Time-domain,shallow-water hydroelastic analysis of VLFS elastically connected to the seabed

In order to ensure the safe operation of a VLFS, a combination of mooring, breakwater and other motion reducing systems is employed. In the present work, the transient hydroelastic response of a floating, thin elastic plate, elastically connected to the seabed, is examined. The plate is modelled as an Euler-Bernoulli strip, while the linearized shallow water equations are used for the hydrodynamic modelling. Elastic connectors are approximated by a series of simple spring-dashpot systems positioned along the strip. A higher order finite element scheme is employed for the calculation of the hydroelastic response of the strip-connector configuration over the shallow bathymetry. After the definition of the initial-boundary value problem, its variational form is derived and discussed. Next, on the basis of the aforementioned formulation, an energy balance expression is obtained. The effect of variable bathymetry on the response of a two connector-strip system is examined by means of three seabed profiles featuring a flat bottom, an upslope and a downslope environment. For the flat bottom case, the strip response mitigating effect exerted by the employment of two and three elastic connectors is considered. Finally, by means of the derived energy balance equation, the energy exchange is monitored, providing a valuable insight into the transient phenomena that take place in the studied configurations.     

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.     

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     

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.     

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.     

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.     

波浪作用下带式舟桥的水弹性响应研究

对于设计和使用在波浪和流作用下作业的浮桥,充分了解其水弹性性能尤为重要.就在国防和桥梁工程中极为重要的带式舟桥而言,预报其在波浪中的水弹性响应在实际工程中就显得十分必要.该文主要研究带式舟桥在波浪作用下的水弹性性能.首先,简要地介绍了预报浮桥动力响应的不同方法及它们与试验比较的结果;其次,在三维水弹性理论的基础上采用模态叠加法对带式舟桥的有限元模型进行了水弹性分析,同时与十分之一模型试验结果做了比较(该试验由上海交通大学海洋工程国家重点实验室承担).研究表明,文中的方法计算分析波浪中浮桥的水弹性响应是可行的.     

Study on sloshing in cargo tanks including hydroelastic effects

The sloshing problem in cargo tanks is studied through experiments and numerical analysis. The fluid motion is described using a higher-order boundary element method and the structural response by a thin plate theory. It was found that hydraulic jumps are formed when the excitation frequency is close to the resonance frequency in the case of low filling depth. In the case of high filling depth, the flow resonates and hits the top of the tank, thus inducing a large impact pressure. The pressure on the flexible plate shows amplified initial peaks followed by oscillatory components, the frequency of which coincides with the natural frequencies of the plate in water as a result of hydroelastic effects. Received for publication on Nov. 18, 1998; accepted on May 14, 1999     

Hydroelastic analysis of oblique irregular waves with a pontoon-type VLFS edged with dual inclined perforated plates

The fluid-structure interaction of oblique irregular waves with a pontoon-type very large floating structure (VLFS) edged with dual horizontal/inclined perforated plates has been investigated in the context of the direct time domain modal expansion theory. For the hydroelastic analysis, the boundary element method (BEM) based on time domain Kelvin sources is implemented to establish water wave model including the viscous effect of the perforated plates through the Darcy’s law, and the finite element method (FEM) is adopted for solving the deflections of the VLFS modeled as an equivalent Mindlin thick plate. In order to enhance the computing efficiency, the interpolation-tabulation scheme is applied to assess rapidly and accurately the free-surface Green function and its partial derivatives in finite water depth, and the boundary integral equation of a half or quarter VLFS model is further established taking advantage of symmetry of flow field and structure. Also, the numerical solutions are validated against a series of experimental tests. In the comparison, the empirical relationship between the actual porosity and porous parameter is successfully applied. Numerical solutions and model tests are executed to determine the hydroelastic response characteristics of VLFS with an attached anti-motion device. This study examines the effects of porosity, submerged depth, inclined angle and gap distance of such dual perforated anti-motion plates on the hydroelastic response to provide information regarding the optimal design. The effects of oblique wave angle on the performance of anti-motion and hydroelastic behavior of VLFS are also emphatically examined.     

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。     

Connection design for two-floating beam system for minimum hydroelastic response

This paper is concerned with the connection design for a two-floating beam system for minimum hydroelastic response. The frequency domain approach is used for the hydroelastic analysis. The fluid is modelled as an ideal fluid, and the floating beams are modelled by the Euler–Bernoulli beam theory. The boundary element method (BEM) and the finite element method (FEM) are applied to solve the governing equation of the fluid motion and the beam equation of motion, respectively. The study aims to investigate the optimum location and rotational stiffness of the connection for the two-floating beam system with the view to minimize the compliance. The study also investigates the effects of relative beam stiffnesses on the hydroelastic response of the two-floating beam system.     

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.     

基于一个二维修正水弹性方法的集装箱船体梁动态前极限强度评估研究

海上极端波因其巨大的波高常常导致船体的极限破坏。该文提出了一个二维的修正水弹性方法来研究一个集装箱船船体梁在极端波中的动态前极限强度。传统的极限强度评估基于准静态方法,没有动态效应被考虑。而船体在波浪下的动态结构响应是基于水弹性方法,传统的水弹性方法并不能计算船体梁的动态非线性强度。该二维修正的水弹性方法考虑时域波浪和非线性船体梁之间的耦合,将水弹性方法和Smith方法结合,用Smith方法计算船体梁的刚度,而其刚度与船体梁的强度和变形曲率有关。所以该时域的非线性刚度被用于修改水弹性方法里的常数项的结构梁刚度。几组极端波模型被用以产生船体梁的大变形和非线性动态垂向弯矩。文中分别采用修正水弹性方法和普通水弹性方法,通过改变四个重要的极端波参数如极端波最大波高、规则波的波高、波速和波长等来研究其对船体梁船中处的大变形转角和非线性垂向弯矩的影响,通过采用修正的水弹性方法计算得来的结果与水弹性方法计算得来的结果相比较,得到了一些差异和结论。     

基于Level-set法的液体晃荡与弹性液舱耦合作用研究

对基于Level-set法模拟液舱液体晃荡的数值模型进行了改进,实现了对大幅晃荡引起的抨击载荷的模拟.运用水弹性力学理论论述了液体晃荡与弹性液舱耦合作用的分析方法,建立了相应的水弹性力学方程.数值算例与实验结果的比较验证了对抨击载荷模拟的正确性;通过对晃荡载荷引起的结构响应的计算分析,得出一些关于结构响应特性的重要结论.     

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.     

Hydroelastic responses and interactions of floating fuel storage modules placed side-by-side with floating breakwaters

This paper is concerned with the hydroelastic responses and hydrodynamic interactions of two large floating fuel storage modules placed side-by-side with the presence of floating breakwaters. These modules and breakwaters form the floating fuel storage facility (FFSF). The floating storage modules and breakwaters are modeled as plates and the linear wave theory is used to model the water waves in the numerical model. The numerical model is verified with existing numerical results and validated with experimental test. Numerical simulations are performed to determine the hydroelastic behavior and hydrodynamic interactions of floating storage modules placed adjacent to each other and enclosed by floating breakwaters under various incident wave angles. The effects of breakwaters, drafts, channel spacing formed by the two adjacent modules and water depth on the hydroelastic responses of the modules are investigated. The wave induced responses of multiple floating storage modules enclosed by floating breakwaters are also examined.     

Hydroelastic Analysis of a Flexible Floating Body for the Variation of Incident Wave

As for the hydroelastic response of a flexible floating body, various kinds of simplified analytical and numerical methods based on the different assumption have been developed, however, the most versatile and applicable approach is the three-dimensional hydroelasticity theory. Currently, most studies mainly focused on the wave condition of head seas without taking the differences for the variation of the incident wave angle into account. In this paper, based on the three-dimensional hydroelasticity theory, an investigation into the variation of the hydroelastic response for different incident wave angles is presented; also some comparisons are demonstrated and discussed.     

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.     

基于不同试验方法和非线性水弹性时域理论的鞭振弹振响应研究

船体主尺度增大会导致严重的鞭振和弹振现象,这会增大船体结构的极限载荷和疲劳损伤.为了深入探究船体的振动响应,文中在拖曳水池对某万箱集装箱船分别进行了分段模型的自航和拖航试验.分析了不同海况下自航和拖航这两种试验方式对鞭振和弹振响应的影响.为计及不同振动频率成分对载荷响应的影响,提出一种考虑波浪记忆效应的非线性水弹性方法.文中提出了一种求解延时函数的方法,能够解决高频区域的阻尼系数的计算限制.最后,船舯弯矩试验结果分别和线性与非线性理论结果进行了比较,发现文中提出的非线性方法能够更好地预报弹性船体的振动响应.     

航行船舶的三维非线性水弹性分析

基于Wu提出的浮体二阶水弹性理论[1],研究大浪中航行船舶的非线性水弹性响应,给出了数值方法和计算结果.在二阶水弹性分析中,主要考虑了大角度刚体转动和瞬时湿表面变化引起的非线性水动力.根据三维线性水弹性理论[2],采用移动脉动源格林函数和Kelvin定常兴波假定,求解了对二阶水动力做主要贡献的一阶速度势及响应.最后以航行于不规则波中的小水线面双体船为例,讨论了航速和定常兴波流场对水弹性响应的影响,并对线性和非线性响应的预报结果进行了比较.