Hydroelasticity Theory Research Articles

Hybrid isogeometric-based analysis and experimental investigation on the dynamic response characteristics of a clamped circular plate partially in contact with fluid

The aim of this study was to analyze the effect of fluid presence on the dynamic response characteristics of the thin circular plate and the distortions associated with the wet mode shapes. To this end, series of numerical calculations and experimental measurements were performed to investigate the free vibration characteristics of clamped circular plate under in-vacuo conditions and when it is partially in contact with fluid. In the experimental studies, the clamped boundary conditions are imposed on the circular end plate of the horizontal rigid cylindrical tank by closely-spaced bolts, and measurements were performed based on roving hammer impact technique. The proposed numerical approach was divided into two parts based on linear hydroelasticity theory. In the first stage, the thin circular plate is considered to be under in-vacuo conditions, and the mathematical model for this problem is developed based on the isogeometric finite element method (IGAFEM). The fluid environment is introduced in the second stage of the study in which the generalized in-vacuo modal displacements constitute the boundary conditions of the potential flow problem. The influence of fluid medium is incorporated in the system of equations in the form of fluid added mass, and the corresponding fluid forces are calculated by the isogeometric boundary element method (IGABEM). It is observed that the fluid presence has significant effects on the dynamic response characteristics of the test structure, and the specifically, the distortions of wet mode shapes were noticeable due to presence of free surface of the water. Overall, it is found that the natural frequencies and corresponding mode shapes obtained by conducted experiments and adapted numerical framework are in favorable agreement.

A frequency-domain hydroelastic analysis of a membrane-based offshore floating photovoltaic platform in regular waves

This study presents an approach for analyzing the hydroelastic response of membrane-based floating photovoltaic (PV) platforms. The structural deformation of the platform’s main components, including a floater and a membrane, is further described through a comprehensive set of in-plane and out-of-plane modes. This analysis employs potential flow theory and 3D hydroelasticity theory to evaluate the hydrodynamic loads. Additionally, the Morison equation is utilized to express the drag term associated with the floater’s in-plane motion. Addressing the connection between the floater and the membrane is achieved through the Lagrange multiplier method. Ultimately, this study establishes a frequency-domain coupled dynamic equation for the platform. The response results provide modal amplitudes and displacement data for test points, revealing that under low-frequency conditions, the flexible floater and the membrane conform to wave profiles. As the frequency increases, the impact of the floater’s stiffness becomes prominent, resulting in a substantial three-dimensional interaction effect. In addition, this study examines various structural parameters, specifically the membrane pretension, elastic modulus, and the bending stiffness of the floater, to illustrate their influence on the motion and deformation of the platform. This work contributes to a deeper comprehension of membrane-based floating PV systems and their practical applications.

Hydroelastic theory for offshore floating plates of variable flexural rigidity

We present a theoretical model of the hydrodynamic behaviour of a floating flexible plate of variable flexural rigidity connected to the seabed by a spring/damper system. Decomposition of the response modes into rigid and bending elastic components allows us to investigate the hydroelastic behaviour of the plate subject to monochromatic incident free-surface waves of constant amplitude. We show that spatially dependent plate stiffness affects the eigenfrequencies and modal shapes, with direct consequences on plate dynamics and wave power extraction efficiency. We also examine how plate length and Power Take-Off (PTO) distribution affect the response of the system and its consequent absorbed energy. This work highlights the need to improve existing models of flexible floating energy platforms, especially given their importance in the Offshore Renewable Energy (ORE) sector.

Reduced order modelling of thickness effects on a cantilevered hydrofoil in homogeneous isotropic turbulence

The response of a cantilevered hydrofoil excited by honeycomb-generated turbulence is studied with a reduced order analytical model that considers the thickness effects of NACA sections. This is achieved by extending a gust response model of the unsteady lift to include realistic 2D sections instead of using a flat plate assumption. The general chordwise thickness profiles are included in the model using the generalized Joukowski transformation. The problem is cast into a constrained optimization problem which is solved with the use of the Lagrange multiplier method. The frequency response function (FRF) of NACA sections with the same maximum thickness to chord ratio but with different leading-edge thickness profiles are calculated to investigate the effect of the hydrofoil leading edge thickness on the high frequency response. This FRF is combined with the Uncorrelated Wall Plane Wave (UWPW) technique to simulate the pressure jump amplitude on the hydrofoil due to the turbulence interaction which excites the hydrofoil in heaving and pitching motion according to Theodorsen’s hydroelastic theory. Finaly, the structural velocity spectra are compared with available experimental results of the turbulence ingestion and the effect of the different leading edge thickness profiles on the vibration response is demonstrated for various NACA sections.

Moving load in an ice channel with a crack

The effect of a crack in the ice cover of a channel on strains and deflections of the ice sheet, which are caused by a load moving along the channel, is investigated. The crack is at the center of the channel. The problem is symmetric with a load moving along the crack at constant speed. The problem is formulated within the linear hydroelastic theory. The fluid in the channel is inviscid and incompressible and its motion is potential. The ice sheets are modeled as viscoelastic thin plates clamped to the walls of the channel. The coupled hydroelastic problem is solved by using the Fourier transform along the channel and the normal mode method across the channel. The effects of the load speeds, depth of the channel, ice thickness and characteristics of the load on the hydroelastic response of the ice sheet are investigated. It is shown that the deflections and strains in the ice sheet strongly depend on the speed of the load with respect to the critical speeds of the hydroelastic waves propagating along the channel. The maximum ice deflection occurs at the critical speed of long waves for relatively large values of the retardation time of ice, and at the critical speed of the lowest hydroelastic wave with minimum phase speed for small retardation time of ice. The strain along the center plane of the channel peaks at the critical speed of long waves for ice sheet without a crack. However, it peaks near the critical speed of the lowest hydroelastic wave with minimum phase speed for ice sheet with a crack. The moving load causes larger strains in the ice cover if the load is elongated along the channel for a given total load and load length. The moving load causes smaller strains in the ice cover if the load is elongated along the channel for a given total load and load width.

Substrate elasticity and surface tension mediate the spontaneous rotation of active chiral droplet on soft substrates

Active chirality is an universal property of macromolecules as well as cellular systems and processes, such as nucleic acid, proteins, bacterial flagella and its motions, actomyosin filaments and network, and the left–right (LR) asymmetric morphogenesis, etc. Despite of attempts to elucidate the relations among cellular chirality, spontaneous cellular rotation and extracellular matrix properties, many features of the chiral active matter that are in contact with elastic substrates are still not clear in terms of fundamental physical principles. For instance, when an active chiral droplet in contact with an elastic substrate, the underline interplay among surface elasticity, chirality, and surface tension is largely unknown. In this work, based on the Gurtin–Murdoch surface elasticity we developed an adhesive surface hydro-elasticity theory of moving line to model and simulate the spontaneous rotation of a chiral active soft matter droplet on soft elastic substrates to study the rich morphological, conformational, and dynamic behaviors of the droplet/substrate interaction. In this study, we have found that both surface tension and substrate elasticity significantly affect the spontaneous rotation of the active chiral droplet on the substrate from several crucial aspects: (1) the geometry and morphology of the rotating droplet; (2) the angular velocity and helical vertices of the rotating droplet; (3) the order parameter distribution inside the rotating droplet, (4) the dynamic contact area of the rotating droplet, and (5) the contact stress distribution in both the droplet as well as the elastic substrate.

Dynamic Response Analysis of a Bulk Carrier by Nonlinear Hydroelastic Method

With increasing demands for huge ship dimensions and the wide use of high-strength steel, the influence of slamming and elastic structure on structural strength cannot be ignored. Therefore, in this paper, a three-dimensional (3D) nonlinear hydroelastic theory is introduced, in which the nonlinear hydrostatic restoring force caused by instantaneous wetted surface as well as slamming force are taken into consideration, and the bending moments with/without slamming effects are calculated, respectively. Numerical simulations of the dynamic response of a flexible hull at different speeds are carried out using the finite element analysis software MSC/PATRAN. By comparison with the results of classical beam theory, the accuracy of the dynamic analysis method is studied. Finally, the dynamic response method is compared with the quasi-static method and classical beam theory. By analyzing and quantifying the influence of forward speed and nonlinear factors on structural responses, the reasonable applicable conditions for different methods are discussed, which can be used as reference in the structure design of bulk carriers.

Simulation based calculation of ship motions in extreme seas with a body-exact strip theory approach

For all design phases of naval vessels, the fidelity of seakeeping calculations in extreme seas is open to discussion due to the inadequacy of the linear theory of ship motions. Currently the computer-generated time series of ship responses and wave height (the real time computer experiments) are utilized to calculate the distribution of the vertical distortion, shear force and bending moment by means of “ship hydroelasticity theory”. Inspired by these studies a simulation based calculation of symmetric ship motions is performed in long crested irregular head seas, in addition with a body-exact strip theory approach. The scope of this study is limited to the ship motions only. Verification is achieved utilizing the spectral analysis procedure which contains the discrete Fourier transform (DFT) and the smoothing algorithms. The results are compared with the experimental data, and the ANSYS AQWA software results. The simulation results provide adequate data for the extreme responses. This state-of-the-art method in addition with a “body-exact strip theory approach” ensures the consistent assessment of the seakeeping performance in extreme sea condition. As a result, it is evaluated that this calculation method can be used in the design stages of naval platforms.

The Response of a Poroelastic Ice Plate to an External Pressure

The response of a poroelastic ice cover to an external load is considered. The ice cover is modeled by a thin poroelastic floating plate within the linear theory of hydroelasticity. The porosity parameter is defined as the coefficient of proportionality of the velocity of liquid penetration into the plate and hydrodynamic pressure. The fluid under the plate is inviscid and incompressible. The flow caused by the ice deflection is potential. The external load is modeled by a localized smooth pressure. The two-dimensional problem of waves caused by a periodic external pressure on a floating porous-elastic plate is considered. The profiles of the generated waves are calculated for a given oscillation frequency of the amplitude of the external pressure. It was found that taking porosity into account leads to damping of oscillations in a distance from the external load

Investigation on effects of springing and whipping on fatigue damages of ultra-large container ships in irregular seas

Springing and whipping play an important role in determining the fatigue damages of ultra-large container ships in waves, and it is widely acknowledged that the separation of the contributions of springing and whipping on fatigue damages is difficult. In this paper, the effects of springing and whipping on a targeted 21,000 TEU container ship are numerically investigated. The springing responses are calculated based on the linear 3D frequency domain hydroelasticity theory, while a 3D nonlinear time domain hydroelasticity formulation which couples the 3D hydrodynamic theory, 1D Timoshenko beam theory, 2D generalized Wagner method and 1D green water theory, is adopted to obtain the slamming-induced whipping response. Spectral analysis method is analyzed and compared with an indirect time domain method. Through investigating the characteristics of the accumulated fatigue damages with respect to the significant wave heights and characteristic wave periods of short-term sea states, the contributions from springing and whipping to the accumulated fatigue damages are generally separated for most short-term sea states. In addition, several short-term sea states are chosen to present detailed information on the extents to which springing and whipping increase the fatigue damages relative to the low-frequency structural responses counterpart.

An isogeometric FE-BE method and experimental investigation for the hydroelastic analysis of a horizontal circular cylindrical shell partially filled with fluid

Abstract In this study, the dynamic characteristics (i.e. natural frequencies and associated mode shapes) of a partially filled horizontal cylindrical shell are investigated experimentally and by an isogeometric finite element-boundary element method. The proposed numerical procedure is divided into two parts. In the first part, the dynamic characteristics of the cylindrical shell under in-vacuo conditions are obtained by the isogeometric finite element method (IGAFEM) based on a linear Kirchhoff-Love shell formulation. In the second part, the fluid-structure interaction effects are calculated in terms of generalized added mass coefficients by using the isogeometric boundary element method (IGABEM), assuming that the structure vibrates in its in-vacuo principle mode shapes. By adopting the linear hydroelasticity theory, it is assumed that the fluid flow is ideal, i.e., an incompressible flow and inviscid fluid. In order to show the versatility of the numerical method, the results are compared with those obtained by the conducted experiments. Relevant numerical challenges in the hydroelastic vibration analysis are highlighted and it is shown that the numerical predictions and experimental results are in good agreement.

Evaluation of hydroelastic responses of a 180k DWT large bulk carrier

The linear hydroelastic theory has been widely used in engineering applications in the past. However, the increasing demand for larger merchant ships makes it necessary to evaluate the influences of second-order nonlinear fluid forces on ship response in seas. In this study, the second-order nonlinear responses induced by sea waves are calculated using generalized second-order wave force theory in the frequency domain. The Fluid-Structure Interaction (FSI) method is presented first in this paper which is used for the assessment of ship response and loads, including both linear and second-order nonlinear methods in the frequency domain. Subsequently, the effects of linear forces on the wave-induced responses and loads for a 180k DWT large bulk carrier with and without forward speed are calculated using pulsating source Green's function and translating-pulsating source Green's function. The second-order nonlinear responses are predicted mainly based on pulsating source Green's function. The numerical results show that the ship responses change significantly at high speed, and there are extra vertical bending moments caused by second-order fluid forces acting on the ship in large-amplitude waves compared to linear results. It indicates that both the speed of the ship and the second-order nonlinear wave forces acting on the ship could amplify the wave-induced responses and vertical bending moments.

Investigation of connector loads of a 3-module VLFS using experimental and numerical methods

The connector loads of a 3-module VLFS (Very Large Floating Structure) deployed in the shallow water areas have been investigated by experimental and numerical methods. For the numerical method, a simplified analysis procedure has been built based on 3D hydroelasticity theory and RMFC (Rigid Module Flexible Connector) model, and the effect of the uneven seabed can be included in this procedure. The model tests of the 3-module VLFS considering the complicated seabed topography and wave environment have been finished. Some key technologies for the model tests have been solved, such as the simulations of the complicated seabed topography and the connector model. A lot of the first-hand model test results have been discussed and compared with the numerical results. Some useful conclusions were obtained, which can provide reference basis for the preliminary and conceptual design of VLFS and its connectors.

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 two-dimensional (2D) generalized Wagner model and a one-dimensional (1D) 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.

Application of the 3D time-domain Green's function for finite water depth in hydroelastic mechanics

Based on the boundary element method and the superposition principle of structural elastic modes, the three-dimensional time-domain Green's function in finite water depth is applied to hydroelasticity, and the theoretical basis of three-dimensional time-domain hydroelasticity is established. To address the difficulty and divergence of the three-dimensional time-domain Green's function in finite water depth, a numerical solution method that has high accuracy and good stability is developed using series expansion, asymptotic methods and fourth-order differential equations. Taking a large bulk carrier as an example, the corresponding predictions of resonance frequency, motion, wave load and hydroelastic response with speed in finite water depth are carried out. The numerical results are compared with the results of the three-dimensional frequency domain method and the time-domain method of inner and outer region matching and are verified by the towing model test. The three-dimensional time-domain hydroelastic theory and numerical method established in this paper are of great significance for fluid coupling analysis, structural dynamic response research and wave load prediction of complex floating bodies with speed.

Ice response to an underwater body moving in a frozen channel

Strains in the ice cover of a frozen channel, which are caused by a body moving under the ice at a constant speed along the channel, are studied. The channel is of rectangular cross section, the fluid in the channel is inviscid and incompressible. The ice cover is modeled by a thin viscoelastic plate clamped to the channel walls. The underwater body is modeled by a three-dimensional dipole. The intensity of the dipole is related to the speed and size of the underwater body. The problem is considered within the linear theory of hydroelasticity. For small deflections of the ice cover the velocity potential of the dipole in the channel is obtained by the method of images without account for ice deflection in the leading order. The problem of a dipole moving in the channel with rigid walls provides the hydrodynamic pressure on the upper boundary of the channel, which corresponds to the ice cover. This pressure distribution does not depend on the deflection of the ice cover in the leading approximation. The deflections of ice and the strains in the ice cover are independent of time in the coordinate system moving together with the dipole. The problem is solved numerically using the Fourier transform along the channel, the method of normal modes across the channel, and the truncation method for resulting infinite systems of linear equations. It was revealed that the strains in the ice strongly depend on the speed of the dipole with respect to the critical speeds of the hydroelastic waves propagating along the frozen channel. The width of the channel matters even it is much larger than the characteristic length of the ice cover.

Movement of external load over free surface of fluid in the ice channel

The solution of a steady three-dimensional problem for the wave disturbances induced by a local pressure distribution moving with uniform speed on open water lead between two semi-infinite floating ice sheets (ice channel) is presented. This external load simulates an air-cushion vehicle (ACV). The problem is formulated within the linear hydroelastic theory. The fluid is assumed to be inviscid and incompressible and its motion is potential. The ice sheets are treated as viscoelastic thin plates. The solution of this problem is constructed using the Fourier transforms and the Wiener-Hopf technique. The displacements of free surface and ice sheets are determined as well as strains in ice and wave resistance acting on ACV at various speeds of its movement: subcritical and supercritical ones relative to the minimum phase velocity of flexural-gravity waves (FGW) in fluid under an ice cover. Special attention is paid to the characteristics of edge waves. It is shown that for some values of load speed, ice thickness and external pressure, ice fracture near the edge is possible.

Time-domain numerical and segmented model experimental study on ship hydroelastic responses and whipping loads in harsh irregular seaways

In this paper, wave-induced motions and loads of a bow flare ship advancing in harsh irregular waves are investigated both numerically and experimentally. A 3D time-domain hydroelasticity theory that includes memory-effect function considering Froude–Krylov nonlinearity is developed to predict ship motions, wave loads and slamming loads in long-crested irregular waves. In the hydroelasticity algorithm, the wave memory effects and forward speed effects are addressed by retardation function method to improve the computing efficiency and provide opportunity for short-term statistical analysis of ship responses in irregular waves. In addition, segmented model tank tests are conducted to experimentally investigate the motions and loads of ship sailing in long-crested irregular waves and also validate the numerical results. To further understand the nonlinear wave loads behavior of ship in short-crested waves, large-scale segmented model sea trials are performed in realistic sea waves. The numerical results and experimental results are systemically analyzed and compared using time series, spectral and probability statistical analysis methods.

Time-domain hydroelastic analysis of nonlinear motions and loads on a large bow-flare ship advancing in high irregular seas

This paper investigates the nonlinear hydroelastic motion and load responses on a large flexible ship advancing in harsh irregular waves. A 3D time-domain nonlinear hydroelasticity theory for the prediction of ship motions, deformations and wave loads in long-crested irregular waves is presented. The nonlinear Froude–Krylov force and hydrostatic restoring force are calculated on the instantaneous wetted hull surface while the linear diffraction force and radiation force are estimated on the static mean wetted surface. The radiation forces are estimated by retardation function method to take account of the wave memory effects and forward speed effects. The slamming loads that were derived by momentum impact theory are also included in the ship motion equation to investigate the whipping responses. The hydrodynamic and structural responses are fully coupled by modal superposition principle to consider the hydroelastic effects including springing and whipping responses. The numerical results are well validated by the experimental data of a segmented model with large flare-bow tested in an ultra-long laboratory tank. The numerical and experimental data of ship responses in different irregular wave conditions are systemically analyzed and compared by time series analysis, spectral analysis, and probability statistics analysis methods.

A direct coupling analysis method of hydroelastic responses of VLFS in complicated ocean geographical environment

In this paper a direct coupling analysis method (DCAM) of hydroelastic responses of a very large floating structures (VLFS) in complicated geographical environment is presented. In this method the three-dimensional hydroelasticity theory of floating bodies is combined with the shallow water wave theory, to allow for proper description of the influence of uneven seabed and sheltering effect of islands on the hydroelastic responses of a VLFS deployed near island and reefs in shallow sea. This method and the numerical procedures were verified and validated by comparison between the predictions and the model test results of a 3-module VLFS and an 8-module VLFS in two simulated shallow sea regions with different seabed topography.