The application of three-dimensional hydroelastic analysis of ship structures in Pekeris hydro-acoustic waveguide environment

The hydroelastic analysis and sonoelastic analysis methods are incorporated with the Green＇s function of the Pekeris ocean hydro-acoustic waveguide model to produce a three-dimensional sonoelastic analysis method for ships in the ocean hydro-acoustic environment. The seabed condition is represented by a penetrable boundary of prescribed density and sound speed. This method is employed in this paper to predict the vibration and acoustic radiation of a 1 500 t Small Water Area Twin Hull （SWATH） ship in shallow sea acoustic environment. The wet resonant frequencies and radiation sound source levels are predicted and compared with the measured results of the ship in trial.

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 better 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 I GN theory can be regarded as an approximation to the linear wave theory of finite water depth. The consequences of the differences between these two theories in the predicted hydroelastic responses are studied quantitatively. And it is found that the linear level I GN theory is not superior to the linear wave theory. Finally, various factors affecting the hydroelastic response of VLFS are studied with the implemented algorithm.

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.

Hydroelastic Analysis of Very Large Floating Structures Using Plate Green Functions

Great attention has been paid to the development of very large floating structures. Owing to their extreme large size and great flexibility, the coupling between the structural deformation and fluid motion is significant. This is a typical problem of hydroelasticity. Efficient and accurate estimation of the hydroelastic response of very large floating structures in waves is very important for design. In this paper, the plate Green function and fluid Green function are combined to analyze the hydroelastic response of very large floating structures. The plate Green function here is a new one proposed by the authors and it satisfies all boundary conditions for free-free rectangular plates on elastic foundations. The results are compared with some experimental data. It is shown that the method proposed in this paper is efficient and accurate. Finally, various factors affecting the hydroelastic response of very large floating structures are also studied.

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 hydroelastic 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.

Hydroelastic Analysis of a Very Large Floating Structure Edged with a Pair of Submerged Horizontal Plates

This paper is concerned with the hydroelastic problem of a very large pontoon-type floating structure(VLFS) edged with a pair of submerged horizontal plates, which is a combination of perforated and non-perforated plates attached to the for-end and back-end of the VLFS. For the hydroelastic analysis, the fluid is assumed to be ideal and its motion is irrotational so that a velocity potential exists. The VLFS is modeled as an elastic plate according to the classical thin plate theory. The fluid-structure interaction problem is separated into conventional hydrodynamics and structure dynamics by using modal expansion method in the frequency-domain. It involves, firstly, the deflection of the VLFS, which is expressed by a superposition of modal functions and corresponding modal amplitudes. Then the boundary element method is used to solve the integral equations of diffraction and radiation on the body surface for the velocity potential, whereas the vibration equation is solved by the Galerkin's method for modal amplitudes, and then the deflection is obtained by the sum of multiplying modal functions with modal amplitudes. This study examines the effects of the width and location of the non-perforated horizontal plates on the hydroelastic response of the VLFS, then the performance of perforated plates is investigated to reduce the motion near the fore-end of the VLFS. Considering the advantages and disadvantages of submerged plates without and with cylindrical holes, we propose a simple anti-motion device, which is a combination of a pair of perforated and non-perforated plates attached to the for-end and back-end of the VLFS. The effectiveness of this device in reducing the deformation and bending moment of the VLFS has been confirmed, and is compared with the results in cases without and with the submerged horizontal plates by the analysis in this paper.

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.

Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid

The wave-induced hydroelastic responses of a thin elastic plate floating on a three-layer fluid, under the assumption of linear potential flow, are investigated for two-dimensional cases. The effect of the lateral stretching or compressive stress is taken into account for plates of either semi-infinite or finite length. An explicit expression for the dispersion relation of the flexural-gravity wave in a three-layer fluid is analytically deduced. The equations for the velocity potential and the wave elevations are solved with the method of matched eigenfunction expansions. To simplify the calculation on the unknown expansion coefficients, a new inner product with orthogonality is proposed for the three-layer fluid, in which the vertical eigenfunctions in the open-water region are involved. The accuracy of the numerical results is checked with an energy conservation equation, representing the energy flux relation among three incident wave modes and the elastic plate. The effects of the lateral stresses on the hydroelastic responses are discussed in detail.

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

Very large floating structures (VLFS) have an extremely large size of several kilometers in length, thus, the environment at one end of the platform may be different from that at the other end. The importance of such an inhomogeneous environment to the hydroelastic response of a VLFS is of obvious concern for practical application. Some studies have been carried out to investigate the effects of shoreline proximity, breakwaters and harbor walls. In this paper, the impact of the variable depth on the hydroelastic responses of a VLFS is investigated. For simplicity, an ascending plane slope is taken to simulate the varying bottom although the method is capable of treating a bottom of arbitrary variation. The long wave theory and the thin plate theory are employed to model the wave field and the mat-like VLFS respectively. The finite difference method is used to numerically solve the boundary value problem. The results for the zero inclination slope are compared with experimental data and an analytical method to validate the present numerical method. Finally the effect of the inclination of the slope on reflection and transmission coefficients and plate deflections are investigated thoroughly.

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 cartier （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.

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 Behaviour and Analysis of Marine Structures

Hydroelasticity of marine structures with and without forward speed is studied directly using time dependent Boundary Integral Equation Method with Neumann-Kelvin linearisation where the potential is considered as the impulsive velocity potential.The exciting and radiation hydrodynamic parameters are predicted in time with transient wave Green function whilst the structural analysis is solved with Euler-Bernoulli beam method at which modeshapes are defined analytically.The modal analysis is used to approximate the hydroelastic behaviour of the floating systems through fully coupling of the structural and hydrodynamic analyses.As it is expected,it is found with numerical experience that the effects of the rigid body modes are greater than elastic modes in the case of stiff structures.The predicted numerical results of the present in-house computational tool ITU-WAVE are compared with experimental results for validation purposes and show the acceptable agreements.

A Hydroelastic Analysis of the Afterbody Vibration of Ships

The paper employs three dimensional hydroelastic theory to describe the afterbody structure and surrounding water unifiedly to establish a hydroelastic analysis approach.It lays emphasis on the development of the method for calculating the afterbody vibration and the development of a software system for the hydroelastic analysis of the afterbody vibration with pre and post processing systems.A special beam element device connecting FE model and beam model to simulate the ship structures is proposed and the general principles are given to determine the relevant parameters of the special beam elements.The afterbody vibration of a ship and its dynamic responses under the excitation of the propeller induced forces are calculated by the software system developed by the author.The numerical results obtained are compared with the measured results.They are in good agreement.Thereby,the reliability and practicability of the method and software system developed in the paper are validated.

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 term wave induced bending moments are also predicted.

A universal bifurcation mechanism arising from progressive hydroelastic waves

A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic nonlinearities, is an extension of the famous Whitham equation. The coefficients of the nonlinear terms are chosen to match with the key properties of the full Euler equations, precisely, the associated cubic nonlinear Schrödinger equation and the amplitude of the solitary wave at the bifurcation point. It is shown that the supercritical bifurcation, rich with Stokes, solitary, generalized solitary, and dark solitary waves in the vicinity of the phase speed minimum, is a universal bifurcation mechanism. The newly developed model can capture the essential features near the bifurcation point and easily be generalized to other nonlinear wave problems in hydrodynamics.

Head-on collision between two hydroelastic solitary waves with Plotnikov-Toland's plate model

Head-on collision between two hydroelastic solitary waves propagating at the surface of an incompressible and ideal fluid covered by a thin ice sheet is analytically studied by means of a singular perturbation method. The ice sheet is represented by the Plotnikov-Toland model with the help of the special Cosserat theory of hyperelastic shells and the Kirchhoff-Love plate theory,which yields the nonlinear and conservative expression for the bending forces. The shallow water assumption is taken for the fluid motion with the Boussinesq approximation. The resulting governing equations are solved asymptotically with the aid of the Poincaré-Lighthill-Kuo method,and the solutions up to the third order are explicitly presented. It is observed that solitary waves after collision do not change their shapes and amplitudes. The wave profile is symmetric before collision, and it becomes, after collision, unsymmetric and titled backward in the direction of wave propagation. The wave profile significantly reduces due to greater impacts of elastic plate and surface tension. A graphical comparison is presented with published results, and the graphical comparison between linear and nonlinear elastic plate models is also shown as a special case of our study.

A nonlinear hydroelastic method considering wave memory effect for ship load responses in irregular waves

Since the amplitude and frequency of irregular waves change with time,great difficulties are brought for solving ship load responses in random waves.To take the effect of various frequencies of irregular waves into consideration in load responses of hull,the wave memory effect is necessary.A semi-analytical method is introduced for the time-domain retardation functions,and then a nonlinear hydroelastic method considering memory effect for ships in irregular waves is proposed.Segmented self-propelling model experiments of a container ship were carried out in a towing tank,a ship motion measuring device for self-propelling model test was designed.Whipping responses of the ship in regular and irregular waves are analyzed.Finally,the calculation results are compared with those measured by segmented model experiments,and the result indicates that the memory effect has little effect on load responses of ship in regular waves,but pronounced effect on results in irregular waves.Moreover,the presented method is reasonable for the prediction of ship load responses in irregular waves.

Hydroelasticity Analysis in Frequency Domain and Time Domain

Hydroelasticity has been introduced in ship seakeeping assessment for more than three decades, and it finally becomes an essential tool in marine industry for design of some types of ship. In the 35 years of evolution, hydroelasticity methods applied in industry of marine and offshore energy grown up from two dimensional to three dimensional and now has analysis models of linear model in frequency domain and nonlinear model in time domain. In this paper, we present the three dimensional hydroelasticity theory model in frequency domain and time domain, show the difference in the approach, and discuss their applications in wave-structure interaction.

Numerical Simulation on Hydroelastic Response of Structure under Impact Load from Water Using Eulerian Scheme with Lagrangian Particles

Hydroelasticity caused by water impact is of concem in many applications of ocean engineering/naval architect and is a complicated physical phenomenon. The authors have developed a coupled Eulerian scheme with Lagrangian particles to combine advantages and to compensate disadvantages in both grid based method and particle based method. In this study, the developed numerical model was applied to hydroelastic problems due to impact pressure such as water entry of an elastic cylinder and elastic tanker motion in wave. The authors showed the numerical results which is overall agreement with experimental results. The proposed numerical scheme can be useful and effectiveness to evaluate hydroelasticity and ship-wave interaction in nonlinear wave motion with breaking.

A Hybrid Particle-Grid Scheme for Computing Hydroelastic Behaviors Caused by Slamming

Capable and accurate predictions of some effects of strongly nonlinear interaction wave-ship associated with hydroelastic behaviors are very required for simulation tool in naval architect and ocean engineering. It can guarantee ship safety at the sea state by producing proper design. Therefore, we have developed a hybrid scheme based on both grid and particle method. In order to clarify hydroelastic behaviors of a ship, a dropping test of a ship with elastic motion has been performed firstly. The developed scheme has been then validated on ship dropping case under the same conditions with experiment. The comparisons showed consistently in good agreement. Furthermore, evaluation on hydroelastic behaviors of ship motion under slamming, the impact pressure tends to increase in increasing Froude number. （Fn） The bending moment and torque defined at the centre gravity due to hogging and sagging events can be predicted well, and their effects on the ship increase in increasing wave length even though the impact pressure decreases in increasing wave length after wave length λ/L, where L is ship length, is equal to 1.0. Moreover, hydroelastie behaviors affect the large heave and pitch amplitudes. Finally, the developed scheme can predict simultaneously hydrodynamic and hydroelastic with a strongly nonlinear interaction between wave and ship.