Dynamicl characteristic analysis of 15×10~4m~3 vertical liquid storage-tanks
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Large-scale unanchored vertical liquid storage tanks are being applied extensively,its dynamic parameters,such as the natural frequency and mode shape,are very often used in seismic engineering.The natural mode of 15×104m3 storage tank was analyzed by ADINA finite element technique using spring element to simulate foundation,and considering the liquid-structure interaction effect.The results show that: there is small difference between the finite element technique and the well-known code formula on mode analysis of tanks;the vibration forms of the low-frequency segment of 15×104m3 storage tank are various,among which cosnθ、sinnθ beam vibrations are the leading one,the vibration forms of the liquid are simple,namely cosnθ、sinnθ beam vibration;the frequencies of liquid-structure coupled vibration are sensitive to foundation stiffness,are followed by the liquid height and the ratio of tank height to radius,and are insensitive to the thickness of tank wall;sloshing frequencies of liquid are insensitive to foundation stiffness as well as the thickness of tank wall,and are sensitive to liquid height as well as the ratio of tank height to radius.Keywords:
Slosh dynamics
Adina
Foundation (evidence)
Natural frequency
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The shipbuilding industry has been in the process of becoming larger and faster. Vessels are made of complex structures and carry a wide variety of cargoes for long periods of time and generally have a long life of more than 30 years. Ships have tanks of various shapes such as fuel, ballast and fresh water tanks, and most of them are in contact with the liquid. The state of the liquid also causes a change in the water level due to the operation of the ship. It has been reported that a resonance, which causes fatigue damage and destruction due to excitation forces of an engine, a propeller, and a wave.BR Therefore, it is considered important to clearly understand the vibration characteristics of these various tanks in contact with the liquid.BR Many vessels currently are equipped with many square shaped tanks and have various conditions of the boundary as well as various ratios of length, width and height of the tanks. Therefore, in this paper, the vibration characteristics of the elastic plate composing the tank through the changes of the boundary condition, the width and the thickness are investigated in a tank structure which is relatively higher than the length and width.
Ballast
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This paper presents a seismic response analysis of a cylindrical liquid storage tank on an elastic foundation subjected to a horizontal earthquake, which is based on the energy method considering the coupled effect between sloshing and bulging. The kinetic energy and the strain one of an empty tank shell are estimated by the finite element method for an axisymmetric shell. On the other hand, the kinetic energy and the potential one of the liquid in the tank are estimated analytically by superposing three types of velocity potentials as follows : (1) Velocity potential for the free surface oscillation ignoring the vibration of the tank side shell. (2) Velocity potential for the coupled vibration between the tank side shell and the liquid ignoring the free surface oscillation and the vibration of the tank bottom plate. (3) Velocity potential for the coupled vibration between the bottom plate and the liquid ignoring the free surface oscillation and the vibration of the tank side shell. Through numerical calculations, effects of the stiffness of the tank foundation and the thickness of the tank bottom plate on vibration characteristics and seismic response ones are investigated.
Slosh dynamics
Foundation (evidence)
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Free surface
Velocity potential
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Slosh dynamics
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Fluid–structure interaction
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The dynamic characteristic parameters of 160,000-m3 LNG storage tanks were studied by considering the liquid-solid coupling effect and using the Lanczos algorithm in ADINA Finite Element Analysis Software.The result shows that: the inner tank's basic vibration frequency of liquid-solid coupling is lower,cosnθ beam vibration is the leading form of vibration and liquid-sloshing is low-frequency vibration;the outer tank's basic vibration frequency is higher and cosnθ beam vibration is also the leading form of vibration.The first three-order frequencies of the inner tank's liquid-solid coupling are 1.979,4.766 and 6.491 Hz respectively;those of liquid sloshing are 0.104,0.185 and 0.235 Hz respectively;those of the outer tank are 6.509,12.37 and 22.16 Hz respectively.
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In order to study the factors of seismic isolation design for 15×104 m3 vertical storage tank,the finite element numerical simulation is used to analyze the effects of isolation stiffness,floating roof quality,reservoir fluid density,tank wall thickness,tank wall material elastic modulus,and liquid storage tank height to radius ratio of the tanks on sloshing frequency and liquid-solid coupling ffrequency.Comparison with the time-history analysis results show that: the liquid-solid coupling vibration frequency is sensitive to isolation stiffness.When the isolation stiffness is lower,the liquid-solid coupling stiffness declines and the base shear force becomes small.Isolation stiffness of the tanks hardly affects the frequency of liquid sloshing.In a certain range of the isolation period,the wave height has no amplification effect.In isolation design,the effects of the floating roof can be neglected.The ratio of the storage tank liquid height to the radius of the tank greatly affects the frequency of the liquid-solid coupling and the shaking frequency.The isolation has the design optimization segmentally.The effects of reservoir fluid density,tank wall thickness,material elastic modulus can be neglected.For shaking table test,other materials may be considered to replace the steel and the analysis results do not be affected.
Slosh dynamics
Earthquake shaking table
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