• Ocean Systems Engineering
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• v.2 no.3
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• pp.229-238
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• 2012

We discuss the bi - stability that is possibly exhibited by a liquid free surface in a parametrically - driven two-dimensional (2D) rectangular tank with finite liquid depth. Following the method of adaptive mode ordering, assuming two dominant modes and retaining polynomial nonlinearities up to third-order, a nonlinear finite-dimensional nonlinear modal system approximation is obtained. A "continuation method" of nonlinear dynamics is then used in order to elicit efficiently the instability boundary in parameters' space and to predict how steady surface elevation changes as the frequency and/or the amplitude of excitation are varied. Results are compared against those of the linear version of the system (that is a Mathieu-type model) and furthermore, against an intermediate model also derived with formal mode ordering, that is based on a second - order ordinary differential equation having nonlinearities due to products of elevation with elevation velocity or acceleration. The investigation verifies that, in parameters space, there must be a region, inside the quiescent region, where liquid surface instability is exhibited. There, behaviour depends on initial conditions and a wave form would be realised only if the free surface was substantially disturbed initially.

• Earthquakes and Structures
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• v.15 no.5
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• pp.513-528
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• 2018

A typical viable technique to decrease the seismic response of liquid storage tanks is to isolate them at the base. Base-isolation systems are an efficient and feasible solution to reduce the vulnerability of structures in high seismic risk zones. Nevertheless, when liquid storage tanks are under long-period shaking, the base-isolation systems could have different impacts. These kinds of earthquakes can damage the tanks readily. Hence, the seismic behaviour and vibration of cylindrical liquid storage tanks, subjected to earthquakes, is of paramount importance, and it is investigated in this paper. The Finite Element Method is used to evaluate seismic response in addition to the reduction of excessive liquid sloshing in the tank when subjected to the long-period ground motion. The non-linear stress-strain behaviour pertaining to polymers and rubbers is implemented while non-linear contact elements are employed to describe the 3-D surface-to-surface contact. Therefore, Nonlinear Procedures are used to investigate the fluid-structure interactions (FSI) between liquid and the tank wall while there is incompressible liquid. Part I, examines the effect of the flexibility of the isolation system and the tank aspect ratio (height to radius) on the tank wall radial displacements of the tank wall and the liquid sloshing heights. Maximum stress and base shear force for various aspect ratios and different base-isolators, which are subjected to three seismic conditions, will be discussed in Part II. It is shown that the composite-base isolator is much more effective than other isolators due to its high flexibility and strength combined. Moreover, the base isolators may decrease the maximum level pertaining to radial displacement.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.7
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• pp.661-668
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• 2009

The slosh natural frequencies, damping ratio, slosh mass and slosh force applying point of the liquid in cylindrical tank are estimated using the nonlinear least squares method in time domain. The estimated slosh model parameters are in good agreement with the results of the theoretical calculations for various liquid depths. Furthermore, this methodology will be applied to predict the sloshing parameters for a liquid propellant tank using ground experimental test-bed.

• Journal of Ocean Engineering and Technology
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• v.36 no.1
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• pp.21-31
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• 2022

In recent years, various studies have been conducted on oscillating-water-column-type wave energy converters (OWC-WECs) with multiple chambers with the objective of efficiently utilizing the limited space of offshore/onshore structures. In this study, a numerical investigation based on a numerical wave tank was conducted on single, dual, and triple OWC chambers to examine the hydrodynamic performances and the energy conversion characteristics of the multiple water columns. The boundary value problem with the Laplace equation was solved by using a numerical wave tank based on a finite element method. The validity of the current numerical method was confirmed by comparing it with the measured data in the previous experimental research. We undertook a series of numerical simulations and observed that the water column motion of sloshing mode in a single chamber can be changed into the piston motion of different phases in multiple OWC chambers. Therefore, the piston motion in the multiple chambers can generate considerable airflow at a specific resonant frequency. In addition, the division of the OWC chamber results in a reduction of the time-dependent variability of the final output power from the device. As a result, the application of the multiple chambers leads to an increase of the energy conversion performance as well as a decrease of the variability of the wave energy converter.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.833-847
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• 2021

The horizontal porous baffle and its effect as an anti-slosh device have been investigated intensively in a swaying and rolling rectangular tank. To accurately assess the level at which porous baffles reduce liquid sloshing, the Matched Eigenfunction Expansion Method (MEEM) has been utilized as an analytical tool. The velocity potentials in the horizontal baffle-covered fluid region are expressed by the sum of the homogeneous and particular solutions to avoid solving the complex dispersion equation. By applying an equivalent linearized quadratic loss model, the nonlinear algebraic equation is derived and solved by implementing the Newton-Raphson iterative scheme. To prove the validity of the present theoretical model, a series of experiments have been conducted with different centered horizontal porous baffles with varying porosities and submerged depths in a swaying and rolling rectangular tank. Reasonably good agreements are obtained regarding the analytical solutions and the experiment's findings. The influence of porosity, submerged depth, and length of a centered horizontal porous baffle on anti-slosh performance have been analyzed, especially at resonance modes. The developed predictive tool can potentially provide guidelines for optimal design of the horizontal porous baffle.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.12-18
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• 1991

Three-dimensional nonlinear sloshing effects due to tank motions are simulated by solving boundary value problem using the panel method based on boundary integral technique. While Shinkai used boundary elements on which source strengths vary linearly between nodes, the source of constant strength is distributed on each triangular panel in the present study. The source strength at each time step is determined by solving the Fredholm integral equation of the second kind obtained from Green's theorem. To avoid cumulative numerical errors as time elapses, Adam-Bashforth-Moulton method is employed. Numerical examples for the case of partially filled spherical tank on board oscillating in harmonic sway mode or pitch mode are solved. The elevation of the free surface is compared with the result by Shinkai and confirmed in good agreement during early time. The input and the output energy are comparatively evaluated to check the overall accuracy of the present numerical scheme. Although some leakage of energy are found as time marches, it is plausible when we take into account nonlinearities of the problem and the number of panels of the model.

• Structural Engineering and Mechanics
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• v.83 no.5
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• pp.627-644
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• 2022

In past major earthquakes (1994 Northridge, 1995 Kobe, Chi-Chi 1999, Kocaeli 1999), significant damages occurred in the liquid storage tanks. The basic failure patterns were observed to be the buckling of the tank wall and uplift of the anchorage system. The damages in the industrial facilities and nuclear power plants have caused the spread of toxic substances to the environment and significant fires. Seismic isolation can be used in liquid storage tanks to decouple the structure and decrease the structural demand in the superstructure in case of ground shaking. Previous studies on the use of seismic isolation systems on liquid storage tanks show that an isolation system reduces the impulsive response but might slightly increase the convective one. There is still a lack of understanding of the seismic response of seismically isolated liquid storage tanks considering the fluid-structure interaction. In this study, one broad tank, one medium tank, and one slender tank are selected and designed. Two- and three-dimensional elastomeric bearings are used as seismic isolation systems. The seismic performance of the tanks is then investigated through nonlinear dynamic time-history analyses. The effectiveness of each seismic isolation system on tanks' performance was investigated. Isolator tension forces, modal analysis results, hydrodynamic stresses, strains, sloshing heights and base shear forces of the tanks are compared. The results show that the total base shear is lower in 3D-isolators compared to 2D-isolators. Even though the tank wall stresses, and strains are slightly higher in 3D-isolators, they are more efficient to prevent the tension problem.