In the present paper, a 3-D homogenized model for beam bundle in fluid is developed and formulated in terms of fluid velocity potential and displacement of beams as fundamental unknowns. It can be seen that the homogenized model is associated with a set of finite element equations in the form of a conservative gyroscopic system. Based on these equations, an algorithm for the modal analysis and the dynamic response analysis of the beam bundle is also given. It is found that both the displacement and the fluid pressure response of the bundle have a similar relation with time, but different amplitudes.

1.
Chen
,
S. S.
,
1978
, “
Crossflow-Induced Vibrations of Heat Exchanger Tube Banks
,”
Nucl. Eng. Des.
,
47
, pp.
67
86
.
2.
Shinohara
,
Y.
, and
Shimogo
,
T.
,
1981
, “
Vibrations of Square and Hexagonal Cylinders in a Liquid
,”
ASME J. Pressure Vessel Technol.
,
103
, pp.
223
239
.
3.
Berdichevskii
,
V. L.
,
1977
, “
On Averaging of Periodic Systems
,”
J. Appl. Math. Mech.
,
41
, pp.
1010
1023
.
4.
Bensoussan, A., Lions, J.-L., and Papanicolaou, G., 1978, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, Holland.
5.
Sanchez-Palencia, E., 1980, “Non-Homogeneous Media and Vibration Theory,” Lecture Notes in Physics, Springer, Berlin, Germany.
6.
Schumann, U., 1981, “Homogenized Equations of Motion for Rod Bundles in the Fluid With Periodic Structure,” Ingenieur-Archiv 50, pp. 203–216.
7.
Schumann
,
U.
,
1981
, “
Virtual Density and Speed of Sound in a Fluid-Solid Mixture With Periodic Structure
,”
Int. J. Multiphase Flow
,
7
, No.
6
, pp.
619
633
.
8.
Planchard
,
J.
,
Remy
,
F.
, and
Sonneville
,
P.
,
1982
, “
A Simplified Method for Determining Acoustic and Tube Eigenfrequencies in Heat Exchangers
,”
ASME J. Pressure Vessel Technol.
,
104
, pp.
175
179
.
9.
Benner
,
J.
,
1985
, “
Homogenized Model for Fluid-Structure Interaction of the PWR Core Internals During Blowdown
,”
Nucl. Eng. Des.
,
90
, pp.
1
11
.
10.
Hammami, L., 1990, “Etude de l’interaction fluide structure dans les faisceaux de tubes par une methode d’homogenisation,” thesis, Universite Paris, France.
11.
Brochard, D., and Hammami, L., 1991, “An Homogenization Method Applied to the Seismic Analysis of LMFBR Cores,” SMiRT 11 Trans. Vol. E, Tokyo, Japan, Aug., pp. 497–503.
12.
Conca, C., Planchard, J., and Vanninathan, M., 1995, Fluids and Periodic Structures, John Wiley & Sons, New York, NY.
13.
Zhang R. J., 1996, “A Unified Homogenization Model of Beam Bundle in Fluid,” XIXth International Congress of Theoretical and Applied Mechanics (Abstracts), Kyoto, Japan, NJ-3, pp. 793.
14.
Zhang
,
R. J.
,
1998
, “
A Unified 3-D Homogenization Model of Beam Bundle in Fluid
,”
ASME J. Pressure Vessel Technol.
,
120
, pp.
56
61
.
15.
Zhang
,
R. J.
,
1998
, “
Structural Homogenized Analysis for Nuclear Reactor Core
,”
Nucl. Eng. Des.
,
183
, pp.
151
156
.
16.
Zhang
,
R. J.
,
1999
, “
A Beam Bundle in a Compressible Inviscid Fluid
,”
ASME J. Appl. Mech.
,
66
, pp.
546
548
.
17.
Everstine
,
G. C.
,
1981
, “
A Symmetric Potential Formulation for Fluid-Structure Interaction
,”
J. Sound Vib.
,
79
, No.
1
,
157
160
.
18.
Dai
,
D. N.
,
Wang
,
X. C.
, and
Du
,
Q. H.
,
1990
, “
A Modal Analysis for the Dynamic Response of Fluid-Structure Systems
,”
Acta Mechaica Solida Sinica
,
11
, No.
4
,
305
312
.
You do not currently have access to this content.