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Research Papers: Fluid-Structure Interaction

Vibration Analysis of a Floating Roof Subjected to Radial Second Mode of 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

J. Pressure Vessel Technol 132(2), 021303 (Mar 30, 2010) (8 pages) doi:10.1115/1.3148083 History: Received August 27, 2008; Revised February 22, 2009; Published March 30, 2010; Online March 30, 2010

In a previous paper, a cost-efficient modal analysis method for the vibration of a floating roof coupled with nonlinear sloshing in a circular cylindrical oil storage tank is presented. This method is extended to the case in which the out-of-plane deformation of the roof-deck caused by the radial second mode of sloshing induces an elliptical deformation of the pontoon around the deck. First, the radial contraction of the deck is calculated from the slope of the out-of-plane deformation of the deck, and the following two points are confirmed: (i) the circumferential variation in this radial contraction results in the elliptical deformation of the pontoon, and (ii) the present theoretical prediction for the radial contraction is in good agreement with a numerical result obtained by LS-DYNA . Based on these points, the stresses arising in the pontoon are calculated by considering the contraction of the deck as an enforced displacement of the pontoon. Numerical results show that (a) the elliptical deformation of the pontoon causes a large circumferential in-plane stress, (b) reduction achieved by the increase in the thickness of the deck is larger for the radial contraction of the deck and the stresses in the pontoon than for the out-of-plane deformation of the deck, and (c) the radial contraction of the deck for a fixed value of the out-of-plane deformation of the deck increases with the decrease in the radius of the deck.

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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

Radial contraction and out-of-plane deformation of deck due to radial second mode of sloshing with circumferential wave number 1: (a) radial contraction at φ=0 deg and (b) Out-of-plane deformation at r=18.9 m and φ=0 deg

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Figure 4

Relation between radial contraction and out-of-plane deformation of deck shown in Figs.  33; ∘, result cited from Fig. 2.6 in Ref. 2

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Figure 5

Responses of radial displacement of joint between deck and pontoon and radial contraction of deck (thin solid line, radial displacement at φ=0 deg; dotted line, radial displacement at φ=180 deg; thick solid line, radial contraction at φ=0 deg)

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Figure 6

Circumferential variation in radial displacement at joint between deck and pontoon (t=31 s)

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Figure 7

Responses of in-plane stresses arising in inner rim at joint between deck and pontoon (φ=0 deg): (a) stress in the vertical direction acting on the horizontal cross section of the inner rim and (b) circumferential stress

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Figure 8

Circumferential variations in in-plane stresses arising in inner rim at joint between deck and pontoon (t=31 s; thin line, stress in the vertical direction acting on the horizontal cross section of the inner rim; thick line, circumferential stress)

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Figure 9

Radial contraction and out-of-plane deformation of deck due to radial second mode of sloshing with circumferential wave number 1 (the case in which thickness of deck is increased to 0.08 m): (a) radial contraction at φ=0 deg and (b) out-of-plane deformation at r=15.0 m and φ=0 deg

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Figure 10

Responses of in-plane stresses arising in inner rim at joint between deck and pontoon (φ=0 deg; the case in which thickness of deck is increased to 0.08 m): (a) stress in the vertical direction acting on the horizontal cross section of the inner rim and (b) circumferential stress

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Figure 11

Equivalent thickness hr corresponding to distance Hr between upper and lower plates

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Figure 12

Relation between radial contraction and out-of-plane deformation of deck (the case in which radius of deck is decreased; ∘, result cited from Fig. 2.6 of Ref. 2)

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