• Journal of the Earthquake Engineering Society of Korea
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• v.26 no.5
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• pp.203-209
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• 2022

A simplified method for earthquake response analysis of a rectangular liquid storage tank is proposed with fluid-structure interaction considered. In order to simplify the complex three-dimensional structural behavior of a rectangular liquid storage tank, it is assumed that structural deformation does not occur in the plane parallel to the direction in which the earthquake ground motion is applied but in the plane perpendicular to the direction. The structural deformation is approximated by combining the natural modes of the simple beam and the cantilever beam. The hydrodynamic pressure, the structure's mass and stiffness, and the hydrodynamic pressure's added mass are derived by applying the Rayleigh-Ritz method. The natural frequency, structural deformation, pressure, effective mode mass, and effective mode height of the rectangular liquid storage tank are obtained. The structural displacement, hydrodynamic pressure, base shear, and overturning moment are calculated. The seismic response analysis of an example rectangular liquid storage tank is performed using the proposed simplified approach, and its accuracy is verified by comparing the results with the reference solution by the finite element method. Existing seismic design codes based on the hydrodynamic pressure in rigid liquid storage tanks are observed to produce results with significant errors that cannot be ignored.

• Journal of Ocean Engineering and Technology
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• v.33 no.2
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• pp.106-115
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• 2019

The interaction between a sloshing liquid damper (SLD) tank and a rectangular pontoon was investigated under the assumption of the linear potential theory. The eigenfunction expansion method was used not only for the sloshing problem in the SLD tank but also for analyzing the motion responses of a rectangular pontoon in waves. If the frictional damping due to the viscosity of the SLD tank was ignored, the effect of the SLD appeared to be an added mass in the coupled equation of motion. The installation of the SLD tank had a greater effect on the roll motion response than the sway and heave motion of the pontoon. One resonance peak for rolling motion showed up in the case of a frozen liquid in the SLD tank. However, if liquid motion in the SLD tank was allowed, two peaks appeared around the first natural frequency of the fluid in the SLD tank. In particular, the peak value located in the low-frequency region had a relatively large value, and the peak frequency located in the high-frequency region moved into the high-frequency region as the depth of the liquid in the tank increased.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1087-1090
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• 2003

In this study, experimental procedures were suggested to investigate the sloshing behavior of a liquid storage tank subjected to inevitably external vibrating conditions. For this purpose. liquid storage tank with rectangular cross section was made of an acrylic resin for the visualization of liquid fluctuation. A specially designed vibrator was used to provide a specified vibrating condition to the liquid storage tank. Extrapolation technique was applied to determine sloshing natural frequency by using various sloshing frequencies at each vibrating displacement and liquid contents at a fixed vibrating frequency. Sloshing mode was also determined from continuous images or liquid fluctuation captured from a video camera. In addition, change in the height of the liquid free surface was measured by using a floating target and a laser displacement sensor. It is found that the suggested method can be applicable to identify the sloshing behavior of liquid storage tank with rectangular cross section.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.2
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• pp.380-388
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• 1994

Study on the chaotic stirring has been performed numerically and experimentally for a shallow rectangular tank accompanying a vortex shedding. The model is composed of a rectangular tank with a vertical plate with a length half the width of the tank. The tank is subject to a horizontal sinusoidal oscillation. The chaotic stirring was analysed by Poincare sections, unstable manifolds and Lyapunov exponents. As Reynolds number is increased the stirring effect is decreased due to the growth of a regular regions near the lower surface of the tank. In the other hand decrease of Reynolds number gives a weaker vortex shedding resulting in the poorer stirring effect. It was also found that the Lyapunov exponent is the highest at the dimensionless period of 1.3-1.5, which seems to be the best condition for the efficient stirring. The experimental visualization for the deformation of materials exhibits the striation pattern similar to the unstable manifold obtained numerically.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.3
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• pp.207-215
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• 2015

This paper deals with a theoretical method to calculate natural frequencies of a fixed-free rectangular tank partially in contact with an outer water gap. Orthogonal polynomials satisfying the boundary conditions of the tank are used as admissible functions in the Rayleigh-Ritz method. A quarter model of the liquid-coupled system is constructed and it is simplified to a line supported flat plate in contact with the liquid. The liquid displacement potential functions satisfying the Laplace equation and water boundary conditions are derived, and the finite Fourier transform is accomplished in conjunction with the compatibility requirement along the contacting interfaces between the tank and water. An eigenvalue problem is derived so that the natural frequencies of the wet rectangular tank can be extracted. The predictions from the proposed analytical method show good agreement with the finite element analysis results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11b
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• pp.65-68
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• 2005

In this paper, a theoretical study is carried out on the hydroelastic vibration of a rectangular tank wall. It is assumed that the tank wall is clamped along the plate edges. The fluid velocity potential is used for the simulation of fluid domain and to obtain the added mass due to wall vibration. In addition, the vibration characteristics of stiffened wall of the rectangular tank are investigated. Assumed mode method is utilized to the stiffened plate model and hydrodynamic force is obtained by the proposed approach. The coupled natural frequencies are obtained from the relationship between kinetic energies of a wall including fluid and the potential energy of the wall. The theoretical result is compared with the three-dimensional finite element method and then added mass effect is discussed due to tank length and potential mode.

• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.1
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• pp.23-34
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• 1998

A dynamic fluid-structure-soil interaction analysis method is developed to investigate the effects of translational and/or rocking motions on the seismic response of flexible rectangular liquid storage tanks founded on the deformable ground. The governing equation for the dynamics of 3-D rectangular tanks subjected to the translational and/or rocking motion is abtained by applying Rayleigh-Ritz method. The dynamic stiffness matrices of a rigid rectangular foundation resting on the surface of a stratum overlaid bedrock are calculated by hyperelement method. The seismic responses of 3-D flexible tank model founded on the deformable ground is calculated by combining the governing equation for the fluid-tank system with the dynamic stiffness matrix of th rigid surface foundation.

• Journal of Power System Engineering
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• v.9 no.4
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• pp.65-70
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• 2005

A liquid storage rectangular tank structures are used in many fields of civil, mechanical and marine engineering. Especially, Ship structures have many tanks in contact with inner or outer fluid, like ballast, fuel and cargo tanks. Fatigue damages are sometimes observed in these tanks which seem to be caused by resonance with exciting force of engine and propeller. Vibration characteristics of these thin walled tanks in contact with fluid near engine propeller are strongly affected by added mass of containing fluid. Therefore it is essentially important to estimate the added mass effect to predict vibration of the tank structures. Many authors have studied vibration of cylindrical and rectangular tanks structures containing fluid. Few research on dynamic interaction among tank walls through fluid are reported in the vibration of rectangular tanks recently. In case of rectangular tanks, structural coupling between adjacent panels and effect of vibration modes of multiple panels on added mass have to be considered. In the present paper, coupling effect between panels of tank structure on added mass of containing fluid, the effect of structural constraint between panels on each vibration mode for fluid region have investigated numerically and experimentally.

• Proceedings of KOSOMES biannual meeting
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• 2009.06a
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• pp.85-86
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• 2009

The sloshing phenomenon can be defined as the nonlinear movement of the free-surface of liquids inside tanks. It generates dynamic loads on the tank structure and thus becomes a problem of relative importance in the design of marine structures. The present study describes a experiment of the sloshing of flows with free-surface which contained in a rectangular tank moving in pitching motion.

• Coupled systems mechanics
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• v.1 no.1
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• pp.79-98
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• 2012

In the present paper, the three-dimensional model of a typical rectangular concrete tank is excited using an artificial and a natural three components earthquake ground motion and the staggered displacement method is utilized for solving the coupled problem of the tank-contained liquid system in time domain. In the proposed method, surface sloshing of the liquid is taken into account in addition to the impulsive term and the appropriate damping values are applied on both of them. The resulted responses are compared with those obtained from the ABAQUS finite element software. It is found that the convective term affects responses extensively and must be considered in seismic design/safety assessment of storage tanks. In addition, the utilized method for solving the coupled problem is stable during the conducted general dynamic analyses and is able to capture the expected phenomena.