Formulation of consistent nonlinear restoring stiffness for dynamic analysis of tension leg platform and its influence on response

Shortcomings of the traditionally used nonlinear restoring stiffness of TLPs, i.e. unrealistically high stiffness of horizontal motions, their uncoupling and secant formulation are pointed out. Therefore, new consistent restoring stiffness is derived. The platform is considered as a rigid body moored by flexible pretensioned tendons. Global horizontal low frequency motions (surge, sway and yaw) with large amplitudes as a result of dominant second order wave excitation and small stiffness, and vertical local motions (heave, roll and pitch) of higher frequency and small amplitudes excited by the first order wave forces, are distinguished. Hence, horizontal displacements represent position parameters in analysis of vertical motions. First, the linear restoring stiffness, which consists of the tendon conventional axial stiffness, the tendon geometric stiffness and the platform hydrostatic stiffness, is established. Then it is extended to large displacements resulting in new secant restoring stiffness. It depends on surge, sway and yaw displacements and is the same in any horizontal direction. Also, the tangent stiffness, which gives more accurate results, is derived. Heave is defined as vertical projection of axial tendon vibrations and platform tangential oscillations, which are analyzed in their natural moving coordinate system. Inertia force due to setdown, as a slave d.o.f. of the master horizontal motions, is taken into account in the dynamic equilibrium equations. As a result the complete tangential stiffness matrix of horizontal and vertical motions includes 7 d.o.f. The known secant restoring stiffness matrices are compared with the new one and noticed differences are discussed. All theoretical contributions are illustrated by relatively simple numerical example.     

3-D computational method of wave loads on turret moored FPSO tankers

A three-dimensional method of calculating wave loads of turret moored FPSO (Floating Production Storage and Offloading) tankers is presented. The linearized restoring forces acting on the ship hull by the mooring system are calculated according to the catenary theory, which are expressed as the function of linear stiffness coefficients and the displacements of the upper ends of mooring chains. The hydrodynamic coefficients of the ship are calculated by the three-dimensional potential flow theory of the linear hydrodynamic problem for ships with a low forward speed. The equations of ship motions are established with the effect of the restoring forces from the mooring system included as linear stiffness coefficients. The equations of motions are solved in frequency domain, and the responses of wave-induced motions and loads on the ship can be obtained. A computer program based on this method has been developed, and some calculation examples are illustrated. Analysis results show that the method can give satisfying prediction of wave loads.     

Truss Spar平台在不同系泊线组合下的动态响应分析（英文）

The dynamic responses of any floating platform are dependent on the mass, stiffness and damping characteristics of the body as well as mooring system. Therefore, it is very essential to study the effect of individual contributions to the system that can finally help to economise their cost. This paper focuses on the effect of mooring stiffness on the responses of a truss spar platform, obtained by different grouping of lines. The study is part of our present researches on mooring systems which include the effect of line pretension, diameter and azimuth angles. The platform is modelled as a rigid body with three degrees-of-freedom and its motions are analyzed in time-domain using the implicit Newmark Beta technique. The mooring lines restoring force-excursion relationship is evaluated using a quasi-static approach. It is observed that the mooring system with lines arranged in less number of groups exhibits better performance in terms of the restoring forces as well as mean position of platform. However, the dynamic motions of platform remain unaffected for different line groups.     

规则迎浪中船舶参数横摇的三维时域预报方法研究

参数横摇是船舶因复原特性改变而引起的典型非线性现象。文章采用三维时域方法预报规则迎浪中船舶的参数横摇运动。该方法引入匹配面将流域分为内域和外域,内域中采用Rankine源来满足物面条件和线性自由面条件,而外域中应用时域格林函数来满足线性自由面条件和远场辐射条件。数值方法中,Froude-Krylov力和恢复力是通过对船舶瞬时湿表面积积分获得,同时考虑了横摇、垂荡和纵摇三自由度之间的耦合作用,以及非线性横摇阻尼的影响。数值结果与试验结果吻合很好,说明该方法可以有效地预报参数横摇。     

Response analysis of a truss spar in the frequency domain

The nonzero added-mass coefficients of a platform are found by using the transformation law for a second-order tensor, and the repeated application of the parallel-axes theorem. The excitation forces acting on the truss section of the platform are derived by an approach that differs from the conventional one commonly seen in the literature. The force decomposition of the Morison equation is used to add viscous effects to linear equations of motion. The nonlinear equation of motion for the heave of the truss spar is solved without any iteration in the frequency domain. The results obtained from this analysis are compared with results obtained from the conventional numerical approach and with experimental data.     

一种基于Taylor展开的系泊刚度矩阵计算方法

系泊系统对于船舶及海上浮式结构物的定位十分重要。钢质系泊缆索是业界广泛采用的一种形式。由于其提供的恢复力与浮体位移之间呈现非线性关系,故针对此种系泊方式基于Taylor展开方法得到了非线性的刚度系数及相应的系泊刚度矩阵,研究了其在系泊定位及水动力计算方面的应用。分析表明该方法可以较为方便地计及刚度非线性的影响。     

复合缆索锚泊下的Spar平台动态响应分析

利用复合索链的计算公式,计算不同配置的复合链组成的锚泊系统的变刚度,并将计算结果运用于Spar平台运动方程中刚度矩阵的修正,分析并比较在不同锚泊系统作用下,Spar平台的动态响应行为。通过计算发现:虽然不同配置的复合缆索对平台的动态响应没有多大影响,但是缆索张力的变化确实截然不同。这些在平台锚泊系统的初步设计中必须考虑。     

系泊油轮与海上平台的碰撞力分析

考虑风、浪、流的联合作用以及平台护舷非线性恢复刚度,研究船舶系泊状态与平台的撞击力及其分布规律。针对不同的风、浪、流的作用方向以及不同的风速、波高及流速,计算波浪和海流的载荷,建立系泊船舶的分析模型,采用频域与时域分析方法,进行系泊船舶运动及其与平台之间碰撞力的仿真,得到系泊船舶与平台的碰撞力时间历程,并分析不同碰撞力发生的概率,确定发生最大碰撞力的风、浪、流方向,比较常量护舷刚度与非线性护舷刚度的计算结果。结果表明,橡胶护舷刚度的选取对于碰撞力的计算结果影响显著,选取非线性护舷刚度计算靠泊碰撞力十分必要,用目前的经验公式计算得到的碰撞力偏差较大。     

船体湿表面脉动压力预报的三维非线性方法

本文给出了一种预报船体湿表面脉动压力响应的三维非线性时历模拟方法.计及瞬时物面变化引起的各种非线性因素,在时域内建立船体非线性运动方程.在每一时刻,认为船体以其瞬时平均湿表面为平衡位置做简谐振荡运动,利用三维线性频域解来简化运算.在此基础上,进一步将绕射和辐射问题在静平衡位置求解,仅考虑占主导地位的入射波和静恢复力变化的非线性,作为一种兼顾工程需要的计算精度和计算效率的简化方法.以此方法为基础编制了计算机程序,对实船进行了计算,并与模型试验进行了对比.分析比较表明,该方法能够给出令人满意的船体湿表面脉动压力响应预报结果.     

浅水沉管船的锚泊定位系统设计

浅水锚泊系统的设计增加了诸多挑战,恶劣的环境使船舶具有较大的低频漂移运动,同时锚泊系统需要有足够的恢复力特性。文章针对深中通道沉管船,基于三维势流理论,在时域下对安装船和沉管系统进行分析,设计出合适的锚泊系统,并验证了锚泊系统设计的安全性。同时为以后类似系统的设计提供借鉴。     

导管架式海洋平台自适应预测逆控制研究

文章提出了一种新的基于动态刚度阵法的导管架式海洋平台模糊神经网络自适应预测逆控制模型。该模型是通过安放在海洋平台桩腿上的压力传感器实时采集海洋平台所受波浪力,然后应用动态刚度阵法快速而准确地计算出平台顶部的响应,再将此响应作为模糊神经网络预测逆控制器的输入信号,预测出下一时刻平台顶部的控制力来对海洋平台振动响应进行控制;同时,通过反馈的自适应预测逆控制器来减小扰动和前馈控制的误差。为了验证该模型的抗干扰能力,文中还对有随机风载荷扰动情况下的导管架式海洋平台主动控制进行了研究。最后的数值算例结果表明,文中所提出的导管架式海洋平台主动控制模型具有较强的抗干扰能力,能很好地解决控制系统中存在的时滞问题,可有效地控制导管架式海洋平台的振动响应。     

铰连接在深水S型铺管中的应用

为了能够在S型铺管过程中将管线、船体和托管架三者作为一个整体进行耦合分析,使用势流理论用于计算船体受到的波浪力,广义弹性接触面法模拟托辊与管线之间的接触,采用带有铰接刚度的铰连接来模拟管线的上弯段,集中质量法用于模拟管线的中垂段和下弯段。通过时域全耦合方程将整个系统联立求解,并将这种方法的结果和未考虑上弯段管线接触的结果与实验值进行了对比发现:新计算方法能够使管线受力和船体运动都更为接近于实际值。对管线张力进行了谱密度分析,得到了对管线张力作用较大的频谱范围,为其在不同海况下的适应性提供了技术参数。     

Numerical Simulation of Float-Over Installation for Offshore Platform

In this paper, a numerical investigation of a float-over installation for an offshore platform is presented to verify the feasibility of the actual installation. The hydrodynamic performance of a T-barge is investigated in the frequency domain, and the coupled motions are analyzed in the time domain. We then compare with those of the model test and determine that the response amplitude operator and the time series agree quite well. The barge exhibits favorable hydrodynamic behavior in the considered sea state, and the equipment loads are allowable. The mooring system and sway fender forces are within the permissible range. Based on these results, we can verify that the actual installation of the offshore platform is feasible. We accurately simulated many important factors and effectively reduced the risk associated with the offshore installation, which is of great importance. As such, we demonstrate that the numerical simulation of the float-over installation for offshore platforms has practical engineering significance.     

系泊系统非线性恢复力研究及其应用(英文)

Mooring system plays an important role in station keeping of floating offshore structures.Coupled analysis on mooring-buoy interactions has been increasingly studied in recent years.At present,chains and wire ropes are widely used in offshore engineering practice.On the basis of mooring line statics,an explicit formulation of single mooring chain/wire rope stiffness coefficients and mooring stiffness matrix of the mooring system were derived in this article,taking into account the horizontal restoring force,vertical restoring force and their coupling terms.The nonlinearity of mooring stiffness was analyzed,and the influences of various parameters,such as material,displacement,pre-tension and water depth,were investigated.Finally some application cases of the mooring stiffness in hydrodynamic calculation were presented.Data shows that this kind of stiffness can reckon in linear and nonlinear forces of mooring system.Also,the stiffness can be used in hydrodynamic analysis to get the eigenfrequency of slow drift motions.     

海洋平台浮拖安装的数值仿真（英文）

In this paper, a numerical investigation of a float-over installation for an offshore platform is presented to verify the feasibility of the actual installation. The hydrodynamic performance of a T-barge is investigated in the frequency domain, and the coupled motions are analyzed in the time domain. We then compare with those of the model test and determine that the response amplitude operator and the time series agree quite well. The barge exhibits favorable hydrodynamic behavior in the considered sea state, and the equipment loads are allowable. The mooring system and sway fender forces are within the permissible range. Based on these results,we can verify that the actual installation of the offshore platform is feasible. We accurately simulated many important factors and effectively reduced the risk associated with the offshore installation, which is of great importance. As such, we demonstrate that the numerical simulation of the float-over installation for offshore platforms has practical engineering significance.     

系泊浮体运动响应分析的非线性水动力学方法（英文）

Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions(QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong(2017) proposed a method to divide the QTFs into different components,which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory.     

考虑晃荡耦合船舶运动的晃荡压力算法（英文）

The effect of coupling between sloshing and ship motions in the evaluation of slosh-induced interior pressures is studied. The coupling between sloshing loads and ship motions is modelled through a hybrid algorithm which combines a potential flow solution based on transient Green function for the external ship hydrodynamics with a viscous flow solution based on a multiphase interface capturing volume of fluid(VOF) technique for the interior sloshing motion. The coupled algorithm accounts for full nonlinear slosh forces while the external forces on the hull are determined through a blended scheme of linear radiationdiffraction with nonlinear Froude-Krylov and restoring forces. Consideration of this level of nonlinearities in ship motions is found to have non-negligible effects on the slosh-coupled responses and slosh-induced loads. A scheme is devised to evaluate the statistical measure of the pressures through long-duration simulation studies in extreme irregular waves. It is found that coupling significantly influences the tank interior pressures, and the differences in the pressures between coupled and uncoupled cases can be as much as 100% or more. To determine the RAO over the frequency range needed for the simulation studies in irregular waves, two alternative schemes are proposed, both of which require far less computational time compared to the conventional method of finding RAO at each frequency, and the merits of these are discussed.     

卸载浮标系统运动响应分析*

深水卸载浮标系统具有相对较小的排水量和惯性,其系泊缆索的质量、阻尼和刚度会对卸载浮标系统产生非常大的影响,因而对浮标和其系泊系统进行准确的耦合动力响应分析十分重要.应用边界元方法计算浮标的水动力,通过快速傅立叶变换,将频域计算结果变换到时域;基于全量的拉格朗日表述和两节点的等参索单元,应用几何非线性有限元方法和Newmark方法计算了系泊缆索张力;最后应用四阶龙哥库塔法计算浮标及其系泊缆索的时域耦合运动方程,得到浮标运动响应和缆索张力.     

Experimental study of freak wave impacts on a tension-leg platform

This study investigates the freak wave impinging on a tension-leg platform through wave flume experiments. The freak waves are generated using the focused wave theory. By adjusting the wave focusing location, different incident wave scenarios at the structure location are produced. Simultaneous measurements of wave shape evolutions upon impingement, wave impact pressures on the platform deck, platform motions and tether forces are carried out for synchronized analyses of the wave kinematics/dynamics and structural responses. The variation of these parameters with the incident wave profile is studied. It is found that although applying less intensive local impact pressures as compared to the highly-breaking freak wave, the slightly-breaking or non-breaking freak wave imposes the same level of adverse effect on the platform's global stability in terms of motions and tether forces. In addition, the high-crest freak wave causes violent motions of the floating platform, which are likely to induce snap loads of large amplitude and high occurrence frequency in tethers. The published results would provide useful benchmarks for validating numerical and analytical models.     

基于完全耦合算法的绕水翼流固耦合特性研究

基于完全耦合算法对绕二维NACA0009水翼流固耦合特性进行了数值模拟研究。采用Theodorsen模型和Munch模型对刚性和弹性水翼的水弹性响应进行了数值计算,分析了流体与结构的相互作用关系,研究了影响结构水弹性响应和流固耦合特性的因素。研究结果表明:考虑了流体黏性的Munch模型与基于势流理论的Theodorsen模型对气动弹性响应的数值计算结果基本一致,而Theodorsen模型由于没有考虑流体黏性在一定程度上低估了结构的水弹性响应。结构的惯性、阻尼和刚度力矩与流体的相应附加载荷均处于同一数量级,故流体与结构的相互作用不可忽略,尤其对于弹性水翼,流体的惯性、附加阻尼作用增大,流固耦合算法的数值稳定性对流固耦合特性的计算结果影响将更大。外部激励频率为非共振频率时,结构的刚度作用是影响水弹性响应的主要因素,外部激励频率为共振频率时,流体的附加阻尼和附加刚度作用减弱,除结构的刚度作用外,流体与结构的惯性作用对水弹性响应和流固耦合特性的影响也较大。