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Research Papers

Internal Resonance of a Floating Roof Subjected to Nonlinear Sloshing

[+] Author and Article Information
M. Utsumi

Department of Machine Element, Technical Research Laboratory, IHI Corporation, 1 Shinnakaharacho, Isogo-ku, Yokohama, Kanagawa Prefecture 235-8501, Japan

K. Ishida

Energy and Plant, IHI Corporation, 1-1, Toyosu 3-chome, Koto-ku, Tokyo 135-8710, Japan

M. Hizume

 IHI Plant Construction, 1-1, Toyosu 3-chome, Koto-ku, Tokyo 135-8710, Japan

J. Appl. Mech 77(1), 011016 (Oct 05, 2009) (8 pages) doi:10.1115/1.3173768 History: Received August 27, 2008; Revised April 22, 2009; Published October 05, 2009

Internal resonance in the vibration of a floating roof coupled with nonlinear sloshing in a circular cylindrical oil storage tank is investigated. The nonlinear system exhibits internal resonance when nonlinear terms of the governing equation have a dominant frequency close to a certain modal frequency of the system. Numerical results show that when internal resonance occurs, the responses of stresses in a floating roof exhibit a long-duration period of large amplitude despite a short duration of the earthquake excitation applied to the tank. Due to the presence of internal resonance, the underestimation of the stresses associated with the use of the linear theory becomes more marked, and thus the importance of nonlinearity of sloshing in the stress estimation is accentuated. It is illustrated that the magnitudes of the stresses increase with the increase in the liquid-filling level, and that the effect of internal resonance on the stresses noted in the case of sinusoidal excitation appears under real earthquake excitation. A method for reducing the stresses is proposed.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Computational model

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Figure 2

Geometry of floating roof used for numerical example

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Figure 3

Response of vertical displacement of floating roof at outer rim of pontoon (thin line, linear; thick line, nonlinear)

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Figure 4

Responses of stresses (thin lines, linear; thick lines, nonlinear). (a) Radial bending stress σs at outer end (r,φ)=(b,0) of bottom of pontoon. (b) Hoop membrane stress σφ at the same position.

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Figure 5

Circumferential variation of hoop membrane stress σφ shown in Fig. 4 (nonlinear, t=60 s)

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Figure 6

Mode shapes of floating roof (thin lines, undisturbed position): (a) ω02-mode and (b) ω22-mode

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Figure 7

Responses of stresses (the case in which internal resonance is not present, h=10.875 m; thin lines, linear; thick lines, nonlinear). (a) Radial bending stress σs at outer end (r,φ)=(b,0) of bottom of pontoon. (b) Hoop membrane stress σφ at the same position.

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Figure 8

Earthquake ground motion record (2003 Tokachi-oki, HKD129EW): (a) acceleration record; (b) Fourier transform of the acceleration record divided by squared angular frequency

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Figure 9

Responses to an actual earthquake ground motion record 2003 Tokachi-oki (thin lines, linear; thick lines, nonlinear). (a) Vertical displacement of floating roof at outer rim of pontoon; (b) radial bending stress σs at outer end (r,φ)=(b,0) of bottom of pontoon. (c) Hoop membrane stress σφ at the same position.

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Figure 10

Nonlinear responses of stresses (the case in which slope angles of pontoon are reduced). (a) Radial bending stress σs at outer end (r,φ)=(b,0) of bottom of pontoon. (b) Hoop membrane stress σφ at the same position.

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