Variational principle is used to derive the nonlinear response of the floating roof of cylindrical liquid storage tanks due to harmonic base excitations. The formulation accounts for nonlinearity due to large deflections of the floating roof. The derived nonlinear governing equation for the sloshing response of the floating roof has a cubic nonlinear stiffness term similar to the well known Duffing equation. It is shown that accounting for large deflections could substantially reduce the wave elevation for near resonance harmonic excitations. Evaluating the response of the nonlinear model for increasing amplitudes of near resonance harmonic excitations gives rise to the appearance of sub and super harmonics in the response. The broadband structure of the frequency spectrum, the fractal structure of the Poincare maps, and the bifurcation diagram as qualitative criteria and Lyapunov exponent evolution as quantitative criterion are used to investigate the emergence of chaotic response.

References

References
1.
Chang
,
J. I.
, and
Lin
,
C.-C.
, 2006, “
Study of Storage Tank Accidents
,”
J. Loss Prev. Process Ind.
,
19
(
1
), pp.
51
59
.
2.
Hatayama
,
K.
,
Zama
,
S.
,
Nishi
,
H.
,
Yamada
,
M.
,
Hirokawa
,
M.
, and
Inoue
,
R.
, 2005, “
The Damages of Oil Storage Tanks During the 2003 Tokachi-oki Earthquake and the Long Period Ground Motions
,”
Proceedings of the JSCE-AIJ Joint Symposium on Huge Subduction Earthquakes—Wide Area Strong Ground Motion Prediction
, pp.
7
18
.
3.
Jacobsen
,
L. S.
, 1949, “
Impulsive Hydrodynamics of Fluid Inside a Cylindrical Tank and of Fluid Surrounding a Cylindrical Pier
,”
Bull. Seismol. Soc. Am.
,
39
(
3
), pp.
189
202
.
4.
Senda
,
K.
, and
Nakagawa
,
K.
, 1954, “
On the Vibration of an Elevated Water Tank I
,”
Technol. Rep. Osaka Univ.
,
4
(
117
), pp.
247
264
.
5.
Matsui
T.
, 2007, “
Sloshing in a Cylindrical Liquid Storage Tank With a Floating Roof Under Seismic Excitation
,”
J. Pressure Vessel Technol.
,
129
, pp.
557
566
.
6.
Isshiki
,
H.
, and
Nagata
,
S.
, 2001, “
Variational Principles Related to Motion of an Elastic Plate Floating on a Water Surface
,”
Proceedings of the 11th International Offshore and Polar Engineering Conference
,
Stavanger
,
Norway
, pp.
190
197
.
7.
Nagata
,
S.
,
Yoshida
,
H.
,
Fujita
,
T.
, and
Isshiki
,
H.
, 1997, “
The Analysis of the Wave Induced Responses of an Elastic Floating Plate
,”
Proceedings of the 16th International Conference on Offshore Mechanics and Arctic Engineering
, vol.
6
.
8.
Ohmatsu
,
S.
, 1997, “
Numerical Calculation of Hydro-Elastic Responses of Pontoon Type VLFS
,”
J. Soc. Nav. Archit. Jpn.
,
182
, pp.
329
340
.
9.
Sakai
,
F.
,
Nishimura
,
M.
, and
Ogawa
,
H.
, 1984, “
Sloshing Behavior of Floating-Roof Oil Storage Tanks
,”
Comput. Struct.
,
19
(
2
), pp.
183
192
.
10.
Shabani
,
R.
,
Tariverdilo
,
S.
,
Salarieh
,
H.
, and
Rezazadeh
,
G.
, 2010, “
Importance of the Flexural and Membrane Stiffnesses in Large Deflection Analysis of Floating Roofs
,”
Appl. Math. model.
,
34
(
9
), pp.
2426
2436
.
11.
Frandsen
,
J. B.
, 2004, “
Sloshing Motions in Excited Tanks
,”
J. Comput. Phys.
,
196
, pp.
53
87
.
12.
Cho
,
J. R.
, and
Lee
,
H. W.
, 2004, “
Numerical Study on Liquid Sloshing in Baffled Tank by Nonlinear Finite Element Method
,”
Comput. Methods Appl. Mech. Eng.
,
193
, pp.
2581
2598
.
13.
Hernandez-Barrios
,
H.
,
Heredia-Zavoni
,
E.
, and
Aldama-Rodrıguez
,
A.
, 2007, “
Nonlinear Sloshing Response of Cylindrical Tanks Subjected to Earthquake Ground Motion
,”
Eng. Struct.
29
, pp.
3364
3376
.
14.
Utsumi
,
M.
,
Ishida
,
K.
, and
Hizume
,
M.
, 2010, “
Internal Resonance of a Floating Roof Subjected to Nonlinear Sloshing
,”
J. Appl. Mech.
,
77
(
1
),
011016
.
15.
Amibili
,
M.
, 2008,
Nonlinear Vibration and Stability of Shells and Plates,
Cambridge University Press
,
Cambridge, England
.
16.
Moon
,
F. C.
, 1992,
Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers, John
Wiley
,
New York
.
17.
Guckenheimer
,
J.
, and
Holmes
,
P. J.
, 1983,
Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields
,
Springer-Verlag
,
Berlin
.
18.
Wolf
,
A.
,
Swift
,
J. B.
,
Swinney
,
H. L.
, and
Vastano
J. A.
, 1985, “
Determining Lyapunov Exponents From a Time Series
,”
Physica D
,
16
(
3
), pp.
285
317
.
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