Effects of Second-Order Sum- and Difference-Frequency Wave Forces on the Motion Response of a Tension-Leg Platform Considering the Set-down Motion

This paper presents a study on the motion response of a tension-leg platform (TLP) under first- and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function (QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.     

Conceptual design of a deep draft semi-submersible platform with a moveable heave-plate

Based on the principle of turned mass damper(TMD) systems,the conceptual design of semi-submersible platform with a moveable heave-plate(MHS) has been put forward.The heave motion response amplitude operator(RAO) and viscous damping of the MHS platform are calculated by iteration,and the coupling stiffness between the MHS hull and the heave-plate is optimized to decrease the maximum heave motion response of the MHS hull under 10-year survival conditions in the South China Sea.The nu-merical results indicate that the heave motion RAO of the MHS hull can be decreased in the range of predominant wave frequencies,which may provide some reference to the heave motion control of offshore platforms.     

Numerical study on global motion of Truss Spar in frequency and time domains for the Liwan 3-1 area

Using frequency and time domain analysis, the authors analyzed the hydrodynamics and motion behavior of a Truss Spar platform at a water depth of 1500 m in the Liwan 3-1 area of the South China Sea. Firstly, the seakeeping ability is acquired in the frequency domain by calculating the hull’s hydrodynamics and comparing with a semi-submersible platform. The random wave analysis for 100-year, 10-year and 1-year return periods in Liwan 3-1 distinctly shows lower heave but larger surge and pitch re-sponses of the Truss Spar than those of a semi-submersible. Secondly, 3-hour motions of the Truss Spar are predicted and compared in the time domain under 100-year return period conditions in Liwan 3-1 and the Gulf of Mexico. Thirdly, the hull/mooring line cou-pled and uncoupled models are compared. Finally, the responses of the Truss Spar under 10-year and 1-year return period conditions are assessed. The results reveal that the mooring line damping reflected by the coupled model distinctly decreases the low frequency motion. The maximum heave response for 100-year return period waves is 1.23m and below 0.1m for the case of 1-year return period.     

Experimental Study on the Influencing Factors of Motion Responses on an Air-Floating Caisson with Multiple Compartments

The structure of an air-floating caisson is suitable for the major structure of caisson-type artificial islands.Thus,it has been rapidly developed and widely used in the exploration and development of oil and gas fields in shallow sea and intertidal zones.Air-floating transportation technology is one of the key technologies employed in this structure.In this paper,the factors influencing the dynamic response characteristics of air-floating caisson with multi-compartments(AFCMC)were studied using model tests.The length and the height of each air-floating structure in the model were 1.0 and 0.1 m,respectively.In addition,the 1:100 models with 6,8,and 10 compartments under regular waves were tested in the wave flume,respectively.In the experiments,the respective water depths were set at 0.2,0.3,and 0.4 m,and the corresponding drafts were 0.05,0.06,and 0.07 m.Results show that with the increase of draft,the heave natural period increased and the maximum amplitude of the heave motion decreased.Meanwhile,the pitch motion decreased at 6 and 8 compartments and increased at 10 compartments.As the water depth increased,the maximum amplitude and amplitude change of heave and pitch motions first increased and then decreased.However,several amplitudes close to the maximum amplitude appeared in the measured period at shallower water depth,thereby indicating the vertical movements of the structure enhanced under shallow water.The increase in the number of compartments reduced the vertical movements under 6.0 m draft,but it increased the vertical movements under 5.0 and 7.0 m draft.Thus,increasing the number of compartments has a limited capacity to improve the motion performance of the structure.     

Estimation of Nonlinear Roll Damping by Analytical Approximation of Experimental Free-Decay Amplitudes

Damping is critical for the roll motion response of a ship in waves. A common method for the assessment of damping in a ship's rolling motion is to perform a free-decay experiment in calm water. In this paper, we propose an approach for estimating nonlinear damping that involves a linear exponential analytical approximation of the experimental roll free-decay amplitudes, followed by parametric identification based on the asymptotic method. The restoring moment can be strongly nonlinear. To validate this method, we first analyzed numerically simulated roll free-decay data using rolling equations with two alternative parametric forms: linear-plus-quadratic and linear-plus-cubic damping. By doing so, we obtained accurate estimates of nonlinear damping coefficients, even for large initial roll amplitudes. Then, we applied the proposed method to real free-decay data obtained from a scale model of a bulk barrier, and found the simulated results to be in good agreement with the experimental data. Using only free-decay peak data, the proposed method can be used to estimate nonlinear roll-damping coefficients for conditions with a strongly nonlinear restoring moment and large initial roll amplitudes.     

Probability Distribution of the Hull Motion and Mooring Line Tension of Two Floating Systems

The statistical and distribution characteristics of the responses of a floater and its mooring lines are essential in designing floating/mooring systems.In general,the dynamic responses of offshore structures obey a Gaussian distribution,assuming that the structural system,and sea loads are linear or weakly nonlinear.However,mooring systems and wave loads are considerably nonlinear,and the dynamic responses of hull/mooring systems are non-Gaussian.In this study,the dynamic responses of two types of floaters,semi-submersible and spar platforms,and their mooring lines are computed using coupled dynamic analysis in the time domain.Herein,the statistical characteristics and distributions of the hull motion and mooring line tension are discussed and compared.The statistical distributions of the dynamic responses have strong non-Gaussianity and are unreasonably fitted by a Gaussian distribution for the two floating and mooring systems.Then,the effects of water depth,wave parameters,and low-frequency and wave-frequency components on the non-Gaussianity of the hull motion,and mooring line tension are investigated and discussed.A comparison of the statistical distributions of the responses with various probability density functions,including the Gamma,Gaussian,General Extreme Value,Weibull,and Gaussian Mixture Model(GMM)distributions,shows that the GMM distribution is better than the others for characterizing the statistical distributions of the hull motion,and mooring line tension responses.Furthermore,the GMM distribution has the best accuracy of response prediction.     

Parametric Instability Analysis of Deepwater Top-Tensioned Risers Considering Variable Tension Along the Length

Parametric instability of a riser is caused by fluctuation of its tension in time due to the heave motion of floating platform. Many studies have tackled the problem of parametric instability of a riser with constant tension. However, tension in the riser actually varies linearly from the top to the bottom due to the effect of gravity. This paper presents the parametric instability analysis of deepwater top-tensioned risers(TTR) considering the linearly varying tension along the length. Firstly, the governing equation of transverse motion of TTR under parametric excitation is established. This equation is reduced to a system of ordinary differential equations by using the Galerkin method. Then the parametric instability of TTR for three calculation models are investigated by applying the Floquet theory. The results show that the natural frequencies of TTR with variable tension are evidently reduced, the parametric instability zones are significantly increased and the maximum allowable amplitude of platform heave is much smaller under the same damping; The nodes and antinodes of mode shape are no longer uniformly distributed along the axial direction and the amplitude also changes with depth, which leads to coupling between the modes. The combination resonance phenomenon occurs as a result of mode coupling, which causes more serious damage.     

基于Stewart的工程机械虚拟实训座椅平台设计

为增强工程机械虚拟实训沉浸效果,设计一套六自由度座椅平台。该平台以Stewart六自由度机构为基础,包括并联运动机构、液压泵站和PLC控制系统。由工程机械驾驶特点确定运动平台位姿参数,与MATLAB建立的上位机软件进行数据交互;经过运动学反解计算各根液压缸杆长变化值,PLC控制器对指令处理并发送命令来控制电液比例阀流量,驱动6根并联的液压缸伸缩,从而使运动平台呈现不同的位置姿态。基于上述原理,搭建实物平台并依据驾驶特点进行测试。结果表明,该平台可以模拟工程机械的在不同工况下的姿态,提高虚拟实训人员的沉浸感。      

Fully coupled time-domain simulation of dynamic positioning semi-submersible platform using dynamic surface control

A fully coupled 6-degree-of-freedom nonlinear dynamic model is presented to analyze the dynamic response of a semi-submersible platform which is equipped with the dynamic positioning （DP） system. In the control force design, a dynamic model of reference linear drift frequency in the horizontal plane is introduced. The dynamic surface control （DSC） is used to design a control strategy for the DP. Compared with the traditional back-stepping methods, the dynamic surface control combined with radial basis function （RBF） neural networks （NNs） can avoid differentiating intermediate variables repeatedly in every design step due to the introduction of a first order filter. Low frequency motions obtained from total motions by a low pass filter are chosen to be the inputs for the RBF NNs which are used to approximate the low frequency wave force. Considering the propellers’ wear and tear, the effect of filtering frequencies for the control force is discussed. Based on power consumptions and positioning requirements, the NN cen-ters are determined. Moreover, the RBF NNs used to approximate the total wave force are built to monitor the disturbances. With the DP assistance, the results of fully coupled dynamic response simulations are given to illustrate the effectiveness of the proposed con-trol strategy.     

Parametric Stability Analysis of Marine Risers with Multiphase Internal Flows Considering Hydrate Phase Transitions

This study investigates the effects of multiphase internal flows that consider hydrate phase transitions on the parametric stability of marine risers.A numerical model of the multiphase internal flow that considers a hydrate phase transition is established.The model first solves the flow parameters and subsequently obtains the natural frequencies of risers with different gas intake ratios.The stability charts of marine risers with different gas intake ratios are plotted by applying Floquet theory,and the effects of the gas intake ratio on the instability and vibration response of the risers are identified.The natural frequency increases with an increase in the gas intake ratio;thus,instability zones move to higher frequency ranges in the stability charts.As the increasing gas intake ratio reduces the damping effect of the Coriolis force,the critical amplitude of the heave in the unstable region decreases,especially when hydrodynamic damping is not considered.As a result,higher-order unstable regions are excited.When in an unstable region,the vibration response curve of a riser with a high gas intake ratio excited by parametric resonance diverges quickly due to parametric resonance.     

Experimental Study on Interaction Between Degrees of Freedom in a Wave Buoy

Increasing degrees of freedom(DOFs) is a useful way to raise the power capture efficiency of oscillating wave energy converters. Thus, this study proposes a buoy with three DOFs, which are surge, heave, and pitch. The hydrodynamic performance and power capture efficiency of the buoy is physically modeled. Amplitudes of unidirectional and coupled motions are compared to analyze the interaction effect between freedoms under conditions with and without power take-off damping. The capture width ratio and corresponding growth rates are also calculated. Results show that the buoy makes a periodic sinusoidal(or approximate) movement in every DOF. Coupling effect can cause an increase in the amplitude in one DOF and a decrease in the amplitudes of the others. This phenomenon shows that the kinematic energy of the buoy redistributes to all DOFs compared with the unidirectional conditions. Adding DOFs can improve the power absorption of the buoy in most cases, but the number of DOFs is not the more the better.     

Experimental Study on the Hydrodynamic Performance of a Heaving Buoy Assembled on a Net Cage Platform

To take advantage of the abundance of both fishery and wave energy resources in offshore sea areas, a novel floating platform with a heaving buoy-based wave energy converter(WEC) assembled with a set of net cages is presented in this work. The floating WEC system provides a power supply, while the net cages are used for aquaculture. It is designed to have an independent and self-operation breeding function. An experimental study is carried out to investigate the hydrodynamic performance of the device in a wave tank considering the factors of net cages, draft depth, and power take-off, and results show that these variables have significant effects on wave energy capture. Incident waves with short periods cause intense interactions that allow the device to undergo large relative motion. The draft depth could be determined according to wave period rather than wave height. This study also explores the response amplitude operator of the device and determines its resonance scope. The experimental results could provide reliable information for future studies on phase differences and the design of two-body WECs.     

大地构造和海陆起源的内波假说（Ⅲ）———内波动力机制及能源分析

莫霍面的起伏波动可看成壳—幔分层介质中的内波现象。引入推动地壳底部物质迁移的驱动力，用有限元数值方法模拟了莫霍面内波的运动，并探究了内波运动的动力来源及潮汐在内波生长中的作用     

Time domain Rankine-Green panel method for offshore structures

To solve the numerical divergence problem of the direct time domain Green function method for the motion simulation of floating bodies with large flare, a time domain hybrid Rankine-Green boundary element method is proposed. In this numerical method, the fluid domain is decomposed by an imaginary control surface, at which the continuous condition should be satisfied. Then the Rankine Green function is adopted in the inner domain. The transient free surface Green function is applied in the outer domain, which is used to find the relationship between the velocity potential and its normal derivative for the inner domain. Besides, the velocity potential at the mean free surface between body surface and control surface is directly solved by the integration scheme. The wave exciting force is computed through the convolution integration with wave elevation, by introducing the impulse response function. Additionally, the nonlinear Froude-Krylov force and hydrostatic force, which is computed under the instantaneous incident wave free surface, are taken into account by the direct pressure integration scheme. The corresponding numerical computer code is developed and first used to compute the hydrodynamic coefficients of the hemisphere, as well as the time history of a ship with large flare; good agreement is obtained with the analytical solutions as well as the available numerical results. Then the hydrodynamic properties of a FPSO are studied. The hydrodynamic coefficients agree well with the results computed by the frequency method; the influence of the time interval and the truncated time is investigated in detail.     

Dynamic response analysis of a floating mooring system

An innovative floating mooring system with two or more independent floating mooring platforms in the middle and one rigid platform on each side is proposed for improving efficiency and safety in shallow water. For this new system, most of collision energy is absorbed through the displacement of floating platforms. In order to illustrate the validity of the system, a series of model tests were conducted at a scale of 1:40. The coupled motion characteristics of the floating mooring platforms were discussed under regular and irregular waves, and the influences of wave direction and other characteristics on dynamic response of the system were analyzed. The results show that the mooring system is safest at 0° of wave incident angle, whereas the most dangerous mooring state occurs at 90° of wave incident angle. Motion responses increase with the increase of wave height, but are not linearly related to changes in wave height.     

Finite water depth effect on wave-body problems solved by Rankine source method

Finite water depth effect for wave-body problems are studied by continuous Rankine source method and non- desingularized technique. Free surface and seabed surface profiles are represented by continuous panels rather than a discretization by isolated points. These panels are positioned exactly on the fluid boundary surfaces and therefore no desingularization technique is required. Space increment method is applied for both free surface source and seabed source arrangements to reduce computational cost and improve numerical efficiency. Fourth order Runge-Kutta iteration scheme is adopted on the free surface updating at every time step. The finite water depth effect is studied quantitatively for a series of cylinders with different B/T ratios. The accuracy and efficiency of the proposed model are validated by comparison with published numerical results and experimental data. Numerical results show that hydrodynamic coefficients vary for cylinder bodies with different ratios of B/T. For certain set of B/T ratios the effect of finite water depth increases quickly with the increase of motion frequency and becomes stable when frequency is relatively large. It also shows that water depths have larger hydrodynamic effects on cylinder with larger breadth to draft ratios. Both the heave added mass and damping coefficients increase across the frequency range with the water depths decrease for forced heave motion. The water depths have smaller effects on sway motion response than on heave motion response.     

Design of Buoys for Mounting Wind Turbines at Exposed Sites

In this study, two designs for a buoy capable of supporting a 10 kW wind turbine and its tower were developed to operate at the University of New Hampshire’s Center of Ocean Renewable Energy testing site located off the Isles of Shoals, New Hampshire. The buoys are to be moored by a catenary chain system. To evaluate wave response, two Froude-scaled models were constructed, tested, and compared at the Ocean Engineering wave tank at the University of New Hampshire. These buoys have been implemented and compared with wave tank measurements of the spar displacement at a reference elevation 2.44 m above the mean water level.     

A theoretical model for the estimation of maximum impact force from a rockfall based on contact theory

Rockfall poses a great threat to buildings and personal security. To understand the dynamic characteristics of rockfalls is a prerequisite for disaster prevention and assessment. Models for rockfalls in different forms are established based on the theory of rigid body motion. The equivalent velocity considering the rotational effect is determined by the energy ratio. Besides, considering plastic deformation and nonlinear hardening, the maximum impact force is estimated based on the Hertz contact theory. Then, a case study is carried out to illustrate the applicability of the model and sensitive analyses on some affecting parameters are also made. Calculation results show that the maximum impact force increases with the increasing of incident velocity, angle and slope gradient reflected by the changing of energy ratio. Moreover, the model for the estimation of maximum impact force is validated by two different scales of experiments and compared with other theoretical models. Simulated maximum impact forces agree well with the experiments.     

Dynamic performance of a semi-submersible platform subject to wind and waves

By applying experimental and numerical simulations, the motion performance of a semi-submersible platform with mooring positoning system under combined actions of wind and waves is studied. The numerical simulation is conducted by the method of nonlinear time domain coupled analysis, and the mooring forces are calculated by the piecewise extrapolating method. The scale in the model experiment is 1:100, and the mooring system of the model is designed with the method of equivalent water-depth truncation by comparing the numerical and the experimental results, the platform motion and mooring forces subject to wind and waves are investigated. The results indicate that the numerically simulated mooring forces agree well with the experimental results in static equivalent field, but show some difference in dynamic equivalent field; the numerically simulated platform motions coincide well with the experimental results. The maximum motion of the platform under operating conditions is 20.5 m. It means that the horizontal displacement is 2% less than the water depth, which satisfies the operating requirements.