Dynamics of an elastically moored floating body by the three-dimensional infinite element method

The three-dimensional problem of the dynamics of a moored floating object under the action of regular waves is solved numerically as a boundary value problem by use of the finite-infinite element method. The cross-sectional shape of the floating body and the mooring arrangements may all be arbitrary. The mathematical formulations of the problem and procedures of the numerical method are presented in this paper. A corresponding computer program WALOAD has been developed, which is capable of computing wave forces on fixed and floating structures. Numerical computations using this program could give very accurate results, even though rather coarse meshes were used. The program is easy to use and is readily applicable in many practical situations.     

Nonlinear hydroelastic analysis of a moored floating body

By integration of the second-order fluid pressure over the instantaneous wetted surface, the generalized first- and second-order fluid forces used in nonlinear hydroelastic analysis are obtained. The expressions for coefficients of the generalized first- and second-order hydrodynamic forces in irregular waves are also given. The coefficients of the restoring forces of a mooring system acting on a flexible floating body are presented. The linear and nonlinear three-dimensional hydroelastic equations of motion of a moored floating body in frequency domain are established. These equations include the second-order forces, induced by the rigid body rotations of large amplitudes in high waves, the variation of the instantaneous wetted surface and the coupling of the first order wave potentials. The first-order and second-order principal coordinates of the hydrelastic vibration of a moored floating body are calculated. The frequency characteristics of the principal coordinates are discussed. The numerical results indicate that the rigid resonance and the coupling resonance of a moored floating body can occur in low frequency domain while the flexible resonance can occur in high frequency domain. The hydroelastic responses of a moored box-type barge are also given in this paper. The effects of the second-order forces on the modes are investigated in detail.     

Mooring forces in horizontal interlaced moored floating pipe breakwater with three layers

The paper presents the results from model scale experiments on the study of forces in the moorings of horizontally interlaced, multi-layered, moored floating pipe breakwaters. The studies are conducted with breakwater models having three layers subjected to waves of steepness H_i/L (H_i is the incident wave height and L the wavelength) varying from 0.0066 to 0.0464, relative width W/L (W is the width of breakwater) varying from 0.4 to 2.65, and relative spacing S/D (S is the spacing of pipes and D the diameter of pipe) of 2 and 4. The variation of measured normalized mooring forces on the seaward side and leeward side are analyzed by plotting non-dimensional graphs depicting f/γW² (f is the force in the mooring per unit length of the breakwater, γ the weight density of sea water) as a function W/L for various values of H_i/d (d is the depth of water). It is found that the force in the seaward side mooring increases with an increase in H_i/L for d/W values ranging between 0.081 and 0.276. The experimental results also reveal that the forces in the seaward side mooring decrease as W/L increases, up to a value of W/L=1.3, and then increases with an increase in W/L. It is also observed that the wave attenuation characteristics of breakwater model with relative spacing of 4 is better than that of the model with relative spacing of 2. The maximum force in the seaward side mooring for model with S/D=4 is lower compared to that for the breakwater model with S/D=2. A multivariate non-linear regression analysis has been carried out for the data on mooring forces for the seaside and leeside.     

Design wave method for the extreme horizontal slow-drift motion of moored floating platforms

The present study introduces a design wave method for estimating the extreme horizontal slow-drift motion of moored floating offshore platforms under extreme conditions. Here, the design wave refers to an irregular incident wave of short duration that induces the extreme response of the desired return period. The present method is composed of the following four steps: linearization of the dynamic system, probabilistic analysis of the second-order Volterra series, generation of the irregular design waves, and the fully-coupled nonlinear simulations. For generating the design waves, two different conditioning methods are presented and compared: the conditioning of the extreme response amplitude and the conditioning of the most likely extreme response profile. The procedure was applied to a deep-water semi-submersible, and the results appeared to be promising compared to the full-length nonlinear simulations.     

MOSES软件在系泊浮体运动计算中的应用研究

采用MOSES软件计算某起重船迎浪下的水动力性能和运动响应,并对该船进行缩尺比为1:50的模型试验。通过软件计算结果和试验结果的对比,分析计算模型的网格划分、二阶波浪力计算方法和粘性阻尼等关键参数的选取对MOSES计算系泊浮体运动的影响,为MOSES软件在系泊下运动计算方面提出建议。     

浮式塔的动力计算

采用频域二阶摄动法研究了浮式塔在给定环境条件下的动力响应.计算了浮式塔在不规则波上的一阶运动响应函数和运动谱以及张力谱,同时进行了相应的模型试验.由结果的比较可以看出,试验结果与理论方法计算得到的结果吻合较好.计算结果表明,波浪的二阶作用对浮式塔的低频纵荡有影响.计算结果与试验结果的比较说明频域二阶摄动法可以用于浮式塔的动力分析.     

Dynamics of a moored barge under regular and random waves

Developments in the study of wave forces and construction techniques in deep water by the offshore oil industry have increased the use of marine terminals at deep water locations. A thorough understanding of moored ship dynamics when subjected to waves, wind and current combined with the use of flexible mooring lines would help to design berthing terminals for exposed areas. In this paper, the three dimensional problem of wave interactions with a barge moored to a single point is dealt with, based on the finite element method. The effect of flexibility of the mooring line and the point of mooring on the response of the barge as well as the mooring line tension is investigated. The paper compares the numerical results with model tests carried out on a barge moored to a fixed support under regular and random waves in head sea. The effect of stiffness of the mooring line on the barge response for different mooring points is discussed, which would be useful for the designers. The effect of viscous damping is also considered. The analytical results are in good agreement with the experimental results in both regular and random waves.     

浮桥结构在移动载荷作用下的振动响应

浮桥的载荷具有移动性，并有可能在同时遭受风、浪、流联合作用的恶劣环境中使用。为了使浮桥的设计做到既经济又安全，必须对浮桥的载荷和强度有一个比较精确的评估方法。推导了适合模型计算的用户单元的特性矩阵，并将该用户单元导入现有大型有限元分析程序ABAQUS，利用其功能强大的求解器，求解了静水中自由浮式均匀梁在移动载荷作用下的振动响应，为后续研究奠定了基础。     

On-line identification and convergence analysis of excitation-force and drag-force models for moored floating structures

This work presents an approach to identify hydrodynamic models for incident, diffraction and viscous forces acting on a moored floating structure. An important aspect treated here is the analysis of the unknown initial condition of the hydrodynamic state for the potential-radiation force. There is established its influence on the parameter convergence and the long-term effects. Afterwards the persistency of excitation of the regressor is analyzed in the case of both poor and rich excitation conditions. Theoretical results show that asymptotic convergence of the estimates takes place under arbitrary conditions of the wave excitation. A case study consisting in the identification of a moored semisubmersible is carried out to exemplify the application of the approach.     

Dynamics of large-truncated mooring systems coupled with a catenary moored semi-submersible

With the floating structures pushing their activities to the ultra-deep water,model tests have presented a challenge due to the limitation of the existing wave basins.Therefore,the concept of truncated mooring system is implemented to replace the full depth mooring system in the model tests,which aims to have the same dynamic responses as the full depth system.The truncated mooring system plays such a significant role that extra attention should be paid to the mooring systems with large truncation factor.Three different types of large truncation factor mooring system are being employed in the simulations,including the homogenously truncated mooring system,non-homogenously truncated mooring system and simplified truncated mooring system.A catenary moored semi-submersible operating at 1000 m water depth is presented.In addition,truncated mooring systems are proposed at the truncated water depth of 200 m.In order to explore the applicability of these truncated mooring systems,numerical simulations of the platform’s surge free decay interacting with three different styles of truncated mooring systems are studied in calm water.Furthermore,the mooring-induced damping of the truncated mooring systems is simulated in the regular wave.Finally,the platform motion responses and mooring line dynamics are simulated in irregular wave.All these simulations are implemented by employing full time domain coupled dynamic analysis,and the results are compared with those of the full depth simulations in the same cases.The results show that the mooring-induced damping plays a significant role in platform motion responses,and all truncated mooring systems are suitable for model tests with appropriate truncated mooring line diameters.However,a large diameter is needed for simplified truncated mooring lines.The suggestions are given to the selection of truncated mooring system for different situations as well as to the truncated mooring design criteria.     

Neuro-fuzzy based approach for wave transmission prediction of horizontally interlaced multilayer moored floating pipe breakwater

The ocean wave system in nature is very complicated and physical model studies on floating breakwaters are expensive and time consuming. Till now, there has not been available a simple mathematical model to predict the wave transmission through floating breakwaters by considering all the boundary conditions. This is due to complexity and vagueness associated with many of the governing variables and their effects on the performance of breakwater. In the present paper, Adaptive Neuro-Fuzzy Inference System (ANFIS), an implementation of a representative fuzzy inference system using a back-propagation neural network-like structure, with limited mathematical representation of the system, is developed. An ANFIS is trained on the data set obtained from experimental wave transmission of horizontally interlaced multilayer moored floating pipe breakwater using regular wave flume at Marine Structure Laboratory, National Institute of Technology Karnataka, Surathkal, India. Computer simulations conducted on this data shows the effectiveness of the approach in terms of statistical measures, such as correlation coefficient, root-mean-square error and scatter index. Influence of input parameters is assessed using the principal component analysis. Also results of ANFIS models are compared with that of artificial neural network models.     

Wave-induced drift of small floating objects in regular waves

Water waves induce a slow drift of an object floating on the water surface. In this study, we examined, by a series of laboratory experiments, the drift motion of small rigid floating objects driven by regular waves in deep water. Different shapes of planar objects, including square, circular and elliptical, were investigated for two different submergences, and their drift motions in waves were determined using an infrared motion monitoring system. The corresponding measurements enabled the quantification of the drift characteristics with respect to the wave characteristics and object shapes. Numerical simulations based on an existing theory were presented and comparisons between the experimental data and the predictions by the existing theory were performed.     

Spatio-temporal distribution of floating objects in the German Bight (North Sea)

Floating objects facilitate the dispersal of marine and terrestrial species but also represent a major environmental hazard in the case of anthropogenic plastic litter. They can be found throughout the world's oceans but information on their abundance and the spatio-temporal dynamics is scarce for many regions of the world. This information, however, is essential to evaluate the ecological role of floating objects. Herein, we report the results from a ship-based visual survey on the abundance and composition of flotsam in the German Bight (North Sea) during the years 2006 to 2008. The aim of this study was to identify potential sources of floating objects and to relate spatio-temporal density variations to environmental conditions. Three major flotsam categories were identified: buoyant seaweed (mainly fucoid brown algae), natural wood and anthropogenic debris. Densities of these floating objects in the German Bight were similar to those reported from other coastal regions of the world. Temporal variations in flotsam densities are probably the result of seasonal growth cycles of seaweeds and fluctuating river runoff (wood). Higher abundances were often found in areas where coastal fronts and eddies develop during calm weather conditions. Accordingly, flotsam densities were often higher in the inner German Bight than in areas farther offshore. Import of floating objects and retention times in the German Bight are influenced by wind force and direction. Our results indicate that a substantial amount of floating objects is of coastal origin or introduced into the German Bight from western source areas such as the British Channel. Rapid transport of floating objects through the German Bight is driven by strong westerly winds and likely facilitates dispersal of associated organisms and gene flow among distant populations.     

Model experiments on moored ships

At present the position keeping of ocean going vessels, offshore service vessels, etc., is performed by mooring systems to resist external forces under severe environments consisting of wave, current and wind. A variety of mooring systems are employed depending on the shape, principal dimensions, etc., of the vessels in addition to the surrounding conditions of the water areas. Ocean going ships are moored to the shore structures through a multiple system of moorings. The determination of the forces in the cables is essential for the design of moorings and the berthing structures. However, the ships engaged for offshore operations are moored by the mooring cables, spread around the ships with the other ends of the moorings anchored to the sea bed. In these cases, the required number and length of cables can be arrived for a given ship of known dimensions and environmental conditions. With the increased overall dimensions of the vessels, it is necessary to conduct a study on enhancing the accuracy in estimating the mooring system performance. Hence, the present work is mainly intended to carry out model tests to investigate the behaviour of moored ships that are subjected to wave and current loadings. These model experiments were conducted in a 30 m × 2 m × 1 m wave-current flume at the Ocean Engineering Centre, Indian Institute of Technology, Madras.     

Tracking the velocity and position of offshore vessels and floating objects with HF Doppler transponders

Experiments with a high-frequency (HF) Doppler radar and a frequency-shifting transponder show that the velocity and position of ships or floating objects can be tracked without the need for accurate differential-position measurements. Maximum-entropy spectral analysis permits tracking during rapid maneuvers using sampling times as short as 4 s.     

LNG-FSRU在软刚臂系泊下水动力特性研究

针对35万立方米超大型LNG-FSRU,采用软刚臂单点系泊系统定位方式,运用模型试验与数值计算两种技术手段开展风、浪、流联合作用下水动力研究。软刚臂系泊系统各构件间的连接方式及Yoke重量模拟是数值计算与模型试验的关键,数值计算对构件间的铰接方式与Yoke重量进行模拟,模型试验同样模拟了系泊系统的相似性,并将数值计算结果与模型试验结果进行对比分析。结果表明,软刚臂系泊系统刚度曲线呈非线性,试验结果与数值结果吻合良好,表明对于软刚臂系泊系统的两种模拟是合理的,反映了LNG-FSRU在风、浪、流联合作用下的运动特性,建立的研究方法可用于软刚臂系统的水动力研究。     

Nonlinear response of a moored buoy

The nonlinear dynamic analysis of a multipoint slack moored buoy is performed under the action of first and second order wave forces. The nonlinearity of the system is caused by the geometric nonlinearity of the mooring lines. The resulting nonlinear equation of motion is solved by an incremental time marching scheme. The nonlinear responses of the system are analysed to investigate different kinds of dynamic instability phenomena that may arise due to the nonlinearity of the system. As an illustrative example, a hollow cylindrical buoy anchored to the sea bed by means of six slack mooring lines is considered. The responses of the system are obtained and analysed for three regular waves namely, 5 m/5 s, 12 m/10 s and 18 m/15 s. The results of the study show that different kinds of instability phenomena like nT subharmonic oscillations, symmetry breaking bifurcation and aperiodic responses may occur in slack mooring systems. Further, a second order wave force may considerably influence the dynamic stability of such systems.     

锚泊光学浮标浮体设计及近海试验

文中设计的光学浮标采用了柱状浮体, 提出了自由旋转的马鞍链结构。理论计算结果表明, 该光学浮标一是初稳性高度大, 二是光学浮标重心位于浮心之下, 浮标的摇摆角较小, 抗倾斜及倾覆能力强。海上试验结果表 明, 对于风力7节、浪高3—4m以下的海况, 浮标倾角≤5°的次数占总采样次数的 54%, 浮标倾角≤10°的次数占总采样次数的83%, 浮标性能较好地满足了水下光辐射测量的技术要求。为减小阴影效应带来的光辐射测量误差, 文中采用了两种解决方法: 一是伸臂结构解决浮标体阴影的影响, 当太阳天顶角为0°时, 在近岸或者清洁水体中浮标体阴影引起的向上辐亮度测量误差分别不大于4% 和1%; 二是光纤光谱仪测量技术减少仪器自阴影的影响, 设计的光谱辐照度和辐亮度光学探头直径均为0.042m, 当水体光束衰减系数为0.12m-1, 太阳天顶角为10°时, 自阴影引起的向上辐亮度测量误差仅为1.5%。     

应用比例边界有限元法求解多种二维浮体水动力特性

比例边界有限元法(SBFEM)是一种半解析的数值方法,比完全数值方法具有更高的精度,该方法结合了有限元和边界元的优点,采用相对少的剖分单元就可以得到较高精度的模拟结果。通过改变有限子域内部比例中心的位置,使这种方法可以应用到多种形式浮体在波浪作用下的水动力特性的计算中。同时还给出了各种形式浮体的波浪力及反射、透射系数的数值结果,并与边界元方法(BEM)计算结果和特征函数展开方法得到解析解进行了比较,均吻合良好。研究表明比例边界有限元不仅可以计算矩形的浮体结构,而且对于多种结构形式的浮体都可以计算,这为多种结构形式浮体的水动力分析提供了一个可行的方法。