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.

1.
Yamauchi
,
Y.
,
Kamei
,
A
,
Zama
,
S.
, and
Uchida
,
Y.
, 2006, “
Seismic Design of Floating Roof of Oil Storage Tanks Under Liquid Sloshing
,”
Sloshing and Fluid Structure Vibration
,
ASME Pressure Vessels and Piping Division Conference
, Paper No. PVP2006-ICPVT-11-93280.
2.
Japanese Hazardous Materials Safety Techniques Association
, 2006, “
Report of Study to Develop Reasonable Modification Procedures to Satisfy Technical Standard Regarding Relatively Long Period Ground Motion for Facilities Handling Hazardous Materials
,” in Japanese.
3.
Abramson
,
H. N.
,
Chu
,
W. H.
, and
Dodge
,
F. T.
, 1966, “
The Dynamic Behavior of Liquids in Moving Containers
,”
H. N.
Abramson
, ed., Report No. NASA SP-106.
4.
Ibrahim
,
R. A.
,
Pilipchuk
,
V. N.
, and
Ikeda
,
T.
, 2001, “
Recent Advances in Liquid Sloshing Dynamics
,”
Appl. Mech. Rev.
0003-6900,
54
, pp.
133
199
.
5.
Bauer
,
H. F.
,
Chang
,
S. S.
, and
Wang
,
J. T. S.
, 1971, “
Nonlinear Liquid Motion in a Longitudinally Excited Container With Elastic Bottom
,”
AIAA J.
0001-1452,
9
, pp.
2333
2339
.
6.
Ibrahim
,
R. I.
, and
El-Sayad
,
M. A.
, 1999, “
Simultaneous Parametric and Internal Resonances in Systems Involving Strong Nonlinearities
,”
J. Sound Vib.
0022-460X,
225
, pp.
857
885
.
7.
Ikeda
,
T.
, and
Nakagawa
,
N.
, 1997, “
Nonlinear Vibrations of a Structure Caused by Water Sloshing in a Rectangular Tank
,”
J. Sound Vib.
0022-460X,
201
, pp.
23
41
.
8.
Ikeda
,
T.
, and
Nakagawa
,
N.
, 1995, “
Nonlinear Vibrations of a Structure Caused by Water Sloshing in a Cylindrical Tank, Fluid Structure Interaction and Structure Mechanics
,”
PVP (Am. Soc. Mech. Eng.)
0277-027X,
310
, pp.
63
76
.
9.
Peterson
,
L. D.
,
Crawley
,
E. F.
, and
Hansman
,
R. J.
, 1989, “
Nonlinear Slosh Coupled to the Dynamics of a Spacecraft
,”
AIAA J.
0001-1452,
27
, pp.
1230
1240
.
10.
Utsumi
,
M.
,
Kimura
,
K.
, and
Sakata
,
M.
, 1987, “
The Non-Stationary Random Vibration of an Elastic Circular Cylindrical Liquid Storage Tank in Simulated Earthquake Excitation (Straightforward Analysis of Tank Wall Deformation)
,”
JSME Int. J., Ser. III
0914-8825,
30
, pp.
467
475
.
11.
Nakagawa
,
K.
, 1955, “
On the Vibration of an Elevated Water Tank-II
,”
Technol. Rep. Osaka Univ.
0030-6177,
5
, pp.
317
336
.
12.
Kondo
,
H.
, 1978, “
Free Vibration Analysis for Vertical Motion of a Floating Roof
,”
Trans. Jpn. Soc. Mech. Eng.
0375-9466,
44
, pp.
1214
1223
.
13.
Sakai
,
F.
,
Nishimura
,
M.
, and
Ogawa
,
H.
, 1984, “
Sloshing Behavior of Floating Roof Oil Storage Tanks
,”
Comput. Struct.
0045-7949,
19
, pp.
183
192
.
14.
Sakai
,
F.
,
Inoue
,
R.
, and
Hayashi
,
S.
, 2006, “
Fluid-Elastic Analysis and Design of Sloshing in Floating-Roof Tanks Subjected to Earthquake Motions
,”
Proceedings of the ASME Pressure Vessels and Piping Division Conference
, Vancouver, BC, Canada, Paper No. PVP2006-ICPVT11-93622, pp.
1
10
.
15.
Matsui
,
T.
, 2007, “
Sloshing in a Cylindrical Liquid Storage Tank With a Floating Roof Under Seismic Excitation
,”
ASME J. Pressure Vessel Technol.
0094-9930,
129
, pp.
557
566
.
16.
Matsui
,
T.
, 2007, “
Sloshing in a Cylindrical Liquid Storage Tank With a Single-Deck Type Floating Roof Under Seismic Excitation
,”
Proceedings of the ASME Pressure Vessels and Piping Division Conference
, San Antonio, TX, Paper No. PVP2007-26249.
17.
Shimizu
,
S.
,
Naito
,
K.
, and
Koyama
,
Y.
, 1984, “
A Study on Sloshing Behaviors of Floating Roof Oil Storage Tanks During Earthquake Excited by Three-Dimensional Dynamic Simulator
,”
Ishikawajima-Harima Eng. Rev.
0578-7904,
24
, pp.
379
384
.
18.
Utsumi
,
M.
, and
Ishida
,
K.
, 2008, “
Vibration Analysis of a Floating Roof Taking Into Account the Nonlinearity of Sloshing
,”
ASME J. Appl. Mech.
0021-8936,
75
, p.
041008
.
19.
Utsumi
,
M.
,
Ishida
,
K.
, and
Hizume
,
M.
, 2010, “
Internal Resonance of a Floating Roof Subjected to Nonlinear Sloshing
,”
ASME J. Appl. Mech.
0021-8936,
77
(
1
), p.
011016
.
20.
Miura
,
M.
, and
Kikuchi
,
T.
, 2005, “
The Sloshing Simulation of Floating Roof Tank
,”
ASME Pressure Vessels and Piping Division Conference
, Paper No. PVP2005-71439.
21.
Seliger
,
R. L.
, and
Whitham
,
G. B.
, 1968, “
Variational Principles in Continuum Mechanics
,”
Proc. R. Soc. London, Ser. A
0950-1207,
305
, pp.
1
25
.
22.
Utsumi
,
M.
, 1998, “
Low-Gravity Propellant Slosh Analysis Using Spherical Coordinates
,”
J. Fluids Struct.
0889-9746,
12
, pp.
57
83
.
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