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Research Papers

Vibration Analysis of a Floating Roof Taking Into Account the Nonlinearity of Sloshing

[+] Author and Article Information
M. Utsumi

Machine Element Department, 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

J. Appl. Mech 75(4), 041008 (May 14, 2008) (10 pages) doi:10.1115/1.2912739 History: Received December 08, 2006; Revised February 06, 2008; Published May 14, 2008

The vibration of a floating roof hydroelastically coupled with nonlinear sloshing is analyzed. Influences of the nonlinearity of sloshing on the magnitude of stresses arising in a floating roof are investigated. Numerical results show that (i) neglecting the nonlinearity of sloshing significantly underestimates the magnitude of the stresses, even when the nonlinear effect is small for the roof displacement; and (ii) the underestimation associated with the use of the linear approximation becomes more marked with the decrease in the liquid depth. The reasons for these results are explained based on the fact that in the nonlinear sloshing, the modal component with circumferential wave number 2 is excited.

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Copyright © 2008 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

Positions A, B, and C at which responses of out-of-plane stresses are computed.

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Figure 4

Comparison between the linear and nonlinear responses (solid line, linear; bold line, nonlinear)

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Figure 5

Results for the case where the thickness of the inner rim of the pontoon is reduced to 0.01m (solid line, linear; bold line, nonlinear)

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Figure 6

Circumferential variations of the out-of-plane stresses shown in Figs.  44 at t=33s (solid line, linear; bold line, nonlinear)

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Figure 7

Vertical displacement modes of the floating roof (circumferential wave number is 0)

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Figure 8

Vertical displacement modes of the floating roof (circumferential wave number is 1)

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Figure 9

Vertical displacement modes of the floating roof (circumferential wave number is 2)

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Figure 10

Displacement of the pontoon in the radial fifth mode with circumferential wave number 2

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Figure 11

Response of the out-of-plane stress σC at Position C shown in Fig. 3 (solid line, linear analysis; bold line, nonlinear analysis neglecting the radial fifth mode shown in Fig. 9)

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Figure 12

Results for the case where the liquid depth is decreased to 12.3m (solid line, linear; bold line, nonlinear)

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Figure 13

The responses of liquid surface displacement (a=1m, h=1.263m; damping ratio 0.005; the tank is excited by the displacement fx(t)=0.2sinω11t where ω11=[gλ11tanh(λ11h)]1∕2 and 0⩽t⩽6π∕ω11)

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