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Fluid-Structure Interaction

Contributions of Fluid to Rocking–Bulging Interaction of Rectangular Tanks Whose Walls Are Rigid and Bottom Plate Rectilinearly Uplifts

[+] Author and Article Information
Tomoyo Taniguchi

Department of Civil Engineering
Tottori University
4-101 Koyama-Minami Tottori
680-8552, Japan
e-mail: t_tomoyo@cv.tottori-u.ac.jp

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received April 28, 2011; final manuscript received June 8, 2012; published online December 4, 2012. Assoc. Editor: Spyros A. Karamanos.

J. Pressure Vessel Technol 135(1), 011304 (Dec 04, 2012) (7 pages) Paper No: PVT-11-1105; doi: 10.1115/1.4007286 History: Received April 28, 2011; Revised June 08, 2012

At the event of severe earthquakes, the tank rocking response appears subsequent to the tank bulging response. A spring-mass-rigid body combined model was proposed for analyzing the tank response and the required quantities for the model have been rigorously defined based on the mathematical solution of fluid pressure on the tank accompanying the tank response of interest. To date, the apparent density of fluid for the rocking and the bulging responses and the effective mass of those are available for this purpose. However, observations revealed that the interaction between the rocking response and the bulging response is stimulated by the effective mass of fluid for the rocking–bulging interaction that is understood as a part of the effective mass of fluid for the tank bulging response that is also under the action of the rotational inertia. Therefore, regarding a ratio of the apparent density of fluid for the tank rocking response to the original density of fluid as the intensity of a contribution of fluid to the tank rocking response, the apparent density of fluid for the rocking–bulging interaction is defined intuitively and conveniently. The effective mass of fluid for the rocking–bulging interaction is subsequently defined. The distribution of the apparent density of fluid for the rocking–bulging interaction inside the tank is drawn for a combination of the various aspects of tank and the ratios of the uplift width of the tank bottom. The ratios of the effective mass of fluid for the rocking–bulging interaction to the total mass of fluid of the tank as well as the ratios of the arm length to the centroid of the effective mass of that to the tank geometry are also depicted by the same manner.

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References

Malhotra, P. K., and Veletsos, A. S., 1994, “Uplifting Response of Unanchored Liquid-Storage Tanks,” ASCE J. Struct. Div., 120(12), pp. 3525–3547. [CrossRef]
Taniguchi, T., 2004, “Experimental and Analytical Studies of Rocking Mechanics of Unanchored Flat-Bottom Cylindrical Shell Model Tanks,” ASME/JSME 2004 Pressure Vessels and Piping Conference (PVP2004), ASME, Vol. 1: Seismic Engineering, Paper No. PVP2004-2913, pp. 119–127. [CrossRef]
Editorial Committee of Vibration Handbook, 1985, Vibration Handbook for Civil Engineers, JSCE, Tokyo, Japan, pp. 414–415 (Japanese).
Taniguchi, T., 2005, “Rocking Mechanics of Flat-Bottom Cylindrical Shell Model Tanks Subjected to Harmonic Excitation,” ASME J. Pressure Vessel Technol., 127(4), pp. 373–386. [CrossRef]
Hayashi, S., Taniguchi, T., Umeda, A., Yamada, H., Kawasaki, T., and Nagahara, H., 2011, “A Study of Fluid-Structure Coupled Analysis for Large LNG Storage Tanks in Consideration of Uplift,” ASME 2011 Pressure Vessels and Piping Conference (PVP2011), ASME, Vol. 8: Seismic Engineering, Paper No. PVP2011-57925, pp. 303–312. [CrossRef]
Nakashima, T., and Taniguchi, T., 2006, “Numerical Investigation Into Significant Reduction in Coefficient of Restitution for Fluid-Container Combined Systems,” ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference (PVP2006-ICPVT-11), ASME, Vol. 8: Seismic Engineering, Paper No. PVP2006-ICPVT-11-93540, pp. 231–237. [CrossRef]
Veletsos, A. S., and TangY., 1987, “Rocking Response of Liquid Storage Tanks,” ASCE J. Eng. Mech., 113(11), pp. 1774–1792. [CrossRef]
Taniguchi, T., and Ando, Y., 2010, “Fluid Pressures on Unanchored Rigid Flat-Bottom Cylindrical Tanks Under Action of Uplifting Acceleration,” ASME J. Pressure Vessel Technol., 132(1), p. 011802. [CrossRef]
Taniguchi, T., and Segawa, T, 2008, “Fluid Pressure on Rectangular Tank Consisting of Rigid Side Walls and Rectilinearly Deforming Bottom Plate Due to Uplift Motion,” ASME 2008 Pressure Vessels and Piping Conference (PVP2008), ASME, Vol. 8: Seismic Engineering, Paper No. PVP2008-61166, pp. 317–323. [CrossRef]
Taniguchi, T., and Ando, Y., 2010, “Fluid Pressures on Unanchored Rigid Rectangular Tanks Under Action of Uplifting Acceleration,” ASME J. Pressure Vessel Technol., 132(1), p. 011801. [CrossRef]
Taniguchi, T., and Segawa, T, 2009, “Effective Mass of Fluid for Rocking Motion of Flat-Bottom Cylindrical Tanks,” Proceedings of Seismic Engineering, ASME, Paper No. PVP2009-77580.

Figures

Grahic Jump Location
Fig. 1

(a) Equilibrium of forces on the small volume, (b) boundary conditions for Laplace's equation, and (c) forces acting on the small volume

Grahic Jump Location
Fig. 2

Ratios of the apparent density of fluid for the tank bulging response to the original fluid density

Grahic Jump Location
Fig. 3

Boundary conditions for Laplace's equation

Grahic Jump Location
Fig. 4

(a) Analytical model, (b) equilibrium of forces on the small volume, and (c) forces acting on the small volume

Grahic Jump Location
Fig. 5

(a) Ratios of the apparent density of fluid for the tank rocking response to the original fluid density (uplift width = 1%), (b) ratios of the apparent density of fluid for the tank rocking response to the original fluid density (uplift width = 50%), and (c) ratios of the apparent density of fluid for the tank rocking response to the original fluid density (uplift width = 100%)

Grahic Jump Location
Fig. 6

(a) Ratios of the apparent density of fluid for the rocking–bulging interaction to the original fluid density (uplift width = 1%), (b) ratios of the apparent density of fluid for the rocking–bulging interaction to the original fluid density (uplift width = 50%), and (c) ratios of the apparent density of fluid for the rocking–bulging interaction to the original fluid density (uplift width = 100%)

Grahic Jump Location
Fig. 7

Ratios of effective mass of fluid for the rocking–bulging interaction to mass of tank content

Grahic Jump Location
Fig. 8

(a) Ratios of the horizontal length of a moment arm to the width of the tank and (b) ratios of the vertical length of a moment arm to the height of the tank

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