Comparison of Linear Level I Green-Naghdi Theory with Linear Wave Theory for Prediction of Hydroelastic Responses of VLFS

Very Large Floating Structures (VLFS) have drawn considerable attention recently due to their potential significance in the exploitation of ocean resources and in the utilization of ocean space. Efficient and accurate estimation of their hydroelastic responses to waves is very important for the design. Recently, an efficient numerical algorithm was developed by Ertekin and Kim (1999). However, in their analysis, the linear Level I Green-Naghdi (GN) theory is employed to describe fluid dynamics instead of the conventional linear wave (LW) theory of finite water depth. They claimed that this linear level I GN theory provided betler predictions of the hydroelastic responses of VLFS than the linear wave theory. In this paper, a detailed derivation is given in the conventional linear wave theory framework with the same quantity as used in the linear level I GN theory framework. This allows a critical comparison between the linear wave theory and the linear level I GN theory. it is found that the linear level     

Extracting energy while reducing hydroelastic responses of VLFS using a modular raft wec-type attachment

This paper presents the use of a modular raft Wave Energy Converter (WEC)-type attachment at the fore edge of a rectangular Very Large Floating Structure (VLFS) for extracting wave energy while reducing hydroelastic responses of the VLFS under wave action. The proposed modular attachment comprises multiple independent auxiliary pontoons (i.e. modules) that are connected to the fore edge of the VLFS with hinges and linear Power Take-Off (PTO) systems. For the hydroelastic analysis, the auxiliary pontoons and the VLFS are modelled by using the Mindlin plate theory while the linear wave theory is used for modelling the fluid motion. The analysis is performed in the frequency domain using the hybrid Finite Element-Boundary Element (FE-BE) method. Parametric studies are carried out to investigate the effects of pontoon length, PTO damping coefficient, gap between auxiliary pontoons, and incident wave angle on the power capture factor as well as reductions in the hydroelastic responses of the VLFS with the modular attachment. It is found that in oblique waves, the modular attachment comprising multiple narrow pontoons outperforms the corresponding rigid attachment that consists of a single wide pontoon with respect to the power capture factor and the reduction in the deflection of the VLFS. In addition, it is possible to have a considerable gap between pontoons without significantly compromising the effectiveness of the modular attachment.     

A Study on Hydroelastic Response of Box-Type Very Large Floating Structures

The application of very large floating structure (VLFS) to the utilization of ocean space and exploitation of ocean resources has become one of the issues of great interest in international ocean engineering field. Owing to the advantage of simplicity in structure and low cost of construction and maintenance, box-type VLFS can be used in the calm water area near the coast as the structure configuration of floating airport. In this paper, a 3D linear hydroelastic theory is used to study the dynamic response of box-type VLFS in sinusoidal regular waves. A beam model and a 3D FEM model are respectively employed to describe the dynamic characteristics of the box-type structure in vacuum. A hydrodynamic model (3D potential theory of flexible body) is applied to investigate the effect of different dry models on the hydroelastic response of box-type structure. Based on the calculation of hydroelastic response in regular waves, the rigid body motion displacement, flexible deflection, and the short term and long     

箱式超大型浮体在非均匀海洋环境下的水弹性试验

超大型浮体(Very Large foating Structure,VLFS)作为人类开发海洋的前沿基地,正在成为世界各国海洋工程界研究的一个热点。由于超大型浮体覆盖的面积比普通的船舶和海洋结构物要大很多,其首尾两端所处的海洋环境可能有显著的差异,因此必须考虑非均匀海洋环境对其水弹性性能的影响。介绍了国内首次进行的箱式超大型浮体在非均匀海洋环境中的水弹性试验,对非均匀海洋环境、超大型浮体的水弹性性能以及两者相互之间的关系进行了研究。     

底部呈二维缓变情况下超大型浮体水弹性响应的两种计算方法比较

超大型浮体在海洋资源开发和海洋空间利用方面有重要应用前景.非均匀海洋环境中的水弹性响应是其应用中的一个重要问题.在近海中最典型的非均匀海洋环境当属由于底部变化引起的非均匀现象.本文分别采用多重尺度法（零阶近似）和常规的有限水深势流格林函数边界积分法,对底部呈二维缓变情况下超大型浮体的水弹性响应问题进行了研究和对比,并与实验工况进行了对照.两种方法与试验结果吻合较好,证明非均匀海洋环境确实对超大型浮体的水弹性响应具有一定的影响.     

Hydroelastic Response Analysis of Mat-Like VLFS over A Plane Slope in Head Seas

1 .IntroductionIntheexploitationofoceanresourcesandintheutilizationofoceanspaces,verylargefloatingstructures (VLFS)suchasMega FloatinJapan (Isobe ,1 999)andMobileOffshoreBase (MOB)inUSA (Remmers ,1 999)playasignificantrole .However,owingtotheirlargesizesandrelativelylowbendingrigidities ,theirhydroelasticresponsesinwavesareofthemostconcern .ManystudieshavebeencarriedoutforthepredictionofthehydroelasticresponsesofVLFS′s (Kashiwagi,2 0 0 0 ;Cui,2 0 0 2 ) .However,inalmostallofthesestu…     

Hydroelastic response of a very large floating structure over a variable bottom topography

An influence of sea-bottom topography on the hydroelastic response of a Very Large Floating Structure (VLFS) is considered. When the floating structure is constructed near the shore, the sea-bottom topographical effect should be considered. In this study, the effect of sea-bottom topography is investigated for four different bottom cases. To calculate the sea-bottom effects rigorously, the finite-element method based on the variational formulation is used in the fluid domain. The pontoon-type floating structure is modeled as the Kirchhoff plate. The mode superposition method is adopted for the hydroelastic behavior of the floating structure.     

Evaluation of bending moments and shear forces at unit connections of very large floating structures using hydroelastic and rigid body analyses

This paper investigates the characteristics of bending moments, shear forces and stresses at unit connections of very large floating structures (VLFS) under wave loads. The responses of VLFS are calculated by solving multi-body motion equation considering hydroelasticity and connection stiffness. Hydroelastic responses are calculated by the direct method. Higher-order boundary element method (HOBEM) is used for fluid analysis and finite element method (FEM) is introduced for structural analysis. The equation of motion is modified to describe the unit connections by employing spring elements. Bending moments and shear forces at the connections are obtained from the dynamic equilibrium condition for pressures and inertia forces. Two types of VLFS units such as tandem arranged units and side-by-side arranged units are considered in the numerical examples. The influences of connection stiffness, wave frequency and heading angle on responses of VLFS are investigated through the numerical examples. Rigid body analysis along with hydroelastic analysis is also carried out in the numerical analysis and comparison of those two approaches is discussed.     

用直接法分析超大型浮体的水弹性响应

探讨了浮舟桥型超大型浮体结构的水弹性响应分析问题。将超大型浮体结构简化成弹性平板模型,用压力分布法计算流体压力,用直接法计算流体-结构系统,给出了它们的数学计算模型。计算表明本计算方法和程序是正确的,并能保证充分的精度,进而计算了更大尺度的超大型浮体,分析了波长、波向等对响应振幅的影响。     

An Improved Simplified Method for Predicting the Hydroelastic Response of Mat-Like VLFS

Very Large Floating Structures (VLFS) have received considerable attention recently. Efficient and accurate estimation of their hydroelastic responses in waves is very important for the design. The most efficient approach would obviously be the analytical one. Within the category of analytical approaches, the simplified method proposed by Ohkusu and his colleague are of special characteristics. However, when one studies their methods, several questions arise. The purpose of this paper is to critically study the simplified methods proposed by Ohkusu and his colleague in order to answer these questions. Some problems in their original methods have been found and possible improvements are suggested. It is concluded that the improved simplified method using the same idea of Ohkusu and his colleague could provide a reasonable estimate of the hydroelastic response of mat-like VLFS in a certain range of incident angles of waves.     

Reduction of hydroelastic responses of a very-long floating structure by a floating oscillating-water-column breakwater system

The hydroelastic responses of a very-long floating structure (VLFS) placed behind a reverse T-shape freely floating breakwater with a built-in oscillating water column (OWC) chamber are analyzed in two dimensions. The Bernoulli–Euler beam equation is coupled with the equations of rigid and elastic motions of the breakwater and the VLFS. The interaction of waves between the floating rigid breakwater and the elastic VLFS is formulated in a consistent manner. It has been shown numerically that the structural deflections of the VLFS can be reduced significantly by a suitably designed reverse T-shape floating breakwater.     

Hydroelastic Response of VLFS with An Attached Submerged Horizontal Solid/Porous Plate Under Wave Action

The hydroelastic responses of a submerged horizontal solid/porous plate attached at the front of a very large rectangular floating structure(VLFS) under wave action has been investigated in the context of linear water wave theory. Darcy's law is adopted to represent energy dissipation in pores. It is assumed that the porous plates are made of material with very fine pores so that the normal velocity across the perforated porous is linearly associated with the pressure drop. In the analytic method, the eigenfunction expansion-matching method(EEMM) for multiple domains is applied to solve the hydrodynamic problem and the elastic equation of motion is solved by the modal expansion method. The performance of the proposed submerged horizontal solid/porous plate can be significantly enhanced by selecting optimal design parameters, such as plate length, horizontal position, submerged depth and porosity. It is concluded that good damping effect can be achieved through installation of solid and porous plate.Porous plate has better damping effect at low frequencies, while solid plate has better damping effect at high frequencies. The optimal ratio of plate length to water depth is 0.25-0.375, and the optimal ratio of submerged depth to water depth is 0.09-0.181.     

Transient Hydroelastic Response of VLFS by FEM with Impedance Boundary Conditions in Time Domain

A time-dependent finite element method (FEM) is developed to analyze the transient hydroelastie responses of very large floating structures (VLFS) subjected to dynamic loads. The hydrodynamic problem is formulated based on the linear theory of fluid and the structural response is analyzed based on the thin plate theory. The FEM truncates the unbounded fluid domain by introducing an artificial boundary surface, thus defining a finite computational domain. At this boundary surface an impedance boundary conditions are applied so that no wave reflections occur. In the proposed scheme, all of the procedures are processed directly in time domain, which is efficient for nonlinear analyses of structure floating on unbounded fluid. Numerical results indicate acceptable accuracy of the proposed method.     

基于CFD-FEM的浮式结构水弹性响应数值模拟

开发并验证了一种基于CFD-FEM耦合的弹性浮体水弹性响应计算模拟方法。采用CFD方法建立黏性数值水池模拟非线性波浪,弹性浮板进行有限元离散,并在交界面进行数据交互实现耦合计算;通过与水池试验数据和三维板理论在各种波浪环境下的浮体垂向位移结果对比,证实CFD-FEM耦合方法的有效性。并进一步研究了浮板的厚度、入射波波幅和浮板的三维效应对浮板水弹性响应的影响。结论表明,波幅的增加会加剧弹性浮板的水弹性响应,浮板各点处的垂向位移随波幅的增加而增大;当浮板厚度改变时,不同厚度浮板自由端处的垂向位移差异较小,而在中部等位置处,厚度对浮板的水弹性响应有较大的影响。     

Oblique Wave-Induced Responses of A VLFS Edged with A Pair of Inclined Perforated Plates

This paper is concerned with the hydroelastic responses of a mat-like, rectangular very large floating structure (VLFS) edged with a pair of horizontal/inclined perforated anti-motion plates in the context of the direct coupling method. The updated Lagrangian formulae are applied to establish the equilibrium equations of the VLFS and the total potential formula is employed for fluids in the numerical model including the viscous effect of the perforated plates through the Darcy''s law. The hybrid finite element-boundary element (FE-BE) method is implemented to determine the response reduction of VLFS with attached perforated plates under various oblique incident waves. Also, the numerical solutions are validated against a series of experimental tests. The effectiveness of the attached perforated plates in reducing the deflections of the VLFS can be significantly improved by selecting the proper design parameters such as the porous parameter, submergence depth, plate width and inclination angle for the given sea conditions.     

Review of hydroelasticity theories for global response of marine structures

Existing hydroelastic theories are reviewed. The theories are classified into different types: two-dimensional linear theory, two-dimensional nonlinear theory, three-dimensional linear theory and three-dimensional nonlinear theory. Applications to analysis of very large floating structures (VLFS) are reviewed and discussed in details. Special emphasis is placed on papers from China and Japan (in native languages) as these papers are not generally publicly known in the rest of the world.     

Hydroelastic responses and drift forces of a very-long floating structure equipped with a pin-connected oscillating-water-column breakwater system

The hydroelastic responses of a very-long floating structure (VLFS) in waves connected to a floating oscillating-water-column (OWC) breakwater system by a pin are analyzed by making use of the modal expansion method in two dimensions. The Bernoulli–Euler beam equation for the VLFS is coupled with the equations of motions of the breakwater taking account of the geometric and dynamic boundary conditions at the pin. The Legendre polynomials are employed as admissible functions representing the assumed modes of the VLFS with pinned-free-boundary conditions. It has been shown numerically that the deflections, bending moments and shear forces of the VLFS in waves can be reduced significantly by a pin-connected OWC breakwater. The time-mean horizontal drift forces of the VLFS equipped with the breakwater calculated by the near-field method are also presented.     

Comparison of hydroelastic computer codes based on the ISSC VLFS benchmark

There has been substantial development in computer codes for linear hydroelasticity in recent years, driven in part by the motivation to investigate the wave-induced response of very large floating structures (VLFSs). A recent International Ship and Offshore Structures Congress (ISSC) state-of-the-art report on VLFS design and analysis [ISSC, 2006. Report of Specialist Task Committee VI.2, very large floating structures. In: Frieze, P.A., Shenoi, R.A. (eds.), Proceedings of the 16th International Ship and Offshore Structures Congress, Elsevier, Southampton, UK, pp. 397-451] included a brief comparative study of the simulation results from different computer codes for a pontoon (mat-like) VLFS. The codes covered a mix of both fluid models (potential and linear Green-Naghdi) and structural models (3-D grillage, 2-D plate, 3-D shell). A more detailed comparison of the results from a select group of models from that study is provided and discussed herein. The similarities in the results increase the confidence level of the state-of-the-art in predicting the hydroelastic response of such structures, and the differences, including in computational efficiency, lead to an understanding of the significance of specific modeling assumptions and their impact on the predicted response.     

Hydroelastic analysis of pontoon-type circular VLFS with an attached submerged plate

This paper is concerned with the hydroelastic analysis of a pontoon-type, circular, very large floating structure (VLFS) with a horizontal submerged annular plate attached around its perimeter. The coupled fluid–structure interaction problem may be solved by using the modal expansion method in the frequency domain. It involves, firstly, the decomposition of the deflection of a circular Mindlin plate with free edges into vibration modes that are obtained analytically. Then the hydrodynamic diffraction and radiation forces are evaluated by using the eigenfunction expansion matching method which can also be done in an exact manner. The hydroelastic equation of motion is solved by the Rayleigh–Ritz method for the modal amplitudes, and then the modal responses are summed up to obtain the total response. The effectiveness of the attached submerged annular plate in reducing the motion of VLFS has been confirmed by the analysis.     

Hydroelastic response of a circular plate in waves on a two-layer fluid of finite depth

The hydroelastic response of a circular, very large floating structure （VLFS）, idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the plate-covered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presentedto investigate the effects of different physical quantities, such as the thickness of the plate, Young＇s modulus, the ratios ofthe densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid.Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.