Hydroelastic Response Research Articles

Water Entry of Cylindrical Shells: Theory and Experiments

Modeling hydroelastic response of lightweight structures to water impact plays a pivotal role in the design of lightweight marine vessels and crew capsules. In contrast to the majority of studies that focus on water entry of wedge-shaped bodies, this study addresses the hydroelastic impact of cylindrical shells. A cylindrical shape allows for a systematic study of the interplay between bending and stretching during water entry. This study puts forward a mathematically tractable framework to study the rigid body motion and elastic deformation of cylindrical shells, free falling onto a quiescent water surface. Donnel thin shell theory is used to model the shell, and Wagner theory is adopted to determine the hydrodynamic loading as a function of the rigid body motion and structural deformation. Galerkin method is employed to cast the problem into a manageable system of coupled ordinary differential equations, which are then solved numerically. Model predictions are validated against experiments on shells with two thicknesses, detailing both the flow physics and elastic response through the cogent integration of direct acceleration measurement, high-speed imaging, and particle image velocimetry. The proposed framework and experimental dataset are expected to constitute the foundations on which to formulate new theories for lightweight composites and testing computational schemes.

An integro-differential equation approach to study the scattering of water waves by a floating flexible porous plate

ABSTRACTIn the present manuscript, the hydroelastic response of a flexible porous plate, floating in water of finite as well as infinite depths, is studied under the assumption of a linearized wave–structure interaction theory. Using Green's integral theorem, the associated boundary value problems are converted into integro-differential equations in terms of the plate deflection. To solve the derived integro-differential equations, the plate deflection is approximated as a superposition of the horizontal eigenfunctions in the plate-covered region. As a result, approximate explicit expressions are obtained for the physical quantities of interests such as reflection and transmission coefficients. The accuracy of the present numerical computations are analysed by comparing the results with the standard results available in the literature. It may be noted that the aforementioned physical problem is similar in nature with that of Koley et al. but the solution technique is completely different. As various results associated with the floating flexible porous plate are presented in Koley, Mondal and Sahoo (Eur. J. Mech. B- Fluid., 2018, vol. 67, 291–305) and therefore in this paper, the major emphasis is on the solution technique and only a few results are provided for comparison purpose.

Resonances of enclosed shallow water basins with slender floating elastic bodies

A model for the hydroelastic response of enclosed shallow water basins with floating slender plates of large span, in variable bathymetry is presented. The eigenproblem for the system’s resonant behaviour is formulated in the strong and variational form. Based on the variational form, and special hydroelastic finite elements, a quadratic eigenvalue problem is derived for the eigenfrequencies and eigenmodes of the basin-floating body system. Benchmark examples, for simplified configurations, are used to study the effects of parameters like the plate’s span, position, draft, mass, stiffness and depth of the basin. It is observed that the presence of the plate can alter significantly the eigenstates of the pond if the depth of the basin is relatively small, compared to the plate draft. In such cases the plate span and position play a crucial role. The hydroelastic analysis can be important even in cases where the depth increases and the upper surface elevation differences, in the presence or absence of the floating plate, appear to be less significant. This is due to the importance in accurately calculating the curvature and hence bending moments inside the plate. The proposed model could be relevant to the seiche formation analysis in reservoirs with floating photovoltaic platforms or ice-covered lakes.

Numerical and experimental analysis of hydroelastic responses of a high-speed trimaran in oblique irregular waves

Investigation of hydroelastic responses of high-speed vessels in irregular sea state is of major interest in naval applications. A three dimensional nonlinear time-domain hydroelastic method in oblique irregular waves is developed, in which the nonlinear hydrostatic restoring force caused by instantaneous wetted surface and slamming force are considered. In order to solve the two technical problems caused by irregular sea state, the time-domain retardation function and Proportional, Integral and Derivative (PID) autopilot model are applied respectively. Besides, segmented model tests of a high-speed trimaran in oblique waves are performed. An oblique wave testing system for trimarans is designed and assembled. The measured results of main hull and cross-decks are analyzed, and the differences in distribution of load responses between trimarans and monohull ships are discussed. Finally, from the comparisons, it is confirmed that the present concept for dealing with nonlinear hydroelastic responses of ships in oblique irregular waves is reliable and accurate.

Energy extraction from an articulated plate anti-motion device of a very large floating structure under irregular waves

Abstract The deformation of a very large floating structure (VLFS) under wave action is termed hydroelastic response and can be mitigated by using various types of anti-motion devices to enhance the structures' workability. This paper focuses on the energy extraction from an articulated plate anti-motion device that is connected to a VLFS by hinges. The aim of the paper is to study the feasibility of the articulated-plate to function both as an anti-motion device and a wave energy converter such that the hydroelastic response of the VLFS can be reduced and at the same time a substantial amount of wave energy can be generated to power the VLFS. The results show interesting findings on the energy generation by the articulated plate where it was found that the energy generation of the articulated plate and its efficiency as an anti-motion device depend significantly on the length of the articulated plate. The results obtained from the irregular wave show that under a certain combination of significant wave height and wave peak period, ( H s − T p ) , it is possible to enhance the workability of the VLFS and ensuring that the VLFS is self-sustained out of renewable sources of energy.

Boundary Element Modelling Aspects for the Hydro-Elastic Analysis of Flexible Marine Propellers

Boundary element methods (BEM) have been used for propeller hydrodynamic calculations since the 1990s. More recently, these methods are being used in combination with finite element methods (FEM) in order to calculate flexible propeller fluid–structure interaction (FSI) response. The main advantage of using BEM for flexible propeller FSI calculations is the relatively low computational demand in comparison with higher fidelity methods. However, the BEM modelling of flexible propellers is not straightforward and requires several important modelling decisions. The consequences of such modelling choices depend significantly on propeller structural behaviour and flow condition. The two dimensionless quantities that characterise structural behaviour and flow condition are the structural frequency ratio (the ratio between the lowest excitation frequency and the fundamental wet blade natural frequency) and the reduced frequency. For both, general expressions have been derived for (flexible) marine propellers. This work shows that these expressions can be effectively used to estimate the dry and wet fundamental blade frequencies and the structural frequency ratio. This last parameter and the reduced frequency of vibrating blade flows is independent of the geometrical blade scale as shown in this work. Regarding the BEM-FEM coupled analyses, it is shown that a quasi-static FEM modelling does not suffice, particularly due to the fluid-added mass and hydrodynamic damping contributions that are not negligible. It is demonstrated that approximating the hydro-elastic blade response by using closed form expressions for the fluid added mass and hydrodynamic damping terms provides reasonable results, since the structural response of flexible propellers is stiffness dominated, meaning that the importance of modelling errors in fluid added mass and hydrodynamic damping is small. Finally, it is shown that the significance of recalculating the hydrodynamic influence coefficients is relatively small. This fact might be utilized, possibly in combination with the use of the closed form expressions for fluid added mass and hydrodynamic damping contributions, to significantly reduce the computation time of flexible propeller FSI calculations.

An extension of a discrete-module-beam-bending-based hydroelasticity method for a flexible structure with complex geometric features

The discrete-module-beam-bending based hydroelasticity method proposed by Lu et al. (2016) deals with the hydroelastic response of a flexible structure by discretising it into several rigid submodules which are connected by Euler-Bernoulli beam elements. A stiffness matrix is determined in terms of the geometrical and physical properties of the flexible structure for each beam element and it has an analytical form for simple geometric features such as a rectangular cross section unchanged along the longitudinal direction. However, the analytical stiffness matrix may not exist for a flexible structure with complex geometric features. In the present study, with the aid of finite element method, the discrete-module-beam-bending-based hydroelasticity method proposed by Lu et al. (2016) is extended to be applicable for a flexible structure with complex geometric features.

The Low-Noise Optimization of a SWATH Ship’s Structures Based on the Three-Dimensional Sono-Elasticity of Ships

Basic equations and numerical methods are presented for the three-dimensional sono-elasticity theory of ships in shallow sea Pekeris acoustic waveguide environment. The corresponding software three-dimensional hydroelastic analysis of floating and traveling structures-Acoustic developed based on this theory is used for low-noise optimization design of the strut structures of a 1500-ton small waterplane area twin hull (SWATH) ship. When the SWATH ship was moored in waves and laying down instruments for ocean survey, it was observed that the waves continuously beat the vertical side walls of the struts, resulting in structural vibration and acoustic radiation in the frequency band below 100 Hz. This is a new phenomenon that the hydroelastic response of a local structure disturbs ocean survey performance. This phenomenon is not good for the performance of underwater acoustic equipment because it increases the background noise in the vicinity of the SWATH ship. This problem needs a low-cost and feasible solution. The mechanism of this phenomenon is first discussed by means of a sono-elastic analysis. After a series of low-noise design calculations for the strut structures, a design of optimal acoustic performance is obtained with only a small increase in the structure weight. Some suggestions on engineering design for solving such problems are also put forward. 1. Introduction The theory of fluid-structure interaction has been widely applied in various engineering practices, including improvement of ship's seakeeping performance and structural safety, ship vibration and noise control, and enhancement of underwater acoustic stealthiness. In the late 1970s of the twentieth century, hydroelasticity of ships was established as one new branch of ship's fluid-structure coupling dynamics (Bishop & Price 1979). In the early 1980s, by combining the three-dimensional potential flow theory of ship motions with the three-dimensional structural dynamics, three-dimensional hydroelasticity was established by Wu (1984) and Bishop et al. (1986) to deal with the dynamic response of arbitrarily shaped three-dimensional deformable body under internal and external loads. Hereafter, the theory was developed continuously into two main subbranches: one is the three-dimensional hydroelasticity with respect to wave-induced dynamic responses of structures in the incompressible fluid field (Wu 1984; Bishop et al. 1986; Wu et al. 1997; Tian & Wu 2006; Kim et al. 2009; Wu & Cui 2009) and the other deals with the acoustic effect in the compressible fluid field (Zhou et al. 2010; Zou et al. 2013; Zou 2014), the latter of which is also called the three-dimensional sono-elasticity of ships.

Statistics of extreme hydroelastic response for large ships

For the safety of crew, ship and cargo, it is essential to assess all aspects of the wave loading to ensure that ships are designed to endure extreme events. This paper describes a practical method for prediction of extreme stresses using as an example measured strain in the deck amidships of a container vessel operating in the North Atlantic. The focus is placed on the whipping structural response, which refers to transient vibratory response of the hull girder due to wave impacts occurring mainly in the bow area.Due to non-stationarity and complicated nonlinearities of the wave induced loads, as well as the human factor in operation of ships, reliable numerical prediction of extreme response, including whipping, is challenging even though significant advances have been made in developing hydro-elastic computational tools in recent decades. Moreover, laboratory tests and numerical simulation tools may not fully reproduce the critical conditions that take place in reality, and these conditions may not even be well understood. Therefore, measurements on real ships provide an opportunity for unique insights into the structural responses when the vessel is at sea.In addition, a discussion of the ACER (Average Conditional Exceedance Rate) method is provided. It is shown that this method is suitable for practical prediction of extreme values of structural stresses. Unlike methods based on asymptotic extreme value theory, the ACER method explores pre-asymptotic statistics. The latter is of great practical importance for engineering and design. This method opens up for the possibility to predict simply and efficiently both short-term and long-term extreme response statistics, which may also be useful for the captain on board.The last, but not least is data clustering issue. Whipping process possesses clustering due to its resonance nature; therefore conventional and widely used Poisson assumption is no more valid. ACER method effectively accounts for data clustering, leading to more accurate extreme response estimate, than Poisson assumption methods.

Experimental and numerical investigation of the hydroelasticity of a floating structure with legs

In the processes of lowering down or raising up the legs of a floating structure, the legs are neither touch with the sea bed nor completely lift up, and the structure is situated in the condition of freely floating on the waves. The existing of the legs equipped on the structure leads to the property different hydroelastic responses from the ordinary floating structures. To investigate the variation of the length of the legs underwater affecting the hydroelastic responses, a plate-cell model is proposed, and the basin tests using the elastic model in waves are carried out. Based on the length of the legs under water, the model is set as 2 cases. The attenuation tests in calm water and test in the regular wave at zero speed in various of the wave conditions are carried out. According to the plate-cell model, a numerical model is constructed to simulate the hydroelastic responses of the 2 cases based on the theory of the three-dimensional (3-D) linear hydroelasticity. Both the experimental and numerical results demonstrate that the legs have significant influences on the hydroelastic responses of the structure.

Analysis on the full scale measurement data of 9400TEU container Carrier with hydroelastic response

Since the advent of hydroelasticity issues in the marine community, a full scale measurement campaign has been considered the most important research to reach a thorough understanding of this complicated physical phenomenon. This study examined the full-scale measurement data of a large container carrier with a 9400TEU capacity. First, modal parameters, such as the mode shapes, natural frequencies, and damping ratios, were examined based upon the measured acceleration data on deck. The evolution of the natural frequencies and damping ratios were also checked and their correlation was explored. In addition, the modal magnitude obtained using the acceleration data was cross-compared with the strain at deck to investigate their temporal relevance. Finally, the fatigue damage was calculated using the measured strain at deck and the expected long-term fatigue damage was estimated based upon the fatigue damage experienced by the vessel during the measurement period.

Experimental Validation of Fluid–Structure Interaction Computations of Flexible Composite Propellers in Open Water Conditions Using BEM-FEM and RANS-FEM Methods

In the past several decades, many papers have been published on fluid–structure coupled calculations to analyse the hydro-elastic response of flexible (composite) propellers. The flow is usually modelled either by the Navier–Stokes equations or as a potential flow, by assuming an irrotational flow. Phenomena as separation of the flow, flow transition, boundary layer build-up and vorticity dynamics are not captured in a non-viscous potential flow. Nevertheless, potential flow based methods have been shown to be powerful methods to resolve the hydrodynamics of propellers. With the upcoming interest in flexible (composite) propellers, a valid question is what the consequences of the potential flow simplifications are with regard to the coupled fluid–structure analyses of these types of propellers. This question has been addressed in the following way: calculations and experiments were conducted for uniform flows only, with a propeller geometry that challenges the potential flow model due to its sensitivity to leading edge vortex separation. Calculations were performed on the undeformed propeller geometry with a Reynolds-averaged-Navier–Stokes (RANS) solver and a boundary element method (BEM). These calculations show some typical differences between the RANS and BEM results. The flexible propeller responses were predicted by coupled calculations between BEM and finite element method (FEM) and RANS and FEM. The applied methodologies are briefly described. Results obtained from both calculation methods have been compared to experimental results obtained from blade deformation measurements in a cavitation tunnel. The results show that, even for the extreme cases, promising results have been obtained with the BEM-FEM coupling. The BEM-FEM calculated responses are consistent with the RANS-FEM results.

Hydroelastic analysis of articulated floating elastic plate based on Timoshenko–Mindlin plate theory

ABSTRACTThe wave interaction with articulated floating elastic plate is investigated considering the Timoshenko–Mindlin thick plate theory for both finite and shallow water depths. The elastic plates are modelled as finite flexible floating structure interconnected with vertical linear/rotational spring stiffness. The eigenfunction expansion method along with the orthogonal mode-coupling relation is used to analyse the hydrodynamic behaviour of the interconnected structure. The study is performed for different articulated edge conditions for varying plate thickness and water depths to understand the behaviour of articulation under the action of an ocean wave. The hydroelastic response of the interconnected floating elastic plate with different connector stiffness is observed to compare well with the result available in the literature. The present study provides an insight into the effect of articulated joints with varying spring stiffness for the suitable design of the structure.

A numerical method for predicting the hydroelastic response of marine propellers

This paper focuses on the development of a numerical model for predicting the hydroelastic responses of marine propellers oscillating in the wake of a submarine. The added-mass and -damping matrices due to strongly coupled fluid-structure interaction were considered. Three-dimensional panel methods in time and frequency domains combined with the finite element method were employed to study the hydrodynamic performance of the propeller. The panel methods were used to evaluate the hydrodynamic forces generated by the wake, and the finite element method was applied to determine the hydroelastic response of the propeller due to the pressure fluctuation. For predicting the structural responses, a mode superposition method combined with Wilson-θ method was employed to overcome the low numerical efficiency caused by the asymmetric added mass and damping matrices. The proposed numerical model was validated by comparing with other numerical solutions. The performance of the propellers was examined by considering one-way and two-way fluid-structure interactions.

A numerical simulation method for predicting global and local hydroelastic response of a ship based on CFD and FEA coupling

In this paper, a simulation method for predicting global and local hydroelastic response of a ship which couples CFD and FEA is developed and validated. By comparing the prediction with linear/nonlinear strip method, 3D panel method and towing tank test results under various wave conditions in terms of rigid body motions and slamming impact pressure, the effectiveness of the CFD-FEA coupling method is confirmed. The hydroelastic behavior, so-called the whipping moment, evaluated from the CFD-FEA coupling method is further validated by comparing with nonlinear strip method, 3D panel method and tank test results. Finally, the proposed method is applied to a realistic large container ship structure in severe waves. The structural response of the double bottom structure subjected to global and local bending moments is investigated.

30) A Study on the Hydroelastic Response of Very Large Floating Structure with Floating Breakwater in Waves

30) A Study on the Hydroelastic Response of Very Large Floating Structure with Floating Breakwater in Waves

대형 컨테이너 선박의 유탄성 실선 계측 데이터 분석 PartⅠ- 모달 파라미터 추정

To understand the dynamic characteristics of the vessel with hydroelastic response, it is very important to estimate the dynamic modal parameters such as mode shapes, natural frequency, and damping ratio. These dynamic modal parameters of full scale ship are a priori unknowns, hence to be estimated directly based upon the full scale measurement data. In this paper, dynamic modal parameters were extracted by signal processing of acceleration and strain data measured from a large container ship whose loading capacity is 9400TEU. The mode shapes of the vibrating hull were identified using the proper orthogonal decomposition and the vibration response of hull was decomposed into its modal magnitudes. Natural frequencies of specific modes were derived via Fourier transform of these modal magnitude. Also, the free decay signal of the vibrating hull was obtained through the random decrement technique and the damping ratio was estimated with accuracy.

Reducing hydroelastic responses of pontoon-type VLFS using vertical elastic mooring lines

This paper is concerned with the reduction of hydroelastic responses of pontoon-type very large floating structures (VLFS) via the use of vertical elastic mooring lines connected at the fore and aft edges of VLFS to the seabed. These vertical mooring lines are used in addition to the mooring dolphin-rubber fender system that is used to restrict the horizontal movement of VLFS. The considered rectangular shaped VLFS is modeled as a Mindlin plate floating on an ideal fluid in which the linear potential theory is applicable. The hydroelastic analysis of VLFS with vertical mooring lines modeled as vertical elastic springs is performed in the frequency domain by using the hybrid finite element–boundary element (FE-BE) method. This study examines the effectiveness of vertical elastic mooring lines in reducing hydroelastic responses for various wavelengths, incident wave angles and aspect ratios. The stiffnesses of the mooring lines are optimized for maximum reduction in the hydroelastic response by using the Differential Evolution algorithm. It was found that hydroelastic responses of VLFS could be significantly reduced by using vertical elastic mooring lines with optimal stiffnesses.

Oblique Wave-Induced Responses of A VLFS Edged with A Pair of Inclined Perforated Plates

This paper is concerned with the hydroelastic responses of a mat-like, rectangular very large floating structure (VLFS) edged with a pair of horizontal/inclined perforated anti-motion plates in the context of the direct coupling method. The updated Lagrangian formulae are applied to establish the equilibrium equations of the VLFS and the total potential formula is employed for fluids in the numerical model including the viscous effect of the perforated plates through the Darcy’s law. The hybrid finite element-boundary element (FE-BE) method is implemented to determine the response reduction of VLFS with attached perforated plates under various oblique incident waves. Also, the numerical solutions are validated against a series of experimental tests. The effectiveness of the attached perforated plates in reducing the deflections of the VLFS can be significantly improved by selecting the proper design parameters such as the porous parameter, submergence depth, plate width and inclination angle for the given sea conditions.

Hydroelastic analysis of global and local ship response using 1D–3D hybrid structural model

ABSTRACTFor relatively ‘soft’ floating bodies (very large ships, floating airports, etc.) using the classical rigid body seakeeping analysis and modelling the hydro-structure interface by the transfer of the pressure is not sufficient. The most appropriate method for rational design is the hydroelastic coupling by solving the interaction between the surface waves and the rigid-elastic body. In this paper, a hybrid structural model based on one-dimensional (1D) beam elements and three-dimensional (3D) finite element elements is developed and used for the analysis of wave induced ship vibrations. Using a hybrid model, both global and local structural response can be determined. The coupling between structural and hydrodynamic model is performed using the modal superposition method. The complete hydroelastic response (motions, accelerations, stresses, …) of a floating unit is performed by using 1D–3D hybrid structural model with 3D hydrodynamic model and compared with full 3D structural model coupled with 3D hydrodynamic model.