The paper is concerned with the finite element analysis of hydroelastic stability of stationary or rotating elastic single and coaxial cylindrical shells subjected to compressible fluid flows having axial and tangential velocity components. The behavior of the flowing and rotating fluid is described in the framework of the potential theory. Consideration of elastic shells is based on the classical shell model. The results of the numerical analysis of shell stability for various boundary conditions, geometrical dimensions and different sizes of the annular gap between the outer and inner shells are discussed. It has been found that single and coaxial shells interacting with the combined fluid flows show qualitative differences in the dynamic behavior.

References

References
1.
Païdoussis
,
M. P.
,
2004
,
Fluid-Structure Interactions: Slender Structures and Axial Flow
, Vol.
2
,
Elsevier Academic
,
London, UK
.
2.
Gosselin
,
F.
, and
Païdoussis
,
M. P.
,
2007
, “
Stability of a Rotating Cylindrical Shell Containing Axial Viscous Flow
,” 18ème Congrès Français de Mécanique (CFM’07),
Grenoble, France
, Aug 27–31, Paper No. CFM2007-1578.
3.
Ilgamov
,
M. A.
,
1969
,
Oscillations of Elastic Shells Containing Liquid and Gas
,
Nauka
,
Moscow, Russia
(in Russian).
4.
Selmane
,
A.
, and
Lakis
,
A. A.
,
1997
, “
Vibration Analysis of Anisotropic Open Cylindrical Shells Subjected to a Flowing Fluid
,”
J. Fluid Struct.
,
11
(
1
), pp.
111
134
.10.1006/jfls.1996.0069
5.
Zhang
,
Y. L.
,
Gorman
,
D. G.
, and
Reese
,
J. M.
,
2001
, “
A Finite Element Method for Modelling the Vibration of Initially Tensioned Thin-Walled Orthotropic Cylindrical Tubes Conveying Fluid
,”
J. Sound Vib.
,
245
(
1
), pp.
93
112
.10.1006/jsvi.2000.3554
6.
Lakis
,
A. A.
,
Van Dyke
,
P.
, and
Ouriche
,
H.
,
1992
, “
Dynamic Analysis of Anisotropic Fluid-Filled Conical Shells
,”
J. Fluid Struct.
,
6
(
2
), pp.
135
162
.10.1016/0889-9746(92)90042-2
7.
Kerboua
,
Y.
,
Lakis
,
A. A.
, and
Hmila
,
M.
,
2010
, “
Vibration Analysis of Truncated Conical Shells Subjected to Flowing Fluid
,”
Appl. Math. Model.
,
34
(
3
), pp.
791
809
.10.1016/j.apm.2009.06.028
8.
Zhang
,
Y. L.
,
Gorman
,
D. G.
, and
Reese
,
J. M.
,
2003
, “
Vibration of Prestressed Thin Cylindrical Shells Conveying Fluid
,”
Thin Walled Struct.
,
41
(
12
), pp.
1103
1127
.10.1016/S0263-8231(03)00108-3
9.
Kochupillai
,
J.
,
Ganesan
,
N.
, and
Padmanabhan
,
C.
,
2002
, “
A Semi-Analytical Coupled Finite Element Formulation for Shells Conveying Fluids
,”
Comput. Struct.
,
80
(
3–4
), pp.
271
286
.10.1016/S0045-7949(02)00008-1
10.
Kochupillai
,
J.
,
Ganesan
,
N.
, and
Padmanabhan
,
C.
,
2002
, “
A Semi-Analytical Coupled Finite Element Formulation for Composite Shells Conveying Fluids
,”
J. Sound Vib.
,
258
(
2
), pp.
287
307
.10.1006/jsvi.2002.5176
11.
Kumar
,
D. S.
, and
Ganesan
,
N.
,
2008
, “
Dynamic Analysis of Conical Shells Conveying Fluid
,”
J. Sound Vib.
,
310
(
1–2
), pp.
38
57
.10.1016/j.jsv.2007.07.020
12.
Bochkarev
,
S. A.
, and
Matveenko
,
V. P.
,
2011
, “
Natural Vibrations and Stability of Shells of Revolution Interacting With An Internal Fluid Flow
,”
J. Sound Vib.
,
330
(
13
), pp.
3084
3101
.10.1016/j.jsv.2011.01.029
13.
Uğurlu
,
B.
, and
Ergin
,
A.
,
2006
, “
A Hydroelasticity Method for Vibrating Structures Containing and/or Submerged in Flowing Fluid
,”
J. Sound Vib.
,
290
(
3–5
), pp.
572
596
.10.1016/j.jsv.2005.04.028
14.
Uğurlu
,
B.
, and
Ergin
,
A.
,
2008
, “
A Hydroelastic Investigation of Circular Cylindrical Shells-Containing Flowing Fluid With Different End Conditions
,”
J. Sound Vib.
,
318
(
4–5
), pp.
1291
1312
.10.1016/j.jsv.2008.05.006
15.
Firouz-Abadi
,
R. D.
,
Noorian
,
M. A.
, and
Haddadpour
,
H.
,
2010
, “
A Fluid-Structure Interaction Model for Stability Analysis of Shells Conveying Fluid
,”
J. Fluids Struct.
,
26
(
5
), pp.
747
763
.10.1016/j.jfluidstructs.2010.04.003
16.
Païdoussis
,
M. P.
,
Chan
,
S. P.
, and
Misra
,
A. K.
,
1984
, “
Dynamics and Stability of Coaxial Cylindrical Shells Containing Flowing Fluid
,”
J. Sound Vib.
,
97
(
2
), pp.
201
235
.10.1016/0022-460X(84)90319-5
17.
El Chebair
,
A.
,
Païdoussis
,
M. P.
, and
Misra
,
A. K.
,
1989
, “
Experimental Study of Annular-Flow-Induced Instabilities of Cylindrical Shells
,”
J. Fluids Struct.
,
3
(
4
), pp.
349
364
.10.1016/S0889-9746(89)80016-7
18.
Païdoussis
,
M. P.
,
Misra
,
A. K.
, and
Chan
,
S. P.
,
1985
, “
Dynamics and Stability of Coaxial Cylindrical Shells Conveying Viscous Fluid
,”
ASME J. Appl. Mech.
,
52
(
2
), pp.
389
396
.10.1115/1.3169059
19.
Amabili
,
M.
, and
Garziera
,
R.
,
2002
, “
Vibrations of Circular Cylindrical Shells With Nonuniform Constraints, Elastic Bed and Added Mass; Part II: Shells Containing or Immersed in Axial Flow
,”
J. Fluids Struct.
,
16
(
1
), pp.
31
51
.10.1006/jfls.2001.0402
20.
Païdoussis
,
M. P.
,
Nguyen
,
V. B.
, and
Misra
,
A. K.
,
1991
, “
A Theoretical Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Fluid
,”
J. Fluids Struct.
,
5
(
2
), pp.
127
164
.10.1016/0889-9746(91)90454-W
21.
Païdoussis
,
M. P.
,
Misra
,
A. K.
, and
Nguyen
,
V. B.
,
1992
, “
Internal- and Annular-Flow-Induced Instabilities of a Clamped–Clamped or Cantilevered Cylindrical Shell in a Coaxial Conduit: The Effects of System Parameters
,”
J. Sound Vib.
,
159
(
2
), pp.
193
205
.10.1016/0022-460X(92)90031-R
22.
Nguyen
,
V. B.
,
Païdoussis
,
M. P.
, and
Misra
,
A. K.
,
1994
, “
A CFD-Based Model for the Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Viscous Fluid
,”
J. Sound Vib.
,
176
(
1
), pp.
105
125
.10.1006/jsvi.1994.1361
23.
Nguyen
,
V. B.
,
Païdoussis
,
M. P.
, and
Misra
,
A. K.
,
1993
, “
An Experimental Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Fluid
,”
J. Fluids Struct.
,
7
(
8
), pp.
913
930
.10.1006/jfls.1993.1054
24.
Bochkarev
,
S. A.
, and
Matveenko
,
V. P.
,
2010
, “
The Dynamic Behaviour of Elastic Coaxial Cylindrical Shells Conveying Fluid
,”
J. Appl. Math. Mech.
,
74
(
4
), pp.
467
474
.10.1016/j.jappmathmech.2010.09.013
25.
Bochkarev
,
S. A.
, and
Matveenko
,
V. P.
,
2010
, “
Stability Analysis of Loaded Coaxial Cylindrical Shells With Internal Fluid Flow
,”
Mech. Sol.
,
45
(
6
), pp.
789
802
.10.3103/S002565441006004X
26.
Chen
,
Y.
,
Zhao
,
H. B.
,
Shen
,
Z. P.
,
Grieger
,
I.
, and
Kröplin
,
B.-H.
,
1993
, “
Vibrations of High Speed Rotating Shells With Calculations for Cylindrical Shells
,”
J. Sound Vib.
,
160
(
1
), pp.
137
160
.10.1006/jsvi.1993.1010
27.
Sivadas
,
K. R.
, and
Ganesan
,
N.
,
1994
, “
Effect of Rotation on Vibration of Moderarately Thick Circular Cylindrical Shells
,”
ASME J. Vib. Acoust.
,
116
(
1
), pp.
198
202
.10.1115/1.2930412
28.
Guo
,
D.
,
Zheng
,
Z.
, and
Chu
,
F.
,
2002
, “
Vibration Analysis of Spinning Cylindrical Shells by Finite Element Method
,”
Int. J. Solids Struct.
,
39
(
3
), pp.
725
739
.10.1016/S0020-7683(01)00031-2
29.
Dey
,
S.
, and
Karmakar
,
A.
,
2012
, “
Natural Frequencies of Delaminated Composite Rotating Conical Shells—A Finite Element Approach
,”
Finite Elem. Anal. Des.
,
56
, pp.
41
51
.10.1016/j.finel.2012.02.007
30.
Hua
,
L.
,
Lam
,
K. Y.
, and
Ng
,
T. Y.
,
2005
,
Rotating Shell Dynamics
,
Elsevier Academic
,
London, UK.
31.
Lai
,
Y.-C.
, and
Chow
,
C.-Y.
,
1973
, “
Stability of a Rotating Thin Elastic Tube Containing a Fluid Flow
,”
Z. Angew Math. Mech.
,
53
(
8
), pp.
511
517
.10.1002/zamm.19730530803
32.
Vorob'ev
,
Y. S.
, and
Detistov
,
S. I.
,
1985
, “
Effect of a Gas Flow on Vibrations of Rotating Cylindrical Shells
,”
Int. Appl. Mech.
,
21
(
7
), pp.
657
660
.10.1007/BF00888110
33.
Chen
,
T. L. C.
, and
Bert
,
C. W.
,
1977
, “
Wave Propagation in Isotropic- or Composite-Material Piping Conveying Swirling Liquid
,”
Nucl. Eng. Des.
,
42
(
2
), pp.
247
255
.10.1016/0029-5493(77)90186-8
34.
Chen
,
T. L. C.
, and
Bert
,
C. W.
,
1977
, “
Dynamic Stability of Isotropic or Composite Material Cylindrical Shells Containing Swirling Fluid Flow
,”
ASME J. Appl. Mech.
,
44
(
1
), pp.
112
116
.10.1115/1.3423973
35.
Bochkarev
,
S. A.
, and
Matveenko
,
V. P.
,
2011
, “
Natural Vibrations and Stability of a Stationary or Rotating Circular Cylindrical Shell Containing a Rotating Fluid
,”
Comput. Struct.
,
89
(
7–8
), pp.
571
580
.10.1016/j.compstruc.2010.12.016
36.
Cortelezzi
,
L.
,
Pong
,
A.
, and
Païdoussis
,
M. P.
,
2004
, “
Flutter of Rotating Shells With a Co-Rotating Axial Flow
,”
ASME J. Appl. Mech.
,
71
(
1
), pp.
143
145
.10.1115/1.1636794
37.
Bochkarev
,
S. A.
, and
Matveenko
,
V. P.
,
2013
, “
Numerical Analysis of Stability of a Stationary or Rotating Circular Cylindrical Shell Containing Axially Flowing and Rotating Fluid
,”
Int. J. Mech. Sci.
,
68
, pp.
258
269
.10.1016/j.ijmecsci.2013.01.024
38.
Srinivasan
,
A. V.
,
1971
, “
Flutter Analysis of Rotating Cylindrical Shells Immersed in a Circular Helical Flowfield of Air
,”
AIAA J.
,
9
(
3
), pp.
394
400
.10.2514/3.6193
39.
David
,
T. S.
, and
Srinivasan
,
A. V.
,
1974
, “
Flutter of Coaxial Cylindrical Shells in a Incompressible Axisymmetric Flow
,”
AIAA J.
,
12
(
12
), pp.
1631
1635
.10.2514/3.49571
40.
Bochkarev
,
S. A.
, and
Matveenko
,
V. P.
,
2013
, “
Stability of a Cylindrical Shell Subject to an Annular Flow of Rotating Fluid
,”
J. Sound Vib.
,
332
(
18
), pp.
4210
4222
.10.1016/j.jsv.2013.03.010
41.
Dowell
,
E. H.
,
Srinivasan
,
A. V.
,
McLean
,
J. D.
, and
Ambrose
,
J.
,
1974
, “
Aeroelastic Stability of Cylindrical Shells Subjected to a Rotating Flow
,”
AIAA J.
,
12
(
12
), pp.
1644
1651
.10.2514/3.49573
42.
McLean
,
J. D.
, and
Dowell
,
E. H.
,
1975
, “
Swirling Flows Between Coaxial Cylinders With Injection by Radial Jets
,”
AIAA J.
,
13
(
11
), pp.
1435
1440
.10.2514/3.7012
43.
Amabili
,
M.
,
Pellicano
,
F.
, and
Païdoussis
,
M. P.
,
2001
, “
Nonlinear Stability of Circular Cylindrical Shells in Annular and Unbounded Axial Flow
,”
ASME J. Appl. Mech.
,
68
(
6
), pp.
827
834
.10.1115/1.1406957
44.
Paak
,
M.
,
Païdoussis
,
M. P.
, and
Misra
,
A. K.
,
2013
, “
Nonlinear Dynamics and Stability of Cantilevered Circular Cylindrical Shells Conveying Fluid
,”
J. Sound Vib.
,
332
(
14
), pp.
3474
3498
.10.1016/j.jsv.2013.01.030
45.
Chen
,
C.
, and
Dai
,
L.
,
2009
, “
Nonlinear Vibration and Stability of a Rotary Truncated Conical Shell With Intercoupling of High- and Low-Order Modals
,”
Comm. Nonlinear Sci. Numer. Simul.
,
14
(
1
), pp.
254
269
.10.1016/j.cnsns.2007.06.007
46.
Liu
,
Y.
, and
Chu
,
F.
,
2012
, “
Nonlinear Vibrations of Rotating Thin Circular Cylindrical Shell
,”
Nonlinear Dyn.
,
67
(
2
), pp.
1467
1479
.10.1007/s11071-011-0082-7
47.
Alfutov
,
N. A.
,
Zinov'ev
,
P. A.
, and
Popov
,
B. G.
,
1984
,
Analysis of Multilayer Plates and Shells of Composite Materials
,
Izdatel'stvo Mashinosiroenie
,
Moscow, Russia
(in Russian).
48.
Matveenko
,
V. P.
,
1980
, “
On an Algorithm of Solving the Problem on Natural Vibrations of Elastic Bodies by the Finite Element Method
,”
Boundary-Value Problems of the Elasticity and Viscoelasticity Theory
, Ural Science Center, USSR Akad. Sci.,
Sverdlovsk
, Russia, pp.
20
24
(in Russian).
49.
Troyanovskii
,
I. Ye.
,
Shardakov
,
I. N.
, and
Shevelev
,
N. A.
,
1991
, “
The Problem of the Eigenvalues and Modes of Rotating Deformable Structures
,”
J. Appl. Math. Mech.
,
55
(
5
), pp.
733
740
.10.1016/0021-8928(91)90121-A
You do not currently have access to this content.