• Journal of the Society of Naval Architects of Korea
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• v.40 no.6
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• pp.88-95
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• 2003

Liquid storage rectangular tank structures are used in many fields of airplane and marine engineering. Fatigue damages are sometimes observed in these tanks which seem to be caused by resonance. Therefore it is essentially important to estimate vibration characteristics of tank structures. Many Investigators studied the vibration of cylindrical and rectangular tank structures containing still fluid. In general, the eigenbehavior of interior liquid is characterized by the sloshing mode while that of the structure by the bulging mode. However, the structure deformation to the sloshing mode and the liquid free-surface fluctuation to the bulging mode have been neglected in the classical added-mass computation. in the present paper, we study the vibration characteristics with sloshing mode effect.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.314-317
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• 2002

The sloshing phenomenon sometimes happens to be occurred in the liquid storage tank due to the unexpected and/or inevitable vibrating conditions and may result in severe effects on the structural stability. This study deals with the development of experimental techniques for the evaluation of sloshing behavior in the liquid storage tank and for the identification of natural frequencies and mode shapes by varying with various vibrating conditions. In addition, suitable method is suggested to minimize the sloshing effect on the liquid storage tank and its validity is experimentally investigate d.

• Journal of the Society of Naval Architects of Korea
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• v.50 no.2
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• pp.69-78
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• 2013

This study is constructed to investigate the sloshing effect on the motions of a two-dimensional rectangular cylinder experimentally and numerically. The modes of motion under consideration are sway and roll, and also experimental cases are divided by two categories; 1-DoF roll motion and 2-DoF motion (Coupling sway and roll). It is found that the sway response is considerably affected by the motion of the fluid, particularly near the sloshing natural frequency, while the roll response changes comparatively small. The dominant mode of motion is analyzed for 2-DoF experiments as well. The measured data for 1-DoF motions is compared with numerical results obtained by the Multi-modal approach. The numerical schemes vary in detail with the number of dominant sloshing modes; i.e. there is a single dominant mode for the Single-dominant method, while the Model 2 method assumes that the first two modes are superior. For the roll motion, numerical results obtained by the two different methods are relatively in good agreement with the experiments, and these two results are similar in most wave frequency range. However, the discrepancies are apparent where the fluid motion is not governed by a single mode. But both of numerical methods over-predict the motion at the vicinity of the sloshing natural frequency. In order to correct the discrepancy, the modal damping needs to be investigated more precisely. Furthermore, another multi-modal approach, such as the Boussinesq-type method, seems to be required in the region of the intermediate liquid.

• Journal of Ocean Engineering and Technology
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• v.27 no.3
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• pp.53-60
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• 2013

A drillship is a representative floating offshore installation. The boom in oil and gas field development has dramatically increased the demands for drillships. Drillships have a moonpool in the center area of the ship for the purpose of drilling. This moonpool has an effect on the seakeeping performance of a drillship in the vicinity of the resonance frequency. Because of the moonpool, drillships act in different resonance modes, called the sloshing mode and piston mode. The objective of this study was to find the moonpool effect on the motion of a drillship through the motion analysis of a currently operating modern compact drillship. The predicted resonance frequencies based on Molin's theoretical formula, Fukuda's empirical formula, and BEM-based numerical analysis are compared. The accuracy of the predictions using the theoretical and empirical formulas is compared with the numerical analysis and evaluated. In the case of the piston mode, the difference between the resonance frequency from theoretical formula and the resonance frequency from the numerical analysis is analyzed. The resonance frequency formula for more a complex moonpool geometry such as a moonpool with a cofferdam is necessarily emphasized.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.619-628
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• 2002

This paper deals with the FE analysis for the free vibration of sloshing in horizontal cylindrical tank with baffles. We use Laplace equation based on potential theory as governing equation. This problem is solved by FEM using lineal isoparametric elements. We assume that the tank as well as baffles is rigid body and by separating nodes into two at the baffle location, baffle effect is obtained by separating nodes into two at the baffle location. For the calculation of natural frequencies and mode shapes, we introduce Lanczos transformation and Jacobi iteration methods. Numerical results of the first longitudinal and transverse modes, while comparing with literature cited, are very good. In order for the baffle effects on the free vibration of sloshing, various combinations of baffle parameters, which are location, inner diameter and number, are examined.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.10
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• pp.751-759
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• 2003

The theoretical method is developed to investigate the vibration characteristics of the sloshing and bulging mode for the circular cylindrical storage tank with an annular plate on free surface. The cylindrical tank is filled with an inviscid and incompressible liquid. The liquid domain is limited by a rigid cylindrical surface and a rigid flat bottom. As the effect of free surface waves Is taken into account in the analysis, the bulging and sloshing modes are studied. The solution for the velocity potential of liquid movement is assumed as a suitable harmonic function that satisfies Laplace equation and the relevant boundary conditions. The Rayleigh-Ritz method is used to derive the frequency equation of the cylindrical tank. The effect of Inner-to-outer radius ratio and thickness of annular plate and liquid volume on vibration characteristics of storage tank is studied. The finite element analysis is performed to demonstrate the validity of present theoretical method.

• International Journal of Naval Architecture and Ocean Engineering
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• v.5 no.2
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• pp.313-323
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• 2013

Offshore floating structures have so-called moonpool in the centre area for the purpose of drilling, installation of subsea structures, recovery of Remotely-Operated Vehicle (ROV) and divers. However, this vertical opening has an effect on the operating performance of floating offshore structure in the vicinity of moonpool resonance frequency; piston mode and sloshing mode. Experimental study based on model test was carried out. Moonpool resonance of floating offshore structure on fixed condition and motion free condition were investigated. And, the effect of cofferdam which is representative inner structure inside moonpool was examined. Model test results showed that Molin's theoretical formula can predict moonpool resonance on fixed condition quite accurately. However, motion free condition has higher resonance frequency when it is compared with that of motion fixed. The installation of cofferdam moves resonance frequency to higher region and also generates secondary resonance at lower frequency. Furthermore, it was found that cofferdam was the cause of generating waves in the longitudinal direction when the vessel was in beam sea.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.3
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• pp.580-594
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• 2015

Liquid sloshing in two-dimensional (2-D) and three-dimensional (3-D) rectangular tanks is simulated by using a level set method based on the finite volume method. In order to examine the effect of natural frequency modes on liquid sloshing, we considered a wide range of frequency ratios ($0.5{\leq}fr{\leq}3.2$). The frequency ratio is defined by the ratio of the excitation frequency to the natural frequency of the fluid, and covers natural frequency modes from 1 to 5. When fr = 1, which corresponds to the first mode of the natural frequency, strong liquid sloshing reveals roof impact, and significant forces are generated by the liquid in the tank. The liquid flows are mainly unidirectional. Thus, the strong bulk motion of the fluid contributes to a higher elevation of the free surface. However, at fr = 2, the sloshing is considerably suppressed, resulting in a calm wave with relatively lower elevation of the free surface, since the waves undergo destructive interference. At fr = 2, the lower peak of the free surface elevation occurs. At higher modes of $fr_3$, $fr_4$, and $fr_5$, the free surface reveals irregular deformation with nonlinear waves in every case. However, the deformation of the free surface becomes weaker at higher natural frequency modes. Finally, 3-D simulations confirm our 2-D results.

• International Journal of Ocean System Engineering
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• v.3 no.4
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• pp.175-187
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• 2013

Moonpools are vertical wells in a floating body used onboard many types of vessels like Exploration and drilling vessels, Production barges, Cable-laying vessels, Rock dumping vessels, Research and offshore support vessels. Moonpool gives passage to underwater activities for different types of ships as per their mission requirements. It is observed that inside a moonpool considerable relative motions may occur, depending on shape, depth of the moonpool and on the frequency range of the waves to which the ship is exposed. The vessel responses are entirely different in zero and non-zero Froude number. Former situation is paid attention in this study as the mission requirement of the platform is to be in the particular location for long period of operation. It is well known that there are two modes of responses depending on the shape of the moonpool viz., piston mode for square shape and sloshing mode for rectangular shapes with different aspect ratios of opening like 1:1.5 and 1:2 ratios. Circular shaped moonpool is also tested for measuring the responses. The vessel moored using heavy lines are modelled and tested in the wave basin. The pretensions of the lines are varied by altering the touchdown points and the dynamic tensions on the lines are measured. The different modes of oscillations of water column are measured using wave gauge and the vessel response at a particular situation is determined. RAOs calculated for various situations provide better insight to the designer.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.4
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• pp.21-29
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• 1987

In this paper the liquid sloshing effects in vertical storage tanks under earthquake loadings are studied. The study focuses on the investigation of the effect of the flexibility of the tank wall on the hydrodynamic forces exerted on it. The tank structure is modelled using finite elements. The motion of the liquid is expressed by the Laplace equation. The equation of motion of the fluid shell system is formulated including the coupling effect between the shell motion and the sloshing motion. A procedure is developed to obtain the natural frequencies and the mode shapes of the sloshing motion as well as the shell vibration. Dynamic analyses have been carried out for several tanks with different dynamic characteristics utilizing the time history method as well as the response spectra method.