Rocking behavior of unanchored flat-bottom cylindrical shell tanks under action of horizontal base excitation

2004 ◽  
Vol 26 (4) ◽  
pp. 415-426 ◽  
Author(s):  
Tomoyo Taniguchi
Keyword(s):  
Cylindrical Shell ◽  
Base Excitation ◽  
Flat Bottom ◽  
Rocking Behavior

Rocking Response of Unanchored Flat-Bottom Cylindrical Shell Tanks Subjected to Horizontal Base Excitation: Part I — Rigid Bottom Plate

2003 ◽  
Author(s):  
Tomoyo Taniguchi
Keyword(s):  
Cylindrical Shell ◽  
Liquid System ◽  
Bottom Plate ◽  
Base Excitation ◽  
Inertial Coordinate System ◽  
Flat Bottom ◽  
Coriolis Forces ◽  
Time Histories ◽  
Rocking Motion ◽  
Reaction Forces

The rocking dynamics of the tank is discussed by introducing the rock-translation interaction. The centrifugal, inertia and Coriolis forces accompanied with non-inertial coordinate system are incorporated into the conventional and translational tank-liquid system. Moreover, the reaction forces from the tank-liquid system are taken rocking system into account. As the beginning of series researches, using a rigid cylinder and a tank with rigid bottom plate, the necessity of the rock-translation interaction for evaluating rocking responses of the tank is highlighted. In addition, the sufficient friction to enter and sustain a rocking motion of the tank is discussed based on time histories of horizontal and vertical reaction forces on the pivoting edge.

Fundamental Mechanics of Walking of Unanchored Flat-Bottom Cylindrical Shell Model Tanks Subjected to Horizontal Harmonic Base Excitation

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Toru Segawa
Keyword(s):  
Cylindrical Shell ◽  
Shell Model ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Bottom Plate ◽  
Primary Role ◽  
Base Excitation ◽  
Flat Bottom ◽  
Rotational Angle ◽  
Slide Displacement

Assuming very large slide displacement subsequent to tank rock motion to be a possible scenario of tank walk motion, fundamental mechanics of the walk motion of unanchored flat-bottom cylindrical shell model tanks subjected to horizontal base excitation is examined. First, employing a 3DOF model consisting of a set of two masses connected by flexible columns, equations of motion are derived through a variational approach. The interaction among the translational motion of a harmonic oscillator consisting of the upper mass and the flexible columns, the rock motion of the 3DOF model and the slide motion of it is thoroughly studied. Comparison of the experimental results and their predictions demonstrate applicability of the proposed analysis. A reduction in nominal friction force accompanying the rock motion that plays a primary role in causing the very large slide displacement is also pointed out. Next, drawing an analogy between the mechanics of the walk motion of the 3DOF model and that of an unanchored flat-bottom cylindrical shell model tank, equations of motion for the tank walk motion are derived. Shaker table test and time domain analysis are conducted, employing a model tank whose bottom plate concentrically uplifts for readily evaluating fluid masses contributing to the tank rock motion. Comparison of the experimental and analytical results of the slide displacement and the rotational angle corroborates the applicability of the proposed analysis.

Rocking Response of Unanchored Flat-Bottom Cylindrical Shell Tanks Subjected to Horizontal Base Excitation: Part II — Flexible Bottom Plate

2003 ◽  
Author(s):  
Tomoyo Taniguchi
Keyword(s):  
Cylindrical Shell ◽  
Effective Mass ◽  
Bottom Plate ◽  
Base Excitation ◽  
Base Shear ◽  
Flat Bottom ◽  
Time Histories ◽  
Rocking Motion ◽  
Reaction Forces ◽  
Overturning Moment

The mechanical analogy of the rock-translation interaction system of the tank is verified by comparing analytical results with experimental ones. To trace actual rocking behaviors of the tank, the existence of effective mass and moment inertia of liquid for a rocking motion, which is proportional to the uplift region of bottom plate, is assumed. The comparison of restoring moment defined by early investigators with overturning moment by proposed methods can identify the region of effective mass for a rocking motion in an iterative manner. Moreover, the base shear and uplift angle calculated agree with ones measured at previous shaking tests. These results corroborate the applicability of proposed methods. Finally, the sufficient friction to enter and sustain a rocking motion of the tank is discussed based on time histories of horizontal and vertical reaction forces on the pivoting edge.

The Sensibility of Rocking Motion of Flat-Bottom Cylindrical Shell Tanks to Sloshing Motion

2004 ◽  
Author(s):  
Tomoyo Taniguchi
Keyword(s):  
Cylindrical Shell ◽  
Ground Motion ◽  
Storage Systems ◽  
Lateral Force ◽  
Flat Bottom ◽  
Natural Period ◽  
Rocking Motion ◽  
Sloshing Mode

This paper examines the sensibility of rock motion of flat-bottom cylindrical shell tanks to the lateral force induced by the sloshing motion. Since the natural period of sloshing motion of the tank may be close to that of rocking motion of the tank, their resonance may result the serious damages of the storage systems. Therefore, it is necessary to examine their fundamental behavior beforehand. Using horizontal sinusoidal ground motion whose period matches the natural period of 1st sloshing mode of the tank, the rocking motion of the tank is numerically examined. The results imply that the sloshing behavior has the potential to make tanks rock.

Rocking Mechanics of Flat-Bottom Cylindrical Shell Model Tanks Subjected to Harmonic Excitation

2005 ◽  
Vol 127 (4) ◽  
pp. 373-386 ◽  
Author(s):  
Tomoyo Taniguchi
Keyword(s):  
Dynamical System ◽  
Cylindrical Shell ◽  
Shell Model ◽  
Effective Mass ◽  
Harmonic Excitation ◽  
Rigid Bodies ◽  
Base Shear ◽  
Flat Bottom ◽  
Rocking Motion

The rocking motion of the tanks is complex and not fully understood. Using model tanks that possess concentric rigid-doughnut-shaped bottom plates, this paper tries to clarify its fundamental mechanics through the analog of rocking motion of rigid bodies. Introducing an effective mass for the internal liquid for rocking motion enables the development of a dynamical system including the rocking-bulging interaction motion and the effective mass of liquid for the interaction motion. Since the base shear and uplift displacement observed during shaking tests match well with computed values, the proposed procedure can explain the mechanics of the rocking motion of the model tanks used herein.

Governing Equations of Motion of Walking Behavior of Unanchored Flat-Bottom Cylindrical Shell Tanks Subjected to Horizontal Sinusoidal Ground Motion

2006 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Koji Imai
Keyword(s):  
Cylindrical Shell ◽  
Ground Motion ◽  
Equations Of Motion ◽  
Time History ◽  
Governing Equations ◽  
Flat Bottom ◽  
Walking Behavior ◽  
Walking Motion ◽  
Rocking Motion ◽  
History Of

The governing equations of motion of walking phenomena of unanchored flat-bottom cylindrical shell tanks subjected to horizontal sinusoidal ground motion are examined. The equations of motion are derived through variational approach. The physical quantities related to the walking phenomena are the mass of tank itself, tank content, the effective mass of liquid for bulging motion, that for rocking motion, that for rocking-bulging interaction motion, and friction force including self-weight reduction effects. The roles of each physical quantity during the walking motion are clearly identified. Comparison of the time history of experimental results and that of analytical ones corroborates accuracy of the proposed equations of motion.

Fluid Pressures on Unanchored Rigid Rectangular Tanks Under Action of Uplifting Acceleration

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Yoshinori Ando
Keyword(s):  
Cylindrical Shell ◽  
Fourier Series ◽  
Velocity Potential ◽  
Fluid Pressure ◽  
Angular Acceleration ◽  
Parabolic Partial Differential Equation ◽  
Bottom Edge ◽  
Flat Bottom ◽  
Mathematical Solution ◽  
Rectangular Tank

Although uplift motion of flat-bottom cylindrical shell tanks has been considered to contribute toward various damages to the tanks, the mechanics were not fully understood. As well as uplift displacement of the tanks, fluid pressure accompanying the uplift motion of the tanks may play an important role in the cause of the damage. An accurate estimate of the fluid pressure induced by the uplift motion of the tanks is indispensable in protecting the tanks against destructive earthquakes. As a first step of a series of research, this study mathematically derives the fluid pressure on a rigid rectangular tank with a unit depth accompanying angular acceleration, which acts on a pivoting bottom edge. The rectangular tank employed herein is equivalent to a thin slice of the central vertical cross section of a rigid flat-bottom cylindrical shell tank. Assuming a perfect fluid and velocity potential, a continuity equation is given by the Laplace equation in Cartesian coordinates. The fluid velocities accompanying the motions of the walls and bottom plate constitute the boundary conditions. Since this problem is set as a parabolic partial differential equation of the Neumann problem, the velocity potential is solved with the Fourier-cosine expansion. The derivative of the velocity potential with respect to time gives the fluid pressure at an arbitrary point inside the tank. A mathematical solution for evaluating the fluid pressure accompanying the angular acceleration acting on the pivoting bottom edge of the tank is given by an explicit function of a dimensional variable of the tank, but with the Fourier series. The proposed mathematical solution well converges with a few first terms of the Fourier series. Values of the fluid pressure computed by the explicit finite element (FE) analysis well agrees with those by the proposed mathematical solution. For the designers’ convenience, diagrams that depict the fluid pressures normalized by the maximum tangential acceleration given by the product of the angular acceleration and diagonals of the tank are also presented. Consequently, the mathematical solution given by the Fourier series converges easily and provides accurate evaluation of the fluid pressures on a rigid rectangular tank accompanying the angular acceleration acting on the pivoting bottom edge. Irregularity in the fluid pressure distribution increases as the tank becomes taller.

Contribution of the Bending Stiffness of the Tank Bottom Plate and Out-of-Round Deformation of Cylindrical Shell to the Tank Rocking Motion

2016 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Teruhiro Nakashima ◽  
Yuuichi Yoshida
Keyword(s):  
Cylindrical Shell ◽  
Significant Influence ◽  
Bending Stiffness ◽  
Bottom Plate ◽  
Flat Bottom ◽  
Fluid Surface ◽  
Rocking Motion ◽  
Tank Bottom

Effects of bending stiffness of the tank bottom plate and out-of-round deformation of cylindrical shell on uplift of the un-anchored flat-bottom cylindrical shell tanks are investigated. Numerical tank models whose bottom plate has different bending stiffness reveal that changes in bending stiffness of the tank bottom plate may have little influence on uplift of the tanks. Contrary, numerical tank models whose cylindrical shell is stiffed differently reveal that out-of-round deformation of the cylindrical shell may have significant influence on uplift of the tanks. In addition, uplift of the tanks may have little influence on development of waves on the fluid surface like sloshing.

A Numerical Study of Uplift Motion of Flat-Bottom Cylindrical Shell Model Tank Subjected to Harmonic Excitation

2010 ◽  
Author(s):  
Teruhiro Nakashima ◽  
Tomoyo Taniguchi
Keyword(s):  
Cylindrical Shell ◽  
Numerical Study ◽  
Harmonic Excitation ◽  
Fe Analysis ◽  
Experimental Result ◽  
Bottom Plate ◽  
Flat Bottom ◽  
Tank Model ◽  
Rocking Motion ◽  
The Impact

In analyzing the rocking motion of unanchored flat-bottom cylindrical shell tanks, the fluid-structure interaction and the impact between the tank bottom plate and tank foundation should be treated adequately. Employing harmonic excitation, this paper examines the applicability of the explicit FE-Analysis technique for analyzing the rocking motion of a flat-bottom cylindrical shell tank model. Since the tank model possesses a thick and elastic bottom plate, the model tank pivots upon from an edge of the bottom plate to another edge of that reciprocally. The rocking motion of the model tank to the harmonic excitation is numerically computed and the uplift displacement of the tank is compared with experimental result. Agreement between the numerical and experimental results implies that the explicit FE-Analysis is capable of analyzing the rocking motion of cylindrical shell tanks subjected to the earthquake excitation.

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