In this paper, a convenient modal analysis method for the linear coupled vibration of a container that is partially filled with a fluid is introduced. This problem is important for various reasons, such as stability analysis. The fluid-structure interactions in an elastic tank with an incompressible liquid are assumed to produce small vibrations. Reduced symmetric finite element equations of the system are acquired according to the component mode synthesis method. Considering that the liquid satisfies the same governing equation as steady heat conduction, general programs can be used to calculate the mass matrix and stiffness matrix of the coupled system. Then, modal analysis of the liquid container using general software, e.g., MSC Nastran, that ensures accuracy and stableness in the process, is applied to demonstrate that this method can determine the modal frequency in a fluid-structure coupled system.

References

References
1.
Abramson
,
H. N.
,
1996
,
The Dynamic Behavior of Liquids in Moving Containers
, NASA SP–106,
National Aeronautics and Space Administration
,
Washington, DC
.
2.
Kruntcheva
,
M. R.
,
2007
, “
Free Vibrations of Cylindrical Storage Tanks: Finite-Element Analysis and Experiments
,”
J. Eng. Mech. ASCE
,
133
(
6
), pp.
728
733
.10.1061/(ASCE)0733-9399(2007)133:6(728)
3.
Maekawa
,
A.
,
Shimizu
,
Y.
,
Suzuki
,
M.
, and
Fujita
,
K.
,
2010
, “
Vibration Test of a 1/10 Reduced Scale Model of Cylindrical Water Storage Tank
,”
ASME J. Pressure Vessel Technol.
,
132
(
5
), p.
051801
.10.1115/1.4001915
4.
Ito
,
T.
,
Morita
,
H.
,
Hamada
,
K.
,
Sugiyama
,
A.
,
Kawamoto
,
Y.
,
Ogo
,
H.
, and
Shirai
,
E.
,
2003
, “
Investigation on Buckling Behavior of Cylindrical Liquid Storage Tanks Under Seismic Excitation: 1st Report—Investigation on Elephant Foot Bulge
,” ASME Paper No. 2003-2120PVP, pp.
193
201
.
5.
Love
,
J. S.
, and
Tait
,
M. J.
,
2011
, “
Equivalent Linearized Mechanical Model for Tuned Liquid Dampers of Arbitrary Tank Shape
,”
ASME J. Fluids Eng. Trans.
,
133
(
6
), p.
061105
.10.1115/1.4004080
6.
Lu
,
J.
,
Wang
,
S. M.
, and
Wang
,
T. S.
,
2012
, “
Coupling Dynamic Analysis of a Liquid-Filled Spherical Container Subject to Arbitrary Excitation
,”
Acta Mech. Sin.
,
28
(
4
), pp.
1154
1162
.10.1007/s10409-012-0119-2
7.
Gavrilova
,
E.
,
2007
, “
Coupled Frequencies of a Fluid in a Circular Cylindrical Tank With a Membrane on Its Upper End and Permanent Axial Loading
,”
J. Vib. Control
,
13
(
9–10
), pp.
1355
1360
.10.1177/1077546307077502
8.
Natsiavas
,
S.
, and
Babcock
,
C. D.
,
1987
, “
Buckling at the Top of a Fluid Filled Tank During Base Excitation
,”
ASME J. Pressure Vessel Technol.
,
109
(
4
), pp.
374
380
.10.1115/1.3264919
9.
Rebouillat
,
S.
, and
Liksonov
,
D.
,
2010
, “
Fluid-Structure Interaction in Partially Filled Liquid Containers: A Comparative Review of Numerical Approaches
,”
Comput. Fluids
,
39
(
5
), pp.
739
746
.10.1016/j.compfluid.2009.12.010
10.
Hou
,
G. N.
,
Wang
,
J.
, and,
Layton
,
A.
,
2012
, “
Numerical Methods for Fluid-Structure Interaction–A Review
,”
Commun. Comput. Phys.
12
(
2
), pp.
337
377
.10.4208/cicp.291210.290411s
11.
Fisher
,
D. F.
, and
Rammerstorfer
,
F. G.
,
1985
, “
Local Instabilities of Liquid Filled Cylindrical Shells Under Earthquake Excitation
,” SMiRT 7th, K4/8, pp.
305
312
.
12.
Mitra
,
S.
, and
Sinhamahapatra
,
K. P.
,
2008
, “
2D Simulation of Fluid-Structure Interaction Using Finite Element Method
,”
Finite Elem. Anal. Des.
45
(
1
), pp.
52
59
10.1016/j.finel.2008.07.006
13.
Biswal
,
K. C.
, and
Bhattacharyya
,
S. K.
,
2010
, “
Dynamic Response of Structure Coupled With Liquid Sloshing in a Laminated Composite Cylindrical Tank With Baffle
,”
Finite Elem. Anal. Des.
,
46
(
11
), pp.
966
981
.10.1016/j.finel.2010.07.001
14.
Souli
,
M.
, and
Aquelet
,
N.
,
2011
, “
Fluid Structure Interaction for Hydraulic Problems
,”
Houille Blanche-Rev. Int. de l‘Eau
,
6
, pp.
5
10
.10.1051/lhb/2011054
15.
Yang
,
Q.
,
Jones
,
V.
, and
McCue
,
L.
,
2012
, “
Free-Surface Flow Interactions With Deformable Structures Using an SPH–FEM Model
,”
Ocean Eng.
,
55
, pp.
136
147
.10.1016/j.oceaneng.2012.06.031
16.
Wang
,
W. L.
, and
Du
,
Z. R.
,
1985
,
Structural Vibration and Dynamic Substructure Method
,
1st ed.
,
Fudan University Press
,
Shanghai [in Chinese]
.
17.
Ohayon
,
R.
,
2001
, “
Reduced Symmetric Models for Modal Analysis of Internal Structural-Acoustic and Hydroelastic-Sloshing Systems
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
24–25
), pp.
3009
3019
.10.1016/S0045-7825(00)00379-0
18.
Tokuda
,
N.
,
Sakurai
,
T.
, and
Teraoku
,
T.
,
1995
, “
Sloshing Analysis Method Using Existing FEM Structural Analysis Code
,”
ASME J. Pressure Vessel Technol.
,
117
(
3
), pp.
268
272
.10.1115/1.2842122
19.
Zhu
,
L.
,
2012
,
Dynamics Analysis and Simulation for Fluid-Structure Coupled Vibration of Rockets
'
Propellant Tank, Fudan University
,
Shanghai [in Chinese]
.
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