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 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 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.

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.

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 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.

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.

Hydroelasticity analysis of a vessel-shaped fish cage under incident,diffraction and radiation wave fields

Vessel-shaped fish cages are promising large aquaculture structures developed in recent years,with an overall length of nearly 400 m.In this paper,a coupled hydroelasticity model of a vessel-shaped fish cage is used to calculate the motion and structural response in the time domain.First,the floating body of the cage is discretized into a multimodule system to calculate the frequency-domain hydrodynamic loads.Then,the multimodule system is connected by equivalent elastic beams to consider the hydroelastic be-havior in the time domain.The hydrodynamic loads of the multimodule system are transformed from the frequency-domain loads.Moreover,based on the velocity field transfer functions and the motion of the multimodule system,coupling wave fields considering incident,diffraction and radiation waves are built and used to calculate the loads on the net and steel frame.By iterating the motion response of the multi-module system and the hydrodynamic loads on the net and steel frame in the time domain,the balanced hydroelasticity response of the whole cage is finally obtained.The results show that the hydroelasticity effects have a significant influence on the vertical displacement and cross-sectional load effects of the vessel-shaped fish cage.

A three-dimensional hydroelasticity theory for ship structures in acoustic field of shallow sea

Nowadays the development of green ship technology requires the vibration and noise control of oceangoing ships. The three-dimensional hydroelasticity theory of ships was previously extended to include the effect of fluid compressibility. This enables the dynamic responses and the acoustic radiations of a ship excited by onboard machineries or fluid fluctuation loads to be predicted. In this paper the hydroelastic analysis and sonoelastic analysis methods are fixrther incorporated with the Green＇s function in the Pekeris ocean hydro-acoustic waveguide model to work out a three-dimensional sonoelastic analysis method for ships in the ocean hydro-acoustic environment. As examples, the sound radiations of a floating elastic spherical shell excited by a concentrated force and a traveling LNG ship excited by the propeller induced pulsating forces acting on the wetted bottom plate of the stem in the shallow sea environment are predicted. The influences of the free surface and the sea bed on the generalized hydrodynamic coefficients and the acoustic pressure distributions in fluid domain are illustrated and discussed.

THREE-DIMENSIONAL HYDROELASTIC ANALYSIS IN TIME DOMAIN WITH APPLICATION TO AN ELASTIC SHIP MODEL

According to the Price-Wu condition at interface between flexible marine structure and surrounding fluid flow, a solution for the 3-D potential flow in time domain around a flexible structure traveling in waves has been expressed with a boundary integral equation. The Green function, which satisfied the linearized free surface condition for the time-dependent problem was employed. A hydroelastic analysis directly in time domain to predict the loads, motions and structural responses of ships at a steady forward speed in a seaway was formulation. The numerical results given by present method were compared with the experimental measurements, and the prediction provided by the 3-D hydroelasticity theory in frequency domain.

Hydroelastic dynamic characteristics of a slender axis-symmetric body

The slender axis-symmetric submarine body moving in the vertical plane is the object of our investigation.A coupling model is developed where displacements of a solid body as a Euler beam(consisting of rigid motions and elastic deformations) and fluid pressures are employed as basic independent variables,including the interaction between hydrodynamic forces and structure dynamic forces.Firstly the hydrodynamic forces,depending on and conversely influencing body motions,are taken into account as the governing equations.The expressions of fluid pressure are derived based on the potential theory.The characteristics of fluid pressure,including its components,distribution and effect on structure dynamics,are analyzed.Then the coupling model is solved numerically by means of a finite element method(FEM).This avoids the complicacy,combining CFD(fluid) and FEM(structure),of direct numerical simulation,and allows the body with a non-strict ideal shape so as to be more suitable for practical engineering.An illustrative example is given in which the hydroelastic dynamic characteristics,natural frequencies and modes of a submarine body are analyzed and compared with experimental results.Satisfactory agreement is observed and the model presented in this paper is shown to be valid.

Slamming and Green Water Loads on Bow-Flare Ship in Regular Head Waves Investigated by Hydroelasticity Theory and Experiment

With the development of ships towards large scale, high speed and light weight, ship hydroelastic responses and slamming strength issues are becoming increasingly important. In this paper, a time-domain nonlinear hydroelasticity theory is developed to predict ship motion and load responses in harsh regular waves.Hydrostatic restoring force, wave excitation force and radiation force are calculated on the instantaneously wetted body surface to consider the nonlinear effects caused by large amplitude motions of ship in steep waves. A twodimensional(2 D) generalized Wagner model and a one-dimensional(1 D) dam-breaking model are used to estimate the impact loads caused by bow flare slamming and green water on deck, respectively;the impact loads are coupled with the hydroelastic equation in time-domain. Moreover, segmented model tests are carried out in a towing tank to investigate the wave and slamming loads acting on the hull sailing in harsh regular head waves and also validate the numerical results.