支撑条件对浮动式厚弹性板水弹性行为的影响分析（英文）

The hydroelastic response of very large floating structures(VLFS) under the action of ocean waves is analysed considering the small amplitude wave theory. The very large floating structure is modelled as a floating thick elastic plate based on TimoshenkoMindlin plate theory, and the analysis for the hydroelastic response is performed considering different edge boundary conditions.The numerical study is performed to analyse the wave reflection and transmission characteristics of the floating plate under the influence of different support conditions using eigenfunction expansion method along with the orthogonal mode-coupling relation in the case of finite water depth. Further, the analysis is extended for shallow water depth, and the continuity of energy and mass flux is applied along the edges of the plate to obtain the solution for the problem. The hydroelastic behaviour in terms of reflection and transmission coefficients, plate deflection, strain, bending moment and shear force of the floating thick elastic plate with support conditions is analysed and compared for finite and shallow water depth. The study reveals an interesting aspect in the analysis of thick floating elastic plate with support condition due to the presence of the rotary inertia and transverse shear deformation. The present study will be helpful for the design and analysis of the VLFS in the case of finite and shallow water depth.     

新型柔性浮堤消浪性能的综合试验研究

针对柔性浮式防波堤对短波、长波均有较好掩护效果的优点,提出一种圆木阻尼式柔性浮式防波堤结构。通过二维水槽中规则波物理模型试验,研究该柔性浮式防波堤在有无浮板时的消浪性能,并对试验结果进行对比分析。结果表明:该柔性浮式防波堤对短波、长波都有良好的消波效果,有浮板柔性浮堤优于无浮板柔性浮堤。     

Vibration reduction of floating elastic plates in water waves

Based on the dynamical theories of water waves and Mindlin plates, the investigation of the wave-induced responses and the vibration reduction of an elastic floating plate in water waves are presented by using the Wiener–Hopf technique. Firstly, without regard for the case of elastic connector, the calculated results obtained by the present method are in good agreement with the results from the literature and the experimental results. Therefore, it can be shown that the present method is valid. Secondly, the relations between the spring stiffness and the parameters of wave-induced responses of floating plates, which is used to connect the sea bottom and the floating plate's edge, are analyzed by the present method. Therefore, these results can be used as theoretical bases at the design stage of super floating platform systems.     

Mathematical modelling of response amplitude operator for roll motion of a floating body: Analysis in frequency domain with numerical validation

This paper investigates mathematical modelling of response amplitude operator （RAO） or transfer function using the frequency-based analysis for uncoupled roll motion of a floating body under the influence of small amplitude regular waves. The hydrodynamic coefficients are computed using strip theory formulation by integrating over the length of the floating body. Considering sinusoidal wave with frequency （ω ） varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed, analytical expressions of RAO in frequency domain is obtained. Using the normalization procedure and frequency based analysis, group based classifications are obtained and accordingly governing equations are formulated for each case. After applying the fourth order Runge-Kutta method numerical solutions are obtained and relative importance of the hydrodynamic coefficients is analyzed. To illustrate the roll amplitude effects numerical experiments have been carried out for a Panamax container ship under the action of sinusoidal wave with a fixed wave height. The effect of viscous damping on RAO is evaluated and the model is validated using convergence, consistency and stability analysis. This modelling approach could be useful to model floating body dynamics for higher degrees of freedom and to validate the result.     

后勤保障浮式码头耐波性能试验

采用模型试验方法对后勤保障浮式码头耐波性能进行研究。设计浮式码头物理模型和系泊系统模型。采用静水衰减试验，得到浮式码头的横摇和纵摇阻尼。采用规则波（Regular Wave，RW）试验，得到浮式码头的运动响应幅值算子（Response Amplitude Operator，RAO）曲线，并与数值计算模型进行对比，相互验证有效性。采用不规则波（Irregular Wave，IRW）试验，分析浮式码头的运动性能和四点锚泊性能，并与数值计算模型进行对比。结果表明模型试验与数值计算模型吻合较好，可为后勤保障浮式码头设计提供相应的参考依据。     

弹性浮筏系统动力学建模及冲击响应分析

浮筏隔振系统是一种集集中质量,弹簧,阻尼和弹性连续体为一体的复杂动力学系统,被广泛应用于船舶重要设备的振动隔离.本文以多体动力学和结构动力学为理论基础,对弹性浮筏隔振系统进行动力学建模,考虑筏体的刚体运动和弹性变形的耦合,由此推导出整个隔振系统的动力学振动方程.结合具体的算例,求出了弹性浮筏隔振系统的固有频率和对不同冲击激励的响应,指出了筏体的弹性变形对系统动力学性能的影响,揭示了弹性模型的全面性和合理性.该研究可对浮筏系统的优化设计提供理论依据和参考,有一定的工程意义.     

三边简支板格的剪切屈曲分析

采用能量法分析三边简支板在剪切荷载作用下的弹性屈曲性能,推导三边简支板格受剪下的临界屈曲应力计算公式。采用有限元方法进行均匀受剪三边简支板格弹性屈曲的数值验证计算。结果表明:当长细比大于1.5时,临界应力计算公式与有限元计算结果吻合较好。     

波能转换型浮式防波堤的水动力性能研究（英文）

The integration of wave energy converters(WECs) with floating breakwaters has become common recently due to the benefits of both cost-sharing and providing offshore power supply. In this study, based on viscous computational fluid dynamics(CFD) theory, we investigated the hydrodynamic performances of the floating box and Berkeley Wedge breakwaters, both of which can also serve as WECs. A numerical wave flume model is constructed using Star-CCM+software and applied to investigate the interaction between waves and wave energy converters while completing the verification of the convergence study of time and space steps. The effects of wave length on motion response and transmission coefficient of the floating box breakwater model are studied. Comparisons of our numerical results and published experimental data indicate that Star-CCM+ is very capable of accurately modeling the nonlinear wave interaction of floating structures, while the analytical potential theory overrates the results especially around the resonant frequency. Optimal damping can be readily predicted using potential flow theory and can then be verified by CFD numerical results. Next, we investigated the relationship between wave frequencies and various coefficients using the CFD model under optimal damping, including the motion response, transmission coefficient, reflection coefficient,dissipation coefficient, and wave energy conversion efficiency. We then compared the power generation efficiencies and wave dissipation performances of the floating box and Berkeley Wedge breakwaters. The results show that the power generation efficiency of the Berkeley Wedge breakwater is always much higher than that of the floating box breakwater. Besides, the wave dissipation performance of the Berkeley Wedge breakwater is much better than that of the floating box breakwater at lower frequency.     

Time-domain numerical and experimental analysis of hydroelastic response of a very large floating structure edged with a pair of submerged horizontal plates

This paper is concerned with the hydroelastic problem of a pontoon-type, very large floating structure (VLFS) edged with the perforated plates, non-perforated plates or their combination anti-motion device both numerically and experimentally. A direct time domain modal expansion method, taking amount of the time domain Kelvin sources in hydrodynamic forces, in which the fluid flows across the perforated anti-motion plate by applying the Darcy's law, is applied to the fluid–structure interaction problem. A quarter of numerical model is built based on the symmetry of flow field and structure in hydrodynamic forces, and special care is paid to the rapid and accurate evaluation of time domain free-surface Green functions and its spatial derivatives in finite water depth by using interpolation–tabulation method. Using the developed numerical tools and the model tests conducted in a wave basin, the response-reduction efficiency of the perforated plates is systematically assessed for various wave and anti-motion plate parameters, such as plate width, porosity and submergence depth. As a result of the parametric study, the porosity 0.11 is selected as the optimal porosity, and the relationship between the porosity and the porous parameter is developed by using the least-squares fitting scheme. After simulation and verification, the dual anti-motion plates which are the perforated-impermeable-plate combination attached to the fore-end and back-end of the VLFS, are designed for more wave energy dissipation and added damping. Considering variation of the water depths in offshore, discussion on the effectiveness of these anti-motion devices at different water depths is highlighted.     

On maximum forces exerted by floating ice on a structure due to constrained thermal expansion of ice

The problem of interaction between a floating ice cover and an engineering structure is considered, in which the ice–structure contact forces are caused by an increase in ice temperature due to solar radiation in situations, when the lateral thermal expansion of ice is constrained. The focus is on the determination of the maximum thermally-induced horizontal force exerted on a structure wall, assuming that the magnitude of this force is bound by the smallest force capable of fracturing the ice cover due to its buckling. The ice cover is modelled as a rectangular plate of uniform thickness, with its four edges being constrained by vertical rigid walls, and it is assumed that ice deforms, and eventually fails, by the mechanism of viscous creep buckling. The plate is subjected to in-plane axial compressive stresses developing in ice to prevent its thermal expansion due to solar heating, and is transversely (vertically) bent by the forces caused by the reaction of underlying water. The floating ice is treated as a material whose elastic and viscous properties depend on temperature and the ice porosity, and therefore they vary with time and the depth of ice. The results of numerical simulations, conducted for a variety of the ice plate horizontal dimensions, thicknesses and daytime temperature-change scenarios, illustrate the evolution of the plate deflection surface prior to its failure, and show the time variation of the maximum forces exerted by ice on a structure wall as functions of the ice thickness and maximum daytime temperature rise at the top surface of ice.     

隔振器分布对浮筏隔振系统隔振性能的影响

目前,国内外对于浮筏隔振系统各个方面的研究都已很多,通常采用的是动力学建模及理论分析的方法。但此法通常是将隔振器简化为只有垂向刚度的弹簧和阻尼的单元,而忽略了隔振器的横向刚度及阻尼对系统的影响,简化模型与实际情况有一定差别,因此本文采用有限元法对浮筏隔振系统进行仿真分析。本文根据隔振器的选用及布置原则提出几种合理的布置方案,利用 ansys 有限元软件对提出的布置方案进行仿真,采用振级落差的隔振指标来评估浮筏隔振系统的隔振效果,为隔振器的布置方案设计提供一种思路。     

Analysis of the slowly varying drift force on a very large floating structure in multidirectional random seas

In designing the mooring system of a very large floating structure (VLFS), it is essential to estimate the slowly varying drift force in random seas. For a small vessel, Hsu's method or Newman's approximation may be used to simulate this slowly varying drift force. However, based on experiments and/or field observations, it was found that the slowly varying drift force acting on a VLFS could be reduced to a great extent from the simulated values based on those methods. Thus, the conventional methods are not applicable for a VLFS. This discovery led to the development of several methods for estimating the slowly varying drift force on a VLFS, e.g., Namba et al. (J Soc Nav Archit Jpn 186:235–242, 1999), and Shimada and Maruyama (J Soc Nav Archit Jpn 190:347–351, 2001). However, Namba's method is only applicable to a pontoon-type VLFS with a shallow draft, and Shimada's method is too simplified to account for the general shape of a VLFS and elastic deformation. These methods have been expanded in this article, and by our proposed method, any shape of VLFS and the effect of elastic deformation of the VLFS can be included. Formulations and several numerical examples are given.     

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.     

考虑浮体弹性变形的锚泊系统分析方法

传统的锚泊系统分析方法一般是假设结构物为刚性不可变形的,这种假设对于常规海洋结构物的锚泊系统分析,其精度是可以接受的,然而对于弹性体(比如超大型浮体)来说,这种浮体刚性的假设显然是不合理的.本文基于摄动理论,分别给出了锚泊浮体(同时包括弹性体和刚性体)和锚泊系统的一阶运动方程.分别用三维水弹性理论和Goodman-Iance法求解浮体的动力响应和锚泊线的运动,并给出了两者之间的协调关系.通过数值算例分析表明,对于超大型浮体,其弹性特性对锚泊系统特性的影响是不可忽略的.     

Hydrodynamic response of a non-ship-shaped FPSO vessel with damping plates

Experimental and numerical hydrodynamic investigations were carried out on a 1:45 scale model of a novel non-ship-shaped floating, production, storage, and offloading (FPSO) vessel that has been designed for use in the icy waters of the Arctic as well as the severe sea states of the North Sea. This FPSO vessel has a turret mooring system that is disconnectable during emergencies and inclement weather conditions. Experiments were conducted on a 1:45 scale model of the FPSO with damping plates consisting of skirt plates and different sizes of keel plates in order to study their influence on the response of the vessel. A numerical study of the scale model was carried out using the Wave Analysis at Massachusetts Institute of Technology code, and the results provided by it were compared with those obtained from model tests in the wave basin.     

Experimental and numerical study of the effects of heave plate on the motion of a new deep draft multi-spar platform

The heave motion of a floating structure is critical, as a favorable heave characteristic permits dry tree systems, amongst other benefits. The heave response can be suppressed by installing heave plates. However, the associated hydrodynamic effects, which include viscous damping and added mass, are very complicated. Moreover, there are limited experimental investigations to understand the heave plate effects on actual platform designs. This paper aims to study the abovementioned issue based on a novel deep draft multi-spar (DDMS) platform, for four different configurations (with/without upper and lower heave plates). A set of experiments (free decay, regular and irregular wave tests) are conducted, and compared with time domain and linearized frequency domain analyses. Amongst other things, the investigations and discussions include the added mass and damping coefficients for the platform and heave plates, comparison of experimental and numerical results, and the influence of the heave plates on the surge, heave and pitch motions.     

波浪作用下单体网格式浮架受力的数值模拟

模型试验表明重力式网箱在波浪作用下，单纯浮架的受力贡献比例较大。本文运用波浪理论，通过建立浮架、锚绳及浮子的运动方程，采用五阶龙格-库塔进行数值求解，得到了单体网格式锚碇单纯浮架的数值计算模式。将计算模型简化为四点锚碇，并将计算结果与实验结果进行了比较，二者符合程度较好。在此基础上，比较了单体网格式锚碇与四点锚碇单纯浮架的受力，结果表明网格式锚碇方式浮架受力较小。     

Motion response prediction by hybrid panel-stick models for a semi-submersible with bracings

A diffraction-radiation analysis is usually required when the hydrodynamic interactions between structural members occur in short waves. For bracings or small cylindrical members, which play important roles in the vicinity of the natural frequency of a floating platform, special care should be taken into account for the effect of viscous damping. Two hybrid panel-stick models are, therefore, developed, through the combination of the standard diffraction-radiation method and the Morison’s formulae, considering the effect of small members differently. The fluid velocity is obtained directly by the panel model. The viscous fluid force is calculated for individual members by the stick model. A semi-submersible type platform with a number of fine cylindrical structures, which is designed as a floating foundation for multiple wind turbines, is analyzed as a numerical example. The results show that viscous force has significant influence on the hydrodynamic behavior of the floating body and can successfully be considered by the proposed hybrid models.     

Hydroelastic analysis of a very large floating plate with large deflections in stochastic seaway

The hydroelasticity of a very large floating plate with large deflections in multidirectional irregular waves is discussed. After a brief introduction on wave loads on a flexible structure, the paper derives the generalised fluid force acting on a floating structure in multidirectional irregular waves. The nonlinear sectional forces induced by the membrane forces in the plate are deduced. The hydroelastic response equations of a floating plate with large deflections in multidirectional irregular waves are established, and a solution method in the frequency domain is discussed including extreme value statistics. A very large floating structure is chosen as an example. The numerical results show that the influence of the membrane forces on the vertical displacements and the bending moments is noticeable but not that large.