Time-domain numerical and segmented ship model experimental analyses of hydroelastic responses of a large container ship in oblique regular waves

Real sea conditions are characterized by multidirectional sea waves. However, the prediction of hull load responses in oblique waves is a difficult problem due to numeral divergence. This paper focuses on the investigation of numerical and experimental methods of load responses of ultra-large vessels in oblique regular waves. A three dimensional nonlinear hydroelastic method is proposed. In order to numerically solve the divergence problem of time-domain motion equations in oblique waves, a proportional, integral and derivative (PID) autopilot model is applied. A tank model measurement methodology is used to conduct experiments for hydroelastic responses of a large container ship in oblique regular waves. To implement the tests, a segmented ship model and oblique wave testing system are designed and assembled. Then a series of tests corresponding to various wave headings are carried out to investigate the vibrational characteristics of the model. Finally, time-domain numerical simulations of the ship are carried out. The numerical analysis results by the presented method show good agreement with experimental results.     

Sensitivity of extreme hydroelastic load effects to changes in ship hull stiffness and structural damping

A new hybrid method for the time-domain nonlinear simulation of the hydroelastic load effects and the peak over threshold (POT) method for the calculation of the short-term extreme responses are briefly described and applied to a flexible SL-7 class containership and a flexible liquefied natural gas (LNG) ship. Three stiffness levels, three stiffness distributions and three modal damping ratios are used to study the influence of the hull flexibility and structural damping on the short-term prediction of extreme vertical hydroelastic load effects. The results give justification for some simplified treatment of the first vertical flexible mode in early design stage when structural details are not available.     

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     

Hydroelastic analysis of flexible floating interconnected structures

Three-dimensional hydroelasticity theory is used to predict the hydroelastic response of flexible floating interconnected structures. The theory is extended to take into account hinge rigid modes, which are calculated from a numerical analysis of the structure based on the finite element method. The modules and connectors are all considered to be flexible, with variable translational and rotational connector stiffness. As a special case, the response of a two-module interconnected structure with very high connector stiffness is found to compare well to experimental results for an otherwise equivalent continuous structure. This model is used to study the general characteristics of hydroelastic response in flexible floating interconnected structures, including their displacement and bending moments under various conditions. The effects of connector and module stiffness on the hydroelastic response are also studied, to provide information regarding the optimal design of such structures.     

不同干结构模型对箱式超大型浮体结构水弹性响应的影响

三维线性水弹性力学利用结构在真空中弹性振型的正交性 ,对结构振动进行模态分析 ,用弹性体三维势流理论计算结构的水动力系数。因此 ,结构的干模态计算是十分重要的。应用三维线性水弹性理论研究箱式超大型浮体结构在波浪中的动力响应时 ,分别采用梁模型和三维空间有限元模型计算结构的干模态 ,并且采用同样的水动力模型 (弹性体三维势流理论 )研究了不同干结构模型对结构水弹性响应的影响     

Study on the Configuration of Towed Flexible Cables

Based on the fundamental equation of flexible cable dynamics for a towed system, an easily solved mathematical model is set up in this paper by means of appropriate simplification. Several regular patterns of spatial motion of towed flexible cables in water are obtained through numerical simulation with the finite difference method, and then modification and verification by trial results at sea. A technical support is provided for the towing ship to maneuver properly when a flexible cable is towed. Furthermore, the relations between two towed flexible cables, which are towed simultaneously by a ship, are investigated. The results show that the ship towing two flexible cables is safe under the suggested arrangement of two winches for the towing system, and the coiling/uncoiling sequences of the cables as well as the suggested way of maneuvering.     

Theoretical and experimental study on dynamic behavior of a damaged ship in waves

Most of the large scaled casualties are caused by loss of structural strength and stability due to the progressive flooding and the effect of waves and wind. To prevent foundering and structural failure, it is necessary to predict the motion of the damaged ship in waves.This paper describes the motion of damaged ship in waves resulting from a theoretical and experimental study. A time domain theoretical model, which can be applied to any type of ship or arrangement, for the prediction of damaged ship motion and accidental flooding has been developed considering the effects of flooding of compartments. To evaluate the accuracy of the model, model tests are carried out in ship motion basin for three different damaged conditions: engine room bottom damage, side shell damage and bow visor damage of Ro–Ro ship in regular and irregular waves with different wave heights and directions.     

Investigation of Hydroelastic Ship Responses of An ULOC in Head Seas

Investigation of hydroelastic ship responses has been brought to the attention of the scientific and engineering world for several decades. There are two kinds of high-frequency vibrations in general ship responses to a large ocean-going ship in its shipping line, so-called springing and whipping, which are important for the determination of design wave load and fatigue damage as well. Because of the huge scale of an ultra large ore carrier (ULOC), it will suffer seldom slamming events in the ocean. The resonance vibration with high frequency is springing, which is caused by continuous wave excitation. In this paper, the wave-induced vibrations of the ULOC are addressed by experimental and numerical methods according to 2D and 3D hydroelasticity theories and an elastic model under full-load and ballast conditions. The influence of loading conditions on high-frequency vibration is studied both by numerical and experimental results. Wave-induced vibrations are higher under ballast condition including the wave frequency part, the multiple frequencies part, the 2-node and the 3-node vertical bending parts of the hydroelastic responses. The predicted results from the 2D method have less accuracy than the 3D method especially under ballast condition because of the slender-body assumption in the former method. The applicability of the 2D method and the further development of nonlinear effects to 3D method in the prediction of hydroelastic responses of the ULOC are discussed.     

Estimation of the Roll Hydrodynamic Moment Model of a Ship by Using the System Identification Method and the Free Running Model Test

When a fast container ship or a naval vessel turns, accompanying roll motions occur. This roll effect must be considered in the horizontal equations of the motion of the ship to predict the maneuverability of the ship properly. In this paper, a new method for determining a model structure of the hydrodynamic roll moment acting on a ship and for estimating the hydrodynamic coefficients is proposed. The method utilizes a system identification technique with the data from sea trial tests or from free running model (FRM) tests. To obtain motion data that is applied to the proposed algorithm, an FRM of a large container ship was developed. Using this model ship, standard maneuvering tests were carried out on a small body of water out of doors. A hydrodynamic roll moment model was constructed utilizing the data from turning circle tests and a 20-20 zig-zag test. This was then confirmed through a 10-10 zig-zag test. It was concluded that a model structure of the hydrodynamic roll moment model could be established without difficulty through a system identification method and FRM tests.     

An integrated dynamic model of ocean mining system and fast simulation of its longitudinal reciprocating motion

An integrated dynamic model of China’s deep ocean mining system is developed and the fast simulation analysis of its longitudinal reciprocating motion operation processes is achieved. The seafloor tracked miner is built as a three-dimensional single-body model with six-degree-of-freedom. The track-terrain interaction is modeled by partitioning the track-terrain interface into a certain number of mesh elements with three mutually perpendicular forces, including the normal force, the longitudinal shear force and the lateral shear force, acting on the center point of each mesh element. The hydrodynamic force of the miner is considered and applied. By considering the operational safety and collection efficiency, two new mining paths for the miner on the seafloor are proposed, which can be simulated with the established single-body dynamic model of the miner. The pipeline subsystem is built as a three-dimensional multi-body discrete element model, which is divided into rigid elements linked by flexible connectors. The flexible connector without mass is represented by six spring-damper elements. The external hydrodynamic forces of the ocean current from the longitudinal and lateral directions are both considered and modeled based on the Morison formula and applied to the mass center of each corresponding discrete rigid element. The mining ship is simplified and represented by a general kinematic point, whose heave motion induced by the ocean waves and the longitudinal and lateral towing motions are considered and applied. By integrating the single-body dynamic model of the miner and the multi-body discrete element dynamic model of the pipeline, and defining the kinematic equations of the mining ship, the integrated dynamic model of the total deep ocean mining system is formed. The longitudinal reciprocating motion operation modes of the total mining system, which combine the active straight-line and turning motions of the miner and the ship, and the passive towed motions of the pipeline, are proposed and simulated with the developed 3D dynamic model. Some critical simulation results are obtained and analyzed, such as the motion trajectories of key subsystems, the velocities of the buoyancy modules and the interaction forces between subsystems, which in a way can provide important theoretical basis and useful technical reference for the practical deep ocean mining system analysis, operation and control.     

Interaction of ocean waves with floating and submerged horizontal flexible structures in three-dimensions

A three-dimensional general mathematical hydroelastic model dealing with the problem of wave interaction with a floating and a submerged flexible structure is developed based on small amplitude wave theory and linear structural response. The horizontal floating and submerged flexible structures are modelled with a thin plate theory. The linearized long wave equations based on shallow water approximations are derived and results are compared. Three-dimensional Green’s functions are derived using fundamental source potentials in water of finite and infinite depths. The expansion formulae associated with orthogonal mode-coupling relations are derived based on the application of Fourier transform in finite and infinite depths in case of finite width in three-dimensions. The usefulness of the expansion formula is demonstrated by analysing a physical problem of surface gravity wave interaction with a moored finite floating elastic plate in the presence of a finite submerged flexible membrane in three-dimensions. The numerical accuracy of the method is demonstrated by computing the complex values of reflected wave amplitudes for different modes of oscillation and mooring stiffness. Further, the effect of compressive force and modes of oscillations on a free oscillation hydroelastic waves in a closed channel of finite width and length for floating and submerged elastic plate system is analysed.     

风和流作用下单链式系泊养殖工船“鱼尾运动”研究

单点系泊船舶在受到风、流等外力作用下通常会产生大幅周期性艏摇运动，称为“鱼尾运动”。剧烈的鱼尾运动可能会导致系泊系统的锚链承受过大的张力从而遭到破坏。为了充分认识单点系泊状态下养殖工船的鱼尾运动，针对一艘十万吨级单链式系泊养殖工船进行了数值分析及模型试验研究。首先，通过风洞模型试验测得养殖工船的风、流载荷系数，以此作为输入对风、流联合作用下养殖工船的动力响应进行了数值模拟分析；同时，开展水池模型试验验证了数值计算结果的准确性和可靠性；最后，通过数值计算研究了不同风速和流速下单链式系泊养殖工船鱼尾运动的特性和规律，为实际工程设计提供一定的参考。     

Response analysis and optimum configuration of a modular floating structure with flexible connectors

In the present paper, a numerical analysis framework evaluating the connectors’ internal loads of a modular Pontoon type Floating Structure (PFS) as well as for identifying the PFS's optimum configuration under the action of regular waves is developed and presented. The PFS consists of flexible floating modules (pontoons) connected with flexible connectors in longitudinal and/or transverse directions. The numerical analysis framework includes: (a) a frequency domain ‘wet’ hydroelastic analysis for computing the PFS's ‘wet’ hydroelastic response and the connectors’ internal loads and (b) a genetic algorithms based optimization process for identifying the optimum configuration of the PFS considering predefined performance criteria. Different configurations of the PFS under the action of normal and oblique waves are taken into account, considering different number and layout of modules (grid type) and different values of the connectors’ rotational stiffness. The effect of the connector's rotational stiffness and the grid type of the PFS on the hydroelastic response and on the connectors’ internal loads is analyzed. For specific wave field characteristics, the optimum design configuration of the PFS is identified through the aforementioned optimization process in terms of performance criteria related to: (a) the vertical hydroelastic response at any predefined point of the deck of the PFS and (b) the internal loads of the PFS's connectors. The results obtained demonstrate the complex relationship between the internal loads of the connectors and the hydroelastic response of the examined PFS configurations with the connectors’ rotational stiffness and the PFS's grid type as well as with the excitation. They also demonstrate the applicability of the developed numerical analysis framework in order to properly direct the PFS's design towards a most preferable optimum configuration.     

Ray theory for predicting hydroelastic behavior of a very large floating structure in waves

The conceptual design of a very large floating structure (VLFS) requires a convenient computer code for predicting hydroelastic behavior of it. The code should not be time consuming, but it should be flexible for all environmental conditions. In order to meet the needs, we apply the ray theory for predicting hydroelastic behavior of a mat-like VLFS. The hydroelastic behavior of the VLFS is treated as wave propagation in the platform. The theory itself is based on the classical ray theory, which yields a quick computational scheme. The parabolic approximation is applied to smoothing the discontinuous deformation obtained by the classical ray theory. An experimental technique in a small wave tank with a mini scale model has been developed. Through comparisons with the mini scale experiment and other data found in literatures, it is confirmed that the ray theory has enough accuracy for the conceptual design, unless the assumptions of the ray theory are completely violated.     

Hydroelastic analysis of floating structures with liquid tanks and comparison with experimental tests

In this study, we develop a numerical method for a 3D linear hydroelastic analysis of floating structures with liquid tanks subjected to surface regular water waves and compare the numerical results with experimental tests. Considering direct couplings among structural motion, sloshing, and water waves, a mathematical formulation and a numerical method extended from a recent work [1] are developed. The finite element method is employed for the floating structure and internal fluid in tanks, and the boundary element method is used for the external fluid. The resulting formulation completely incorporates all the interaction terms including hydrostatic stiffness and the irregular frequency effect is removed by introducing the extended boundary integral equations. Through various numerical tests, we verify the proposed numerical method. We also performed 3D hydroelastic experimental tests of a floating production unit (FPU) model in an ocean basin. The measured dynamic motions are compared with the numerical results obtained using the proposed method.     

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.     

Statistical analysis of wave-induced extreme nonlinear load effects using time-domain simulations

A new hybrid method for the time-domain nonlinear simulation of the hydroelastic load effects and the peak-over-threshold (POT) method for the calculation of the short-term extreme responses are briefly described and applied to a flexible containership of the latest design. Statistical analysis has been carried out to study the sensitivity of the predicted extreme vertical bending moments and vertical shear forces to the changes in the threshold of the POT method, as well as the statistical uncertainty in the prediction due to the limited duration of the nonlinear simulation. It is recommended that 90%–95% quantile should be used as the threshold in the POT method and more than 100 h of time-domain simulation should be carried out in order to obtain satisfactory predictions of the short-term extreme nonlinear load effects.     

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.     

Measures to diminish the parameter drift in the modeling of ship manoeuvring using system identification

System identification provides an effective way to predict the ship manoeuvrability. In this paper several measures are proposed to diminish the parameter drift in the parametric identification of ship manoeuvring models. The drift of linear hydrodynamic coefficients can be accounted for from the point of view of dynamic cancellation, while the drift of nonlinear hydrodynamic coefficients is explained from the point of view of regression analysis. To diminish the parameter drift, reconstruction of the samples and modification of the mathematical model of ship manoeuvring motion are carried out. Difference method and the method of additional excitation are proposed to reconstruct the samples. Using correlation analysis, the structure of a manoeuvring model is simplified. Combined with the measures proposed, support vector machines based identification is employed to determine the hydrodynamic coefficients in a modified Abkowitz model. Experimental data from the free-running model tests of a KVLCC2 ship are analyzed and the hydrodynamic coefficients are identified. Based on the regressive model, simulation of manoeuvres is conducted. Comparison between the simulation results and the experimental results demonstrates the validity of the proposed measures.     

Nonlinear hydroelastic analysis of a moored floating body

By integration of the second-order fluid pressure over the instantaneous wetted surface, the generalized first- and second-order fluid forces used in nonlinear hydroelastic analysis are obtained. The expressions for coefficients of the generalized first- and second-order hydrodynamic forces in irregular waves are also given. The coefficients of the restoring forces of a mooring system acting on a flexible floating body are presented. The linear and nonlinear three-dimensional hydroelastic equations of motion of a moored floating body in frequency domain are established. These equations include the second-order forces, induced by the rigid body rotations of large amplitudes in high waves, the variation of the instantaneous wetted surface and the coupling of the first order wave potentials. The first-order and second-order principal coordinates of the hydrelastic vibration of a moored floating body are calculated. The frequency characteristics of the principal coordinates are discussed. The numerical results indicate that the rigid resonance and the coupling resonance of a moored floating body can occur in low frequency domain while the flexible resonance can occur in high frequency domain. The hydroelastic responses of a moored box-type barge are also given in this paper. The effects of the second-order forces on the modes are investigated in detail.