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.     

On the hydroelastic behavior of two-dimensional articulated plates

The hydroelastic behavior of two-dimensional articulated plates is investigated analytically within the scope of linear theory. The connectors are modeled by singular line loading and its derivatives. The velocity potential under the free surface and plate is obtained by use of a wave-maker theory. The characteristics of large displacements at the upstream and downstream edges of the plate and the connectors are obtained from the closed-form solutions. It is also shown that the hydroelastic properties are strongly dependent on the stiffness of the connectors and incoming wave frequency. Finally, the method is used to solve for the response of a multi-module articulated plate.     

On the dispersion relation of hydroelastic waves in a plate

This paper deals with the dispersion relation of hydroelastic waves in pontoon-type very large floating structures (VLFS) using a simple beam modeling, where the term hydroelastic waves means propagation of deflection vibrations in VLFS. The purpose of this paper is to show the properties of the hydroelastic waves. The dispersion relation of hydroelastic waves propagating in an infinite plate floating on the water is derived based on the linear water wave theory. The effects of the water depth and of the bending rigidity of the floating plate on the wavelength, phase velocity, and group velocity of the hydroelastic waves are shown theoretically or numerically. Then, the dispersion relation of hydroelastic waves in a finite plate floating on shallow water is investigated. It is shown that the wavelength or the phase velocity of the hydroelastic waves varies with the location in the plate. Received for publication on April 7, 1999; accepted on Aug. 20, 1999     

Hydroelasticity based fatigue assessment of the connector for a ribbon bridge subjected to a moving load

In this paper, the prediction of the hydroelastic response of the floating bridge and the fatigue behavior of the connectors is presented. And based on the hydroelastic response analysis of the ribbon bridge, the dynamic alternating load of the connector can be obtained, in that the fatigue behavior analysis of the connector simulated by the solid elements can be conducted by employing the local stress–strain approach. It is revealed that the sequence of the dynamic loads acting on the connectors, the value of various fatigue parameters and the ultimate tensile strength should be sufficiently considered, especially the passing speed of a moving load, so that it can significantly reduce the fatigue damage of the connectors.     

Dynamics of ships running aground

A comprehensive dynamic model is presented for analysis of the transient loads and responses of the hull girder of ships running aground on relatively plane sand, gravel, or rock sea bottoms. Depending on the seabed soil characteristics and the geometry of the ship bow, the bow will plow into the seabed to some extent. The soil forces are determined by a mathematical model based on a theory for frictional soils in rupture and dynamic equilibrium of the fluid phase in the saturated soil. The hydrodynamic pressure forces acting on the decelerated ship hull are determined by taking into account the effect of shallow water. Hydrodynamic memory effects on the transient hull motions are modeled by application of an impulse response technique. The ship hull is modeled as an elastic beam to determine the structural response in the form of flexural and longitudinal stress waves caused by the transient ground reaction and hydrodynamic forces. A number of numerical analysis results are presented for a VLCC running aground. The results include bow trajectory in the seabed, time variation of the grounding force, and the maximum values of the sectional shear forces and bending moments in the hull girder.     

The influence of water depth on the hydroelastic response of a very large floating platform

The hydroelastic response of a two-dimensional very large floating platform to plane incident wave is investigated for three different cases: infinite, finite and shallow water depth. An integro-differential equation is presented to describe the deflection of the platform due to incident waves. Reflection and transmission coefficients are obtained as well. We consider the case of a strip and a half-plane. Numerical results are obtained for various values of the parameters. The results for the strip and for the semi-infinite platform are compared for different values of depth.     

Numerical analysis of the hydroelastic behavior of a vertical plate due to solitary waves

Interactions of a vertical elastic plate with fully nonlinear water waves were simulated. Utilizing the mixed Eulerian Lagrangian method for the free-surface flow and the finite element method for the deflection of an elastic plate, a fully coupled scheme for accurately determining fluid–plate motions was developed. Using this scheme, some modifications to the solvers for both fluid and plate were made. A hybrid wave-absorbing beach was installed to prevent wave reflection from the end of the wave tank. A fourth-order Runge–Kutta time-marching scheme with a uniform time step was applied to achieve numerical stability. The method was validated by simulating the wave generated by the initial deformation of a vertical plate and comparing the result with the corresponding analytical solution. For further validation, the hydroelastic behavior of a vertical plate induced by a pulse-type wave (where the initial pulse-type elevation of the free surface is specified) was computed, and the result was compared with another numerical result from a mode-expansion method. The interaction of a surface-piercing plate with nonzero initial free surface was then simulated, and the result was compared with the corresponding linear analytical solution. Finally, the hydroelastic response of a surface-piercing vertical plate due to a solitary wave (generated by actuating the vertical plate at the right end of the tank only at the beginning) was computed and investigated systematically.     

水下波能装置的波致弹性变形研究（英文）

Structural integrity has remained a challenge for design and analysis of wave energy devices. A difficulty in assessment of the structural integrity is often laid in the accurate determination of the wave-induced loads on the wave energy devices and the repones of the structure. Decoupled hydroelastic response of a submerged, oscillating wave energy device to extreme nonlinear wave loads is studied here. The submerged wave energy device consists of an oscillating horizontal disc attached to a direct-drive power take-off system. The structural frame of the wave energy device is fixed on the seafloor in shallow water. Several extreme wave conditions are considered in this study. The nonlinear wave loads on members of the submerged structure are obtained by use of the level I Green-Naghdi equations and Morison's equation for cylindrical members.Distribution of Von Mises stresses and the elastic response of the structure to the extreme wave loads are determined by use of a finite element method. The decoupled hydroelastic analysis of the structure is carried out for devices built by four different materials, namely stainless steel, concrete, aluminium alloy, and titanium alloy. The elastic response of these devices is studied and results are compared with each other. Points of maximum stress and deformations are determined and the structural integrity under the extreme conditions is assessed. It is shown that the proposed approaches provide invaluable information about the structural integrity of wave energy devices.     

Hydroelastic analysis of a rectangular plate subjected to slamming loads

A hydroelastic analysis of a rectangular plate subjected to slamming loads is presented. An analytical model based on Wagner theory is used for calculations of transient slamming load on the ship plate. A thin isotropic plate theory is considered for determining the vibration of a rectangular plate excited by an external slamming force. The forced vibration of the plate is calculated by the modal expansion method. Analytical results of the transient response of a rectangular plate induced by slamming loads are compared with numerical calculations from finite element method. The theoretical slamming pressure based on Wagner model is applied on the finite element model of a plate. Good agreement is obtained between the analytical and numerical results for the structural deflection of a rectangular plate due to slamming pressure. The effects of plate dimension and wave profile on the structural vibration are discussed as well. The results show that a low impact velocity and a small wetted radial length of wave yield negligible effects of hydroelasticity.     

结构刚度变化对船舶水弹性响应的影响

水弹性力学是研究水动力、惯性力和弹性力之间相互作用的力学分支。本文利用三维线性频域水弹性程序计算了某船在单位幅值正弦规则波中的水弹性响应 ,在结构质量分布不变的前提条件下 ,研究了结构刚度变化对结构水弹性响应的影响 ,得到了一些很有价值的结论。     

Hydroelastic analysis of a nonlinearly connected floating bridge subjected to moving loads

In this paper, the motion equations for the nonlinearly connected floating bridge, considering the nonlinear properties of connectors and vehicles’ inertia effects, are proposed. The super-element method is used to condense the whole calculation scale, and the direct integration and Newton–Raphson iteration method are applied to solve the reduced equations. Based on the modal and static analyses, the dynamic displacement and connection forces characteristics of a floating bridge with nonlinear connectors subjected to moving loads are investigated. It is found that nonlinearity and initial gap of the connectors are important for the hydroelastic response of a nonlinearly connected floating bridge.     

超大型浮体结构考虑非线性项的波浪力响应计算

为求解超大型浮体结构波浪响应问题,将其简化成弹性梁板模型。以有限元软件为基础来建立超大型浮体结构的弹性梁板模型,在势流理论的基础上,将速度势分解为入射势、绕射势和辐射势三部分,并利用格林函数法推导出一阶、二阶波浪速度势的表达式。以此为理论基础,编制了相应的计算程序来计算浮体结构所受到的二阶波浪力,最后建立了梁板模型的水弹性响应方程,对非线性波浪力作用下的浮体结构的水弹性响应进行求解分析,并分析了波向对响应振幅的影响。     

极浅水多体波浪能发电装置锚泊系统设计

采用三维势流理论对多体波浪能发电装置进行频域水动力计算,分析极浅水效应和多体间相互作用对单体发电装置的水动力性能的影响。利用Orcaflex软件建立多体波浪能发电装置数值模型,浮体间采用铰接进行连接,并利用弹簧单元模拟发电液压缸的弹性阻尼作用。为极浅水多体波浪能发电装置设计合理的锚泊方案,采用时域动态耦合方法进行分析,同时考虑极浅水效应、多体影响和二阶低频力,根据API规范对自存工况下的锚泊缆强度进行校核,并对确定选用的锚泊方案进行敏感性分析。通过对计算结果进行分析,发现在进行浅水多浮体锚泊设计时,低频波浪载荷、多体相互作用和海底摩擦不可忽视;对于极浅水的锚泊系统设计,Lazy wave 型锚泊形式优于传统悬链线式锚泊。上述研究工作为近海极浅水海域新型海洋能发电装置锚泊系统的设计提供了新的参考和思路。     

超大型FPSO原油质量分布模拟与水弹性响应研究

FPSO在近海油气田开发中得到了越来越广泛的应用.大多数在渤海海域服役的FPSO工作在浅水海域.主尺度大与水深吃水小,直接导致FPSO水动力特性与深水条件下船舶的水动力特性有较大区别,因此采用水弹性理论研究超大型FPSO在浅水中的运动与波浪诱导载荷响应具有重要意义.浅水超大型FPSO满载时原油重量将近占载重量的80%,因此如何正确模拟原油重量分布对干结构的固有频率、广义质量和振型的计算非常重要.本文建立了基于三维水弹性理论的数值模型,开发了有限水深复合格林函数的数值计算程序模块,对一艘300K DWT FPSO在特定水深海况下的运动与波浪载荷响应进行了研究;同时采用三种方法模拟了原油质量分布.计算结果表明,不同的原油质量分布模拟方法对水弹性计算分析影响很大.     

基于特征函数展开方法计算水深变化区域驳船运动响应

本文主要研究在近岸水深变化区域两维矩形驳船的运动.变化底部被分解为连续的阶梯且驳船所在流体域被划分为一系列矩形子域.在每个流体子域中采用特征函数展开方法表达速度势,并通过连续性假设求解速度势的值.文中对计算方法的收敛性进行了讨论并给出表达式中参数的推荐值.本文计算驳船在平底和斜底条件下的水动力系数并与文献结果进行对比,同时把驳船在非规则波中的运动响应与水池试验结果进行了对比验证.     

An advanced theory of thin-walled girders with application to ship vibrations

The paper presents an outline of the advanced theory of thin-walled girders. The improvement includes shear influence on torsion as an extension of shear influence on bending. The analogy between bending and torsion is recognized and pointed out throughout the paper. Complete differential equations of coupled flexural and torsional vibrations for a prismatic girder are derived. In addition, the 8 d.o.f. beam finite element, utilizing the energy approach, is constituted with stiffness and mass matrices, and load vectors. The paper describes determining of geometrical properties of multi-cell open cross-sections by employing the strip element method. Numerical procedures for vibration analyses are outlined. Furthermore, dry natural vibrations of a VLCS (Very Large Container Ship) are analysed by 1D FEM model as a prerogative for hydroelastic analyses of these relatively flexible vessels. Influence of transverse bulkheads is taken into account by increasing torsional stiffness of the ship hull proportionally to their deformation energies. Validation of 1D FEM model is checked by correlation analysis with the vibration response of the fine 3D FEM model.     

A study on the estimation of the seaquake response of a floating structure considering the characteristics of seismic wave propagation in the ground and the water

 Seaquakes, which are characterized by the propagation of vertical earthquake motion at the sea bottom as a compression (longitudinal) wave, are reported to cause damage to ships, and their effect on floating structures is a matter of great concern. To comprehend the basic properties of seaquakes, we first discuss a method to calculate the displacement of the seabed when it is subjected to hydrodynamic pressure. To investigate the interrelationship between the vibration of a floating structure and the deformation of the seabed, a new boundary integral equation is derived which assumes that the seabed is a semiinfinite homogeneous elastic solid in order to analyze the seaquake-induced hydrodynamic pressure acting on the floating structure. By considering the propagation of the seismic wave in the ground and in the water, the incident wave potential in seaquake problems is also deduced and its characteristics are discussed. Finally, the response of a very large floating structure in a seaquake is investigated using a fluid force analysis method, and considering the interrelationship between the vibration of the floating structure and the deformation of the seabed. Received: August 19, 2002 / Accepted: November 11, 2002 Address correspondence to: H. Takamura (hiroaki_takamura@nishimatsu.co.jp) Updated from the Japanese original, which won the 2002 SNAJ prize (J Soc Nav Archit Jpn 2001;189:87–92,93–100 and 190:381–386)     

Hydroelasticity of large container ships

The importance of hydroelastic analysis of large and flexible container ships of today is pointed out for structure design. A methodology for investigation of this challenging phenomenon is drawn up and a mathematical model is worked out. It includes the definition of ship geometry, mass parameters, structure stiffness, and combines ship hydrostatics, hydrodynamics, wave load, ship motion and vibrations. The modal superposition method is employed. Based on the presented theory, a computer program is developed and applied for hydroelastic analysis of a large container ship. The transfer functions for heave, pitch, roll, vertical and horizontal bending and torsion are presented. Rigid body and elastic responses are correlated.     

Overview: Research on hydroelastic responses of VLFS in complex environments

In the past several decades, extensive investigations have been carried out on the hydroelastic responses of Very Large Floating Structures (VLFS) in the deep open sea by researchers around the world. However, when tackling the hydroelastic problems of VLFS used as the protection and exploitation of marine resources near offshore and islands, the effects of complex environments, such as the seabed profile and inhomogeneous wave conditions should be taken into account. Based on the development history of VLFS and the process of classical hydroelasticity of VLFS, the research results of hydroelastic responses of VLFS in complex environments have been systematically summarized in this paper, so as to provide a basis for the further research.     

浅层水中爆炸载荷作用下舰船动态响应及设备冲击环境研究

以MSC/Dytran为平台,对浅层水中爆炸载荷作用下舰船结构的动态响应及设备冲击环境进行了研究。在对4种不同水底介质的浅层水中爆炸冲击波研究的基础上,模拟了偏恶劣的绝对刚性水底条件下浅层水中爆炸时某舰的动态响应,再以舰船主机为对象、以结构加速度响应为输入对舰船设备冲击环境作进一步分析,并以无限水深情况下的舰船响应和设备冲击环境为参照,对水底反射波的影响规律做了一些初步的探讨。