom plate of the stem in the shallow sea environment are predicted. The influences of the free surface and the sea bed on the generalized hydrodynamic coefficients and the acoustic pressure distributions in fluid domain are illustrated and discussed.

Model Testing for Ship Hydroelasticity: A Review and Future Trends

Conducting model experiments is an effective and reliable way in the investigation of ship hydrodynamic and hydroelastic behaviors. A survey of model testing techniques for ship hydroelasticity and its prospect are presented in this paper. The research highlights with respect to ship hydroelasticity and key points in model testing are summarized at first. Then testing techniques including laboratory tank test and full-scale sea trial are reviewed, and both their advantages and disadvantages are analyzed comprehensively. Based on the conventional testing approaches, a state-of-the-art testing approach which includes performing tests using large-scale model at sea is proposed. Furthermore, recommendations towards the further development of ship hydroelasticity tests are forecasted and discussed.

Ribbon bridge in waves based on hydroelasticity theory

For the design and operation of a floating bridge,the understanding of its hydroelastic behavior in waves is of great importance.This paper investigated the hydroelastic performances of a ribbon bridge under wave action.A brief introduction on the estimation of dynamic responses of the floating bridge and the comparisons between the experiments and estimation were presented.Based on the 3D hydroelasticity theory,the hydroelastic behavior of the ribbon bridge modeled by finite element method(FEM)was analyzed by employing the mode superposition method.And the relevant comparisons between the numerical results and experimental data obtained from one tenth scale elastic model test in the ocean basin were made.It is found that the present method is applicable and adaptable for predicting the hydroelastic response of the floating bridge in waves.

Slamming and Green Water Loads on Bow-Flare Ship in Regular Head Waves Investigated by Hydroelasticity Theory and Experiment

With the development of ships towards large scale, high speed and light weight, ship hydroelastic responses and slamming strength issues are becoming increasingly important. In this paper, a time-domain nonlinear hydroelasticity theory is developed to predict ship motion and load responses in harsh regular waves.Hydrostatic restoring force, wave excitation force and radiation force are calculated on the instantaneously wetted body surface to consider the nonlinear effects caused by large amplitude motions of ship in steep waves. A twodimensional(2 D) generalized Wagner model and a one-dimensional(1 D) dam-breaking model are used to estimate the impact loads caused by bow flare slamming and green water on deck, respectively;the impact loads are coupled with the hydroelastic equation in time-domain. Moreover, segmented model tests are carried out in a towing tank to investigate the wave and slamming loads acting on the hull sailing in harsh regular head waves and also validate the numerical results.

超大浮体与OWC集成系统的水动力性能:半解析研究

Responses of the very large floating Structures(VLFS)can be mitigated by implementing oscillating water columns(OWCs).This paper explores the fundamental mechanism of present wave interactions with both structures and examines the hydrodynamic performance of VLFS equipped with OWCs(VLFS-OWCs).Under the linear potential flow theory framework,the semi-analytical model of wave interaction with VLFS-OWCs is developed using the eigenfunction matching method.The semi-analytical model is verified using the Haskind relationship and wave energy conservation law.Results show that the system with dual-chamber OWCs has a wider frequency bandwidth in wave power extraction and hydroelastic response mitigation of VLFS.It is worth noting that the presence of Bragg resonance can be trigged due to wave interaction with the chamber walls and the VLFS,which is not beneficial for the wave power extraction performance and the protection of VLFS.

The application of three-dimensional hydroelastic analysis of ship structures in Pekeris hydro-acoustic waveguide environment

The hydroelastic analysis and sonoelastic analysis methods are incorporated with the Green＇s function of the Pekeris ocean hydro-acoustic waveguide model to produce a three-dimensional sonoelastic analysis method for ships in the ocean hydro-acoustic environment. The seabed condition is represented by a penetrable boundary of prescribed density and sound speed. This method is employed in this paper to predict the vibration and acoustic radiation of a 1 500 t Small Water Area Twin Hull （SWATH） ship in shallow sea acoustic environment. The wet resonant frequencies and radiation sound source levels are predicted and compared with the measured results of the ship in trial.

Hydrodynamic Coefficients for a 3-D Uniform Flexible Barge UsingWeakly Compressible Smoothed Particle Hydrodynamics

The numerical modelling of the interactions between water waves and floating structures is significant for different areas of the marine sector, especially seakeeping and prediction of wave-induced loads. Seakeeping analysis involving severe flow fluctuations is still quite challenging even for the conventional RANS method. Particle method has been viewed as alternative for such analysis especially those involving deformable boundary, wave breaking and fluid fragmentation around hull shapes. In this paper, the weakly compressible smoothed particle hydrodynamics(WCSPH), a fully Lagrangian particle method, is applied to simulate the symmetric radiation problem for a stationary barge treated as a flexible body. This is carried out by imposing prescribed forced simple harmonic oscillations in heave, pitch and the two-and three-node distortion modes. The resultant,radiation force predictions, namely added mass and fluid damping coefficients, are compared with results from 3-D potential flow boundary element method and 3-D RANS CFD predictions, in order to verify the adopted modelling techniques for WCSPH.WCSPH were found to be in agreement with most results and could predict the fluid actions equally well in most cases.

Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid

The wave-induced hydroelastic responses of a thin elastic plate floating on a three-layer fluid, under the assumption of linear potential flow, are investigated for two-dimensional cases. The effect of the lateral stretching or compressive stress is taken into account for plates of either semi-infinite or finite length. An explicit expression for the dispersion relation of the flexural-gravity wave in a three-layer fluid is analytically deduced. The equations for the velocity potential and the wave elevations are solved with the method of matched eigenfunction expansions. To simplify the calculation on the unknown expansion coefficients, a new inner product with orthogonality is proposed for the three-layer fluid, in which the vertical eigenfunctions in the open-water region are involved. The accuracy of the numerical results is checked with an energy conservation equation, representing the energy flux relation among three incident wave modes and the elastic plate. The effects of the lateral stresses on the hydroelastic responses are discussed in detail.

Experimental Study of An Aquaculture Net Cage in Waves and Current

Model experiments of a floating fish cage subjected to waves and current have been performed. The objective was to study the dynamic behaviour of the fish cage model in waves and current. The fish cage model was composed of a model net, a flexible floating collar of the circular plastic type and a weight system. It was found that there are many wave periods in which cancellation of the wave-induced forces on the model occur. These cancellation wave periods are within the range of dimensioning wave periods commonly used for testing of fish farm structures and hence are important to be aware of. Large deformations of the net under realistic wave and current conditions were observed, where contact between the net and other parts of the structure were identified. This may cause damages to the net due to abrasion.

Flexural-gravity wave resistances due to a surface-moving line source on a fluid covered by a thin elastic plate

Analytical solutions for the flexural-gravity wave resistances due to a line source steadily moving on the surface of an infinitely deep fluid are investigated within the framework of the linear po- tential theory. The homogenous fluid, covered by a thin elastic plate, is assumed to be incompressible and inviscid, and the motion to be irrotational. The solution in integral form for the wave resistance is obtained by means of the Fourier transform and the explicitly analytical solutions are derived with the aid of the residue theorem. The dispersion relation shows that there is a minimal phase speed cmin, a threshold for the existence of the wave resistance. No wave is generated when the moving speed of the source V is less than emin while the wave resistances firstly increase to their peak values and then decrease when V ~〉 Crnin. The effects of the flexural rigidity and the inertia of the plate are studied. @ 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1302202]

Estimation of Springing Response for 550 000 DWT Ore Carrier

The desire to benefit from economy of scale is one of the major driving forces behind the continuous growth in ship sizes. However, models of new large ships need to be thoroughly investigated to determine the carrier's response in waves. In this work, experimental and numerical assessments of the motion and load response of a 550,000 DWT ore carrier are performed using prototype ships with softer stiffness, and towing tank tests are conducted using a segmented model with two schemes of softer stiffness. Numerical analyses are performed employing both rigid body and linear hydroelasticity theories using an in-house program and a comparison is then made between experimental and numerical results to establish the influence of stiffness on the ore carrier's springing response. Results show that softer stiffness models can be used when studying the springing response of ships in waves.

Review of Ship Slamming Loads and Responses

The paper presents an overview of studies of slamming on ship structures. This work focuses on the hull slamming, which is one of the most important types of slamming problems to be considered in the ship design process and the assessment of the ship safety. There are three main research aspects related to the hull slamming phenomenon, a) where and how often a slamming event occurs, b) slamming load prediction and c) structural response due to slamming loads. The approaches used in each aspect are reviewed and commented, together with the presentation of some typical results. The methodology, which combines the seakeeping analysis and slamming load prediction, is discussed for the global analysis of the hull slamming of a ship in waves. Some physical phenomena during the slamming event are discussed also. Recommendations for the future research and developments are made.

Hydroelastic Behaviour and Analysis of Marine Structures

Hydroelasticity of marine structures with and without forward speed is studied directly using time dependent Boundary Integral Equation Method with Neumann-Kelvin linearisation where the potential is considered as the impulsive velocity potential.The exciting and radiation hydrodynamic parameters are predicted in time with transient wave Green function whilst the structural analysis is solved with Euler-Bernoulli beam method at which modeshapes are defined analytically.The modal analysis is used to approximate the hydroelastic behaviour of the floating systems through fully coupling of the structural and hydrodynamic analyses.As it is expected,it is found with numerical experience that the effects of the rigid body modes are greater than elastic modes in the case of stiff structures.The predicted numerical results of the present in-house computational tool ITU-WAVE are compared with experimental results for validation purposes and show the acceptable agreements.

A nonlinear hydroelastic method considering wave memory effect for ship load responses in irregular waves

Since the amplitude and frequency of irregular waves change with time,great difficulties are brought for solving ship load responses in random waves.To take the effect of various frequencies of irregular waves into consideration in load responses of hull,the wave memory effect is necessary.A semi-analytical method is introduced for the time-domain retardation functions,and then a nonlinear hydroelastic method considering memory effect for ships in irregular waves is proposed.Segmented self-propelling model experiments of a container ship were carried out in a towing tank,a ship motion measuring device for self-propelling model test was designed.Whipping responses of the ship in regular and irregular waves are analyzed.Finally,the calculation results are compared with those measured by segmented model experiments,and the result indicates that the memory effect has little effect on load responses of ship in regular waves,but pronounced effect on results in irregular waves.Moreover,the presented method is reasonable for the prediction of ship load responses in irregular waves.

On Wave-Induced Elastic Deformations of a Submerged Wave Energy Device

Structural integrity has remained a challenge for design and analysis of wave energy devices.A difficulty in assessment of the structural integrity is often laid in the accurate determination of the wave-induced loads on the wave energy devices and the repones of the structure.Decoupled hydroelastic response of a submerged,oscillating wave energy device to extreme nonlinear wave loads is studied here.The submerged wave energy device consists of an oscillating horizontal disc attached to a direct-drive power take-off system.The structural frame of the wave energy device is fixed on the seafloor in shallow water.Several extreme wave conditions are considered in this study.The nonlinear wave loads on members of the submerged structure are obtained by use of the level I Green-Naghdi equations and Morison’s equation for cylindrical members.Distribution of Von Mises stresses and the elastic response of the structure to the extreme wave loads are determined by use of a finite element method.The decoupled hydroelastic analysis of the structure is carried out for devices built by four different materials,namely stainless steel,concrete,aluminium alloy,and titanium alloy.The elastic response of these devices is studied and results are compared with each other.Points of maximum stress and deformations are determined and the structural integrity under the extreme conditions is assessed.It is shown that the proposed approaches provide invaluable information about the structural integrity of wave energy devices.

Dynamics of a fluid-filled curvilinear pipeline

A mathematical model is presented, and numerical experiments are performed to describe the mechanics of the slow movement of a pipeline. The problem reduction algorithm to one-dimensional formulation is offered. Results of numerical experiment for the model problem are adduced. The proposed mathematical model is found to adequately describe the dynamics of known phenomena of pipes. The cross-sections of the extended curvilinear thin-walled pipeline are numerically demonstrated to experience warping, which has experimental confirmation in the literature.

Numerical Simulation on Hydroelastic Response of Structure under Impact Load from Water Using Eulerian Scheme with Lagrangian Particles

Hydroelasticity caused by water impact is of concem in many applications of ocean engineering/naval architect and is a complicated physical phenomenon. The authors have developed a coupled Eulerian scheme with Lagrangian particles to combine advantages and to compensate disadvantages in both grid based method and particle based method. In this study, the developed numerical model was applied to hydroelastic problems due to impact pressure such as water entry of an elastic cylinder and elastic tanker motion in wave. The authors showed the numerical results which is overall agreement with experimental results. The proposed numerical scheme can be useful and effectiveness to evaluate hydroelasticity and ship-wave interaction in nonlinear wave motion with breaking.

A Hybrid Particle-Grid Scheme for Computing Hydroelastic Behaviors Caused by Slamming

Capable and accurate predictions of some effects of strongly nonlinear interaction wave-ship associated with hydroelastic behaviors are very required for simulation tool in naval architect and ocean engineering. It can guarantee ship safety at the sea state by producing proper design. Therefore, we have developed a hybrid scheme based on both grid and particle method. In order to clarify hydroelastic behaviors of a ship, a dropping test of a ship with elastic motion has been performed firstly. The developed scheme has been then validated on ship dropping case under the same conditions with experiment. The comparisons showed consistently in good agreement. Furthermore, evaluation on hydroelastic behaviors of ship motion under slamming, the impact pressure tends to increase in increasing Froude number. （Fn） The bending moment and torque defined at the centre gravity due to hogging and sagging events can be predicted well, and their effects on the ship increase in increasing wave length even though the impact pressure decreases in increasing wave length after wave length λ/L, where L is ship length, is equal to 1.0. Moreover, hydroelastie behaviors affect the large heave and pitch amplitudes. Finally, the developed scheme can predict simultaneously hydrodynamic and hydroelastic with a strongly nonlinear interaction between wave and ship.