This literature review focuses mainly on geometrically nonlinear (finite amplitude) free and forced vibrations of circular cylindrical shells and panels, with and without fluid-structure interaction. Work on shells and curved panels of different geometries is but briefly discussed. In addition, studies dealing with particular dynamical problems involving finite deformations, eg, dynamic buckling, stability, and flutter of shells coupled to flowing fluids, are also discussed. This review is structured as follows: after a short introduction on some of the fundamentals of geometrically nonlinear theory of shells, vibrations of shells and panels in vacuo are discussed. Free and forced vibrations under radial harmonic excitation (Section 2.2), parametric excitation (axial tension or compression and pressure-induced excitations) (Section 2.3), and response to radial transient loads (Section 2.4) are reviewed separately. Studies on shells and panels in contact with dense fluids (liquids) follow; some of these studies present very interesting results using methods also suitable for shells and panels in vacuo. Then, in Section 4, shells and panels in contact with light fluids (gases) are treated, including the problem of stability (divergence and flutter) of circular cylindrical panels and shells coupled to flowing fluid. For shells coupled to flowing fluid, only the case of axial flow is reviewed in this paper. Finally, papers dealing with experiments are reviewed in Section 5. There are 356 references cited in this article.
Issue Section:
Review Articles
1.
Evensen DA (1974), Nonlinear vibrations of circular cylindrical shells, Thin-Shell Structures: Theory, Experiment and Design, YC Fung and EE Sechler (eds), Prentice-Hall, Englewood Cliffs, NY, 133–155.
2.
Leissa AW (1973), Vibration of Shells, NASA SP-288, Government Printing Office, Washington DC; Now available from The Acoustical Society of America (1993).
3.
Amabili
M
, Pellicano
F
, and Paı¨doussis
MP
(1998
), Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid
, J. Fluids Struct.
12
, 883
–918
.4.
Paı¨doussis MP (2003), Fluid-Structure Interactions: Slender Structures and Axial Flow, Vol 2, Elsevier/Academic Press, London, UK.
5.
Kubenko
VD
and Koval’chuk
PS
(1998
), Nonlinear problems of the vibration of thin shells (review
), International Applied Mechanics
34
, 703
–728
.1.
Kubenko
VD
and Koval’chuk
PS
(2000
), Nonlinear problems of the dynamics of elastic shells partially filled with a liquid
(in Russian), Oncologica
36
(4
), 3
–34
2.
(English version in
International Applied Mechanics
36
, 421
–448
).1.
Dowell
EH
(1970
), Panel flutter: A review of the aeroelastic stability of plates and shells
, AIAA J.
8
, 385
–399
.2.
Bismarck-Nasr
MN
(1992
), Finite element analysis of aeroelasticity of plates and shells
, Appl. Mech. Rev.
45
(12
), 461
–482
.3.
Mei
C
, Abdel-Motagaly
K
, and Chen
R
(1999
), Review of nonlinear panel flutter at supersonic and hypersonic speeds
, Appl. Mech. Rev.
52
(10
), 321
–332
.4.
Sathyamoorthy
M
(1987
), Nonlinear vibrations analysis of plates: a review and survey of current developments
, Appl. Mech. Rev.
40
(11
), 1553
–1561
.5.
Chia
CY
(1988
), Geometrically nonlinear behavior of composite plates: A review
, Appl. Mech. Rev.
41
(12
), 439
–451
.6.
Donnell
EH
(1934
), A new theory for the buckling of thin cylinders under axial compression and bending
, Trans. ASME
56
, 795
–806
.7.
von Ka´rma´n
T
and Tsien
HS
(1941
), The buckling of thin cylindrical shells under axial compression
, J. Aeronaut. Sci.
8
, 303
–312
.8.
Mushtari KHM and Galimov KZ (1957), Non-Linear Theory of Thin Elastic Shells, Academy of Sciences (Nauka), Kazan’ (English version, NASA-TT-F62 in 1961).
9.
Vorovich II (1999), Nonlinear Theory of Shallow Shells, Springer-Verlag, New York.
10.
Sanders
Jr LJ
(1963
), Nonlinear theories for thin shells
, Q. Appl. Math.
21
, 21
–36
.11.
Koiter
WT
(1966
), On the nonlinear theory of thin elastic shells
, Proc Koninklijke Nederlandse Akademie van Wetenschappen
B 69
, 1
–54
.12.
Budiansky
B
(1968
), Notes on nonlinear shell theory
, ASME J. Appl. Mech.
35
, 393
–401
.13.
Yamaki N (1984), Elastic Stability of Circular Cylindrical Shells, North-Holland, Amsterdam.
14.
Ginsberg
JH
(1973
), Large-amplitude forced vibrations of simply supported thin cylindrical shells
, ASME J. Appl. Mech.
40
, 471
–477
.15.
Novozhilov VV (1953), Foundations of the Nonlinear Theory of Elasticity, Graylock Press, Rochester, NY (now available from Dover, NY).
16.
Naghdi
M
and Nordgren
P
(1963
), On the nonlinear theory of elastic shells under the Kirchhoff hypothesis
, Q. Appl. Math.
21
, 49
–59
.17.
Libai A and Simmonds JG (1988), The Nonlinear Theory of Elastic Shells, Academic Press, London, UK.
18.
Reddy
JN
and Chandrashekhara
K
(1985
), Geometrically non-linear transient analysis of laminated, doubly curved shells
, Int. J. Non-Linear Mech.
20
, 79
–90
.19.
Reddy
JN
(1984
), Exact solutions of moderately thick laminated shells
, J. Eng. Mech.
110
, 794
–809
.20.
Librescu
L
(1987
), Refined geometrically non-linear theories of anisotropic laminated shells
, Q. Appl. Math.
45
, 1
–22
.21.
Tsai
CT
and Palazotto
AN
(1991
), On the finite element analysis of non-linear vibration for cylindrical shells with high-order shear deformation theory
, Int. J. Non-Linear Mech.
26
, 379
–388
.22.
Kobayashi
Y
and Leissa
AW
(1995
), Large-amplitude free vibration of thick shallow shells supported by shear diaphragms
, Int. J. Non-Linear Mech.
30
, 57
–66
.23.
Sansour
C
, Wriggers
P
, and Sansour
J
(1997
), Nonlinear dynamics of shells: theory, finite element formulation, and integration schemes
, Nonlinear Dyn.
13
, 279
–305
.24.
Gummadi
LNB
and Palazotto
AN
(1999
), Nonlinear dynamic finite element analysis of composite cylindrical shells considering large rotations
, AIAA J.
37
, 1489
–1494
.25.
Pai
PF
and Nayfeh
AH
(1994
), A unified nonlinear formulation for plate and shell theories
, Nonlinear Dyn.
6
, 459
–500
.26.
Dennis
ST
(1997
), A Galerkin solution to geometrically nonlinear laminated shallow shell equations
, Comput. Struct.
63
, 859
–874
.27.
Reissner E (1955), Nonlinear effects in vibrations of cylindrical shells, Ramo-Wooldridge Corp Report, AM 5–6.
28.
Grigolyuk
EI
(1955
), Vibrations of circular cylindrical panels subjected to finite deflections (in Russian
), Prikl. Mat. Mekh.
19
, 376
–382
.29.
Chu
HN
(1961
), Influence of large-amplitudes on flexural vibrations of a thin circular cylindrical shell
, J. Aerosp. Sci.
28
, 602
–609
.30.
Cummings
BE
(1964
), Large-amplitude vibration and response of curved panels
, AIAA J.
2
, 709
–716
.31.
Nowinski
J
(1963
), Nonlinear transverse vibrations of orthotropic cylindrical shells
, AIAA J.
1
, 617
–620
.32.
Evensen
DA
(1963
), Some observations on the nonlinear vibration of thin cylindrical shells
, AIAA J.
1
, 2857
–2858
.33.
Olson
MD
(1965
), Some experimental observations on the nonlinear vibration of cylindrical shells
, AIAA J.
3
, 1775
–1777
.34.
Kan˜a DD (1966), Interaction between liquid propellants and the elastic structure, The Dynamic Behavior of Liquids in Moving Containers, HN Abramson (ed), NASA-SP-106, Washington DC, Government Printing Office, 303–352.
35.
Kan˜a
DD
, Lindholm
US
, and Abramson
HN
(1966
), Experimental study of liquid instability in a vibrating elastic tank
, J. Spacecr. Rockets
3
, 1183
–1188
.36.
Evensen DA (1967), Nonlinear flexural vibrations of thin-walled circular cylinders, NASA TN D-4090.
37.
Evensen DA and Fulton E (1967), Some studies on the nonlinear dynamic response of shell-type structures, Proc of the Int Conf on Dynamic Stability of Structures, Evanston, IL, Oct 18–20 1965, Pergamon Press, 237–254.
38.
Evensen DA (1964), Non-linear flexural vibrations of thin circular rings, PhD Thesis, California Institute of Technology, Pasadena, CA.
39.
Evensen DA (1965), A theoretical and experimental study of nonlinear flexural vibrations of thin circular rings, NASA TR R-227, Washington, DC, Government Printing Office.
40.
Evensen
DA
(1966
), Nonlinear flexural vibrations of thin circular rings
, ASME J. Appl. Mech.
33
, 553
–560
.41.
Dowell
EH
(1967
), On the nonlinear flexural vibrations of rings
, AIAA J.
5
, 1508
–1509
.42.
Evensen
DA
(1968
), Nonlinear vibrations of an infinitely long cylindrical shell
, AIAA J.
6
, 1401
–1403
.43.
Evensen DA (2000), The influence of initial stress and boundary restraints on the nonlinear vibrations of cylindrical shells, Nonlinear Dynamics of Shells and Plates, MP Paı¨doussis, M Amabili, and PB Gonc¸alves (eds), ASME, New York, AMD 238, 47–59.
44.
Vol’mir AS (1956), Flexible Plates and Shells (in Russian), Gittl, Moscow.
1.
Agamirov
VL
and Vol’mir
AS
(1959
), Behavior of cylindrical shells under dynamic loading by hydrostatic pressure or by axial loading (in Russian
), Izvestiya Akademii Nauk SSSR, Ordelenie Tekhnicheskykh Nauk, Mekhanika i Mashinostroeni
3
, 78
–83
2.
(In English in 1961 by ARS Journal (
Journal of the American Rocket Society
) 31
, 98
–101
).1.
Paı¨doussis MP, Amabili M, and Gonc¸alves PB (eds) (2000), Nonlinear Dynamics of Shells and Plates, Proc of ASME Int Mechanical Engineering Congress and Exposition, ASME, New York, AMD 238.
2.
Mayers J and Wrenn BG (1967), On the nonlinear free vibrations of thin circular cylindrical shells, Developments in Mechanics, Proc of 10th Midwestern Mechanics Conf, 819–846.
3.
Matsuzaki
Y
and Kobayashi
S
(1969
), An analytical study of the nonlinear flexural vibration of thin circular cylindrical shells (in Japanese
), Journal of the Japan Society for Aeronautical and Space Sciences
17
, 308
–315
.4.
Matsuzaki
Y
and Kobayashi
S
(1969
), A theoretical and experimental study of the nonlinear flexural vibration of thin circular cylindrical shells with clamped ends
, Transactions of the Japan Society for Aeronautical and Space Sciences
12
, 55
–62
.5.
Dowell
EH
and Ventres
CS
(1968
), Modal equations for the nonlinear flexural vibrations of a cylindrical shell
, Int. J. Solids Struct.
4
, 975
–991
.6.
Atluri
S
(1972
), A perturbation analysis of non-linear free flexural vibrations of a circular cylindrical shell
, Int. J. Solids Struct.
8
, 549
–569
.7.
Dowell EH, Ventres CS, and Tang D (1998), Modal equations for the nonlinear flexural vibrations of a cylindrical shell, Duke Univ Research Report, DT 98-1.
8.
Evensen
DA
(1978
), Author’s reply
, J. Sound Vib.
56
, 305
–308
.9.
Evensen
DA
(1978
), Author’s reply
, J. Sound Vib.
60
, 597
–598
.10.
Dowell
EH
(1978
), Comments on non-linear flexural vibrations of a cylindrical shell
, J. Sound Vib.
60
, 596
–597
.11.
Varadan
TK
, Prathap
G
, and Ramani
HV
(1989
), Nonlinear free flexural vibration of thin circular cylindrical shells
, AIAA J.
27
, 1303
–1304
.12.
Amabili
M
, Pellicano
F
, and Paı¨doussis
MP
(1999
), Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, Part II: large-amplitude vibrations without flow
, J. Sound Vib.
228
, 1103
–1124
.13.
Amabili
M
, Pellicano
F
, and Paı¨doussis
MP
(2000
), Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, Part III: truncation effect without flow and experiments
, J. Sound Vib.
237
, 617
–640
.14.
Sun
CL
and Lu
SY
(1968
), Nonlinear dynamic behavior of heated conical and cylindrical shells
, Nucl. Eng. Des.
7
, 113
–122
.15.
Leissa
AW
and Kadi
AS
(1971
), Curvature effects on shallow shell vibrations
, J. Sound Vib.
16
, 173
–187
.16.
El-Zaouk
BR
and Dym
CL
(1973
), Non-linear vibrations of orthotropic doubly-curved shallow shells
, J. Sound Vib.
31
, 89
–103
.17.
Ginsberg
JH
(1974
), Nonlinear axisymmetric free vibration in simply supported cylindrical shells
, ASME J. Appl. Mech.
41
, 310
–311
.18.
Chen
JC
and Babcock
CD
(1975
), Nonlinear vibration of cylindrical shells
, AIAA J.
13
, 868
–876
.19.
Amabili
M
, Pellicano
F
, and Vakakis
AF
(2000
), Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, Part 1: Equations of motion and numerical results
, ASME J. Vibr. Acoust.
122
, 346
–354
.20.
Vol’mir
AS
, Logvinskaya
AA
, and Rogalevich
VV
(1973
), Nonlinear natural vibrations of rectangular plates and cylindrical panels
, Sov. Phys. Dokl.
17
, 720
–721
.21.
Radwan
H
and Genin
J
(1975
), Non-linear modal equations for thin elastic shells
, Int. J. Non-Linear Mech.
10
, 15
–29
.22.
Radwan
HR
and Genin
J
(1976
), Nonlinear vibrations of thin cylinders
, ASME J. Appl. Mech.
43
, 370
–372
.23.
Harari
A
(1976
), Generalized non-linear free vibrations of prestressed plates and shells
, Int. J. Non-Linear Mech.
11
, 169
–181
.24.
Raju
KK
and Rao
GV
(1976
), Large-amplitude asymmetric vibrations of some thin shells of revolution
, J. Sound Vib.
44
, 327
–333
.25.
Evensen
DA
(1977
), Comment on “Large-amplitude asymmetric vibrations of some thin shells of revolution
,” J. Sound Vib.
52
, 453
–454
.26.
Prathap
G
(1978
), Comments on the “Large-amplitude asymmetric vibrations of some thin shells of revolution
,” J. Sound Vib.
56
, 303
–305
.27.
Prathap
G
(1978
), On the large amplitude vibration of circular cylindrical shells
, J. Sound Vib.
59
, 295
–297
.28.
Evensen
DA
(1978
), Author’s reply
, J. Sound Vib.
59
, 297
–298
.29.
Ueda
T
(1979
), Non-linear free vibrations of conical shells
, J. Sound Vib.
64
, 85
–95
.30.
Bhattacharya
AP
(1976
), Nonlinear flexural vibrations of thin shallow translational shells
, ASME J. Appl. Mech.
43
, 180
–181
.31.
Ramachandran
J
and Murthy
PAK
(1976
), Non-linear vibrations of a shallow cylindrical panel on an elastic foundation
, J. Sound Vib.
47
, 495
–500
.32.
Massalas
C
and Kafousias
N
(1979
), Non-linear vibrations of a shallow cylindrical panel on a non-linear elastic foundation
, J. Sound Vib.
66
, 507
–512
.33.
Sinharay
GC
and Banerjee
B
(1985
), Large-amplitude free vibrations of shallow spherical shell and cylindrical shell—a new approach
, Int. J. Non-Linear Mech.
20
, 69
–78
.34.
Sinharay
GC
and Banerjee
B
(1986
), Large-amplitude free vibrations of shells of variable thickness—A new approach
, AIAA J.
24
, 998
–1004
.35.
Yamaki N (1982), Dynamic behavior of a thin-walled circular cylindrical shell, Developments in Thin-Walled Structures 1, J Rhodes and AC Walker (eds), Applied Science Publishers, London, 81–118.
36.
Maewal
A
(1986
), Miles’ evolution equations for axisymmetric shells: simple strange attractors in structural dynamics
, Int. J. Non-Linear Mech.
21
, 433
–438
.37.
Maewal
A
(1986
), Finite element analysis of steady nonlinear harmonic oscillations of axisymmetric shells
, Comput. Methods Appl. Mech. Eng.
58
, 37
–50
.38.
Nayfeh
AH
and Raouf
RA
(1987
), Non-linear oscillation of circular cylindrical shells
, Int. J. Solids Struct.
23
, 1625
–1638
.39.
Nayfeh
AH
and Raouf
RA
(1987
), Nonlinear forced response of infinitely long circular cylindrical shells
, ASME J. Appl. Mech.
54
, 571
–577
.40.
Raouf
RA
and Nayfeh
H
(1990
), One-to-one autoparametric resonances in infinitely long cylindrical shells
, Comput. Struct.
35
, 163
–173
.41.
Nayfeh
NH
, Raouf
RA
, and Nayfeh
JF
(1991
), Nonlinear response of infinitely long circular cylindrical shells to subharmonic radial loads
, ASME J. Appl. Mech.
58
, 1033
–1041
.42.
Gonc¸alves
PB
and Batista
RC
(1988
), Non-linear vibration analysis of fluid-filled cylindrical shells
, J. Sound Vib.
127
, 133
–143
.43.
Watawala
L
and Nash
WA
(1983
), Influence of initial geometric imperfections on vibrations of thin circular cylindrical shells
, Comput. Struct.
16
, 125
–130
.44.
Koval’chuk
PS
and Podchasov
NP
(1988
), Nonlinear flexural waves in cylindrical shells with periodic excitation
, Soviet Applied Mechanics
24
, 1086
–1090
.45.
Kubenko
VD
, Koval’chuk
PS
, and Krasnopol’skaya
TS
(1982
), Effect of initial camber on natural nonlinear vibrations of cylindrical shells
, Soviet Applied Mechanics
18
, 34
–39
.46.
Raouf
RA
and Palazotto
AN
(1991
), Nonlinear dynamic response of anisotropic, arbitrarily laminated shell panels: an asymptotic analysis
, Compos. Struct.
18
, 163
–192
.47.
Raouf
RA
and Palazotto
AN
(1992
), Non-linear free vibrations of symmetrically laminated, slightly compressible cylindrical shell panels
, Compos. Struct.
20
, 249
–257
.48.
Raouf
RA
(1993
), A qualitative analysis of the nonlinear dynamic characteristics of curved orthotropic panels
, Composites Engineering
3
, 1101
–1110
.49.
Raouf
RA
and Palazotto
AN
(1994
), On the non-linear free vibrations of curved orthotropic panels
, Int. J. Non-Linear Mech.
29
, 507
–514
.50.
Andrianov
IV
and Kholod
EG
(1993
), Non-linear free vibration of shallow cylindrical shell by Bolotin’s asymptotic method
, J. Sound Vib.
165
, 9
–17
.51.
Andrianov
IV
, Kholod
EG
, and Olevsky
VI
(1996
), Approximate non-linear boundary value problems of reinforced shell dynamics
, J. Sound Vib.
194
, 369
–387
.52.
Chiba
M
(1993
), Non-linear hydroelastic vibration of a cantilever cylindrical tank, I Experiment (Empty case
), Int. J. Non-Linear Mech.
28
, 591
–599
.53.
Koval’chuk
PS
and Lakiza
VD
(1995
), Experimental study of induced oscillations with large deflections of fiberglass shells of revolution
, International Applied Mechanics
31
, 923
–927
.54.
Thompson
JMT
and de Souza
JR
(1996
), Suppression of escape be resonant modal interactions: in shell vibration and heave-roll capsize
, Proc. R. Soc. London, Ser. A
452
, 2527
–2550
.55.
Ganapathi
M
and Varadan
TK
(1996
), Large-amplitude vibrations of circular cylindrical shells
, J. Sound Vib.
192
, 1
–14
.56.
Ganapathi
M
and Varadan
TK
(1995
), Nonlinear free flexural vibrations of laminated circular cylindrical shells
, Compos. Struct.
30
, 33
–49
.57.
Selmane
A
and Lakis
AA
(1997
), Influence of geometric non-linearities on free vibrations of orthotropic open cylindrical shells
, Int. J. Numer. Methods Eng.
, 40
, 1115
–1137
.58.
Lakis
AA
, Selmane
A
, and Toledano
A
(1998
), Non-linear free vibration analysis of laminated orthotropic cylindrical shells
, Int. J. Mech. Sci.
40
, 27
–49
.59.
Sansour
C
, Wagner
W
, Wriggers
P
, and Sansour
J
(2002
), An energy-momentum integration scheme and enhanced strain finite elements for the non-linear dynamics of shells
, Int. J. Non-Linear Mech.
, 37
, 951
–966
.60.
Amabili
M
, Pellicano
F
, and Paı¨doussis
MP
(1999
), Addendum to “Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid
,” J. Fluids Struct.
13
, 785
–788
.61.
Amabili
M
, Pellicano
F
, and Paı¨doussis
MP
(1999
), Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, Part I: Stability
, J. Sound Vib.
225
, 655
–699
.62.
Amabili
M
, Pellicano
F
, and Paı¨doussis
MP
(2000
), Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, Part IV: Large-amplitude vibrations with flow
, J. Sound Vib.
237
, 641
–666
.63.
Amabili
M
, Garziera
R
, and Negri
A
(2002
), Experimental study on large-amplitude vibrations of water-filled circular cylindrical shells
, J. Fluids Struct.
16
, 213
–227
.64.
Pellicano
F
, Amabili
M
, and Paı¨doussis
MP
(2002
), Effect of the geometry on the non-linear vibration of circular cylindrical shells
, Int. J. Non-Linear Mech.
37
, 1181
–1198
.65.
Amabili M (2003), Nonlinear vibrations of empty and fluid-filled, circular cylindrical shells with different boundary conditions, AIAA J. (in press).
66.
Pellicano
F
, Amabili
M
, and Vakakis
F
(2000
), Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, Part 2: perturbation analysis
, ASME J. Vibr. Acoust.
122
, 355
–364
.67.
McRobie
FA
, Popov
AA
, and Thompson
JMT
(1999
), Auto-parametric resonance in cylindrical shells using geometric averaging
, J. Sound Vib.
227
, 65
–84
.68.
Popov
AA
, Thompson
JMT
, and McRobie
FA
(2001
), Chaotic energy exchange through auto-parametric resonance in cylindrical shells
, J. Sound Vib.
248
, 395
–411
.69.
Popov
AA
, Thompson
JMT
, and McRobie
FA
(1998
), Low dimensional models of shell vibrations. Parametrically excited vibrations of cylindrical shells
, J. Sound Vib.
209
, 163
–186
.70.
Laing
CR
, McRobie
A
, and Thompson
JMT
(1999
), The post-processed Galerkin method applied to non-linear shell vibrations
, Dyn. Stab. Syst.
14
, 163
–181
.71.
Foale
S
, Thompson
JMT
, and McRobie
FA
(1998
), Numerical dimension-reduction methods for non-linear shell vibrations
, J. Sound Vib.
215
, 527
–545
.72.
Kubenko VD and Koval’chuk PS (2000), Problems of nonlinear multiple-mode vibrations of thin elastic shells of revolution, Nonlinear Dynamics of Shells and Plates, MP Paı¨doussis, M Amabili, and PB Gonc¸alves (eds), ASME, New York, AMD 238, 147–153.
73.
Amiro
IY
and Prokopenko
NY
(1999
), Study of nonlinear vibrations of cylindrical shells with allowance for energy dissipation
, International Applied Mechanics
35
, 134
–139
.74.
Yamaguchi
T
and Nagai
K
(1997
), Chaotic vibration of a cylindrical shell-panel with an in-plane elastic-support at boundary
, Nonlinear Dyn.
13
, 259
–277
.75.
Nagai K and Yamaguchi T (1995), Chaotic oscillations of a shallow cylindrical shell with rectangular boundary under cyclic excitation, ASME Proc, New York, PVP 297, 107–115.
76.
Yamaguchi T and Nagai K (2000), Chaotic oscillations of a shallow cylindrical shell-panel with a concentrated elastic-support, Nonlinear Dynamics of Shells and Plates, MP Paı¨doussis, M Amabili, and PB Gonc¸alves (eds), ASME, New York, AMD 238, 85–94.
77.
Nagai K, Yamaguchi T, and Murata T (2001), Chaotic oscillations of a cylindrical shell-panel with concentrated mass under gravity and cyclic load, Proc of the 3rd Int Symp on Vibration of Continuous Systems, July 23–27, Grand Teton National Park, WY, 49–51.
78.
Shin
DK
(1997
), Large amplitude free vibration behavior of doubly curved shallow open shells with simply-supported edges
, Comput. Struct.
62
, 35
–49
.79.
Abe
A
, Kobayashi
Y
, and Yamada
G
(2000
), Non-linear vibration characteristics of clamped laminated shallow shells
, J. Sound Vib.
234
, 405
–426
.80.
Mao
R
and Williams
FW
(1998
), Post-critical behavior of orthotropic circular cylindrical shells under time dependent axial compression
, J. Sound Vib.
210
, 307
–327
.81.
Mao
R
and Williams
FW
(1998
), Nonlinear analysis of cross-ply thick cylindrical shells under axial compression
, Int. J. Solids Struct.
35
, 2151
–2171
.82.
Han
Q
, Hu
H
, and Yang
G
(2000
), A study of chaotic motion in elastic cylindrical shells
, Eur. J. Mech. A/Solids
18
, 351
–360
.83.
Gunawan L (1998), Experimental study of nonlinear vibrations of thin-walled cylindrical shells, PhD Thesis, Technische Univ Delft, The Netherlands.
84.
Mikhlin YV (2000), Stability of regular or chaotic post-buckling vibration of elastic shells, Nonlinear Dynamics of Shells and Plates, MP Paı¨doussis, M Amabili, and P B Gonc¸alves (eds), ASME, New York, AMD 238, 95–103.
85.
Lee
Y-S
and Kim
Y-W
(1999
), Nonlinear free vibration analysis of rotating hybrid cylindrical shells
, Comput. Struct.
70
, 161
–168
.86.
Moussaoui
F
, Benamar
R
, and White
RG
(2000
), The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic shells, Part I: Coupled transverse-circumferential mode shapes of isotropic circular cylindrical shells of infinite length
, J. Sound Vib.
232
, 917
–943
.87.
Nayfeh
JF
and Rivieccio
NJ
(2000
), Nonlinear vibration of composite shell subjected to resonant excitations
, Journal of Aerospace Engineering
13
(2
), 59
–68
.88.
Jansen
EL
(2002
), Non-stationary flexural vibration behavior of a cylindrical shell
, Int. J. Non-Linear Mech.
37
, 937
–949
.89.
Jansen EL (2001), Nonlinear vibration analysis of composite cylindrical shells using semi-analytical formulation, Proc of the 42th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf, Seattle, WA (AIAA paper 2001-1314), 1–10.
90.
Amabili
M
, Pellegrini
M
, and Tommesani
M
(2003
) Experiments on large-amplitude vibrations of a circular cylindrical panel
, J. Sound Vib.
260
, 537
–547
.91.
Hu
KK
and Kirmser
PG
(1971
), Non-linear beam-type vibrations of long cylindrical shells
, ASME J. Appl. Mech.
38
, 461
–466
.92.
Birman
V
and Bert
CW
(1987
), Non-linear beam-type vibrations of long cylindrical shells
, Int. J. Non-Linear Mech.
22
, 327
–334
.93.
Birman
V
and Twinprawate
P
(1988
), Free nonlinear vibrations of statically loaded long cylindrical shells
, Journal of Applied Mathematics and Physics (ZAMP)
39
, 768
–775
.94.
Likhoded
AI
(1976
), Nonlinear vibrations of shells of revolution with concentrated masses
, Mech. Solids
11
, 127
–132
.95.
Paliwal
DA
and Bhalla
V
(1993
), Large amplitude free vibrations of cylindrical shell on Pasternak foundations
, Int. J. Pressure Vessels Piping
54
, 387
–398
.96.
Dowell
EH
(1998
), Comments on the nonlinear vibrations of cylindrical shells
, J. Fluids Struct.
12
, 1087
–1089
.97.
Amabili
M
, Pellicano
F
, and Paı¨doussis
MP
(1999
), Further comments on the non-linear vibrations of cylindrical shells
, J. Fluids Struct.
13
, 159
–160
.98.
Evensen
DA
(1999
), Non-linear vibrations of cylindrical shells: Logical rationale
, J. Fluids Struct.
13
, 161
–164
.99.
Amabili M (2003), Comparison of different shell theories for large-amplitude vibrations of empty and fluid-filled circular cylindrical shells with and without imperfections: Lagrangian approach, J. Sound Vib. (in press).
100.
Koiter
WT
(1963
), The effect of axisymmetric imperfections on the buckling of cylindrical shells under axial compression
, Proc Koninklijke Nederlandse Akademie van Wetenschappen
B 66
, 265
–279
.101.
Hutchinson
J
(1965
), Axial buckling of pressurized imperfect cylindrical shells
, AIAA J.
3
, 1461
–1466
.102.
Vol’mir AS (1972), Nonlinear Dynamics of Plates and Shells (in Russian), Academy of Sciences (Nauka), Moscow.
1.
Kil’dibekov
IG
(1977
), Investigation of the characteristic nonlinear oscillations of a cylindrical shell (in Russian
), Prikl. Mekh.
13
(11
), 46
–52
2.
(English version in
Soviet Applied Mechanics
13
, 1109
–1114
).1.
Koval’chuk
PS
and Krasnopol’skaya
TS
(1980
), Resonance phenomena in nonlinear vibrations of cylindrical shells with initial imperfections
, Soviet Applied Mechanics
15
, 867
–872
.2.
Hui
D
(1984
), Influence of geometric imperfections and in-plane constraints on non-linear vibrations of simply supported cylindrical panels
, ASME J. Appl. Mech.
51
, 383
–390
.3.
Jansen EL (1992), Nonlinear vibrations of imperfect composite cylindrical shells, Proc of 17th Int Seminar on Modal Analysis, Katholieke Uni-Leuven, Leuven, 3, 1463–1479.
4.
Chia
CY
(1987
), Non-linear free vibration and postbuckling of symmetrically laminated orthotropic imperfect shallow cylindrical panels with two adjacent edges simply supported and the other edges clamped
, Int. J. Solids Struct.
23
, 1123
–1132
.5.
Chia
CY
(1987
), Nonlinear vibration and postbuckling of unsymmetrically laminated imperfect shallow cylindrical panels with mixed boundary conditions resting on elastic foundation
, Int. J. Eng. Sci.
25
, 427
–441
.6.
Chia
CY
(1988
), Nonlinear analysis of doubly curved symmetrically laminated shallow shells with rectangular platform
, Ingenieur Archiv
58
, 252
–264
.7.
Iu
VP
and Chia
CY
(1988
), Effect of transverse shear on nonlinear vibration and postbuckling of anti-symmetric cross-ply imperfect cylindrical shells
, Int. J. Mech. Sci.
30
, 705
–718
.8.
Fu
YM
and Chia
CY
(1989
), Multi-mode non-linear vibration and postbuckling of anti-symmetric imperfect angle-ply cylindrical thick panels
, Int. J. Non-Linear Mech.
24
, 365
–381
.9.
Iu
VP
and Chia
CY
(1988
), Non-linear vibration and postbuckling of unsymmetric cross-ply circular cylindrical shells
, Int. J. Solids Struct.
24
, 195
–210
.10.
Fu
YM
and Chia
CY
(1993
), Non-linear vibration and postbuckling of generally laminated circular cylindrical thick shells with non-uniform boundary conditions
, Int. J. Non-Linear Mech.
28
, 313
–327
.11.
Elishakoff
I
, Birman
V
, and Singer
J
(1987
), Small vibrations of an imperfect panel in the vicinity of a non-linear static state
, J. Sound Vib.
114
, 57
–63
.12.
Librescu
L
and Chang
M-Y
(1993
), Effects of geometric imperfections on vibration of compressed shear deformable laminated composite curved panels
, Acta Mech.
96
, 203
–224
.13.
Librescu
L
, Lin
W
, Nemeth
MP
, and Starnes
Jr. JH
(1996
), Vibration of geometrically imperfect panels subjected to thermal and mechanical loads
, J. Spacecr. Rockets
33
, 285
–291
.14.
Librescu
L
and Lin
W
(1997
), Vibration of thermomechanically loaded flat and curved panels taking into account geometric imperfections and tangential edge restraints
, Int. J. Solids Struct.
34
, 2161
–2181
.15.
Hause
T
, Librescu
L
, and Johnson
TF
(1998
), Non-linear response of geometrically imperfect sandwich curved panels under thermomechanical loading
, Int. J. Non-Linear Mech.
33
, 1039
–1059
.16.
Librescu
L
and Lin
W
(1997
), Postbuckling and vibration of shear deformable flat and curved panels on a non-linear elastic foundation
, Int. J. Non-Linear Mech.
326
, 211
–225
.17.
Librescu
L
and Lin
W
(1999
), Non-linear response of laminated plates and shells to thermomechanical loading: implications of violation of interlaminar shear traction continuity requirement
, J. Solids Struct.
36
, 4111
–4147
.18.
Cheikh
L
, Pauchon
C
, Lamarque
CH
, Combescure
A
, and Gibert
J
(1996
), Nonlinear stability of a defective cylindrical shell
, Mech. Res. Commun.
23
, 151
–164
.19.
Amabili M (2003), Theory and experiments for large-amplitude vibrations of empty and fluid-filled circular cylindrical shells with imperfections, J. Sound Vib. (in press).
20.
Maewal
A
(1978
), Nonlinear flexural vibration of an elastic ring
, ASME J. Appl. Mech.
45
, 428
–429
.21.
Maewal
A
(1981
), Nonlinear harmonic oscillations of gyroscopic structural systems and the case of a rotating ring
, ASME J. Appl. Mech.
48
, 627
–633
.22.
Simmonds
JG
(1979
), Accurate nonlinear equations and a perturbation solution for the free vibrations of a circular elastic ring
, ASME J. Appl. Mech.
46
, 156
–160
.23.
Prathap
G
and Pandalai
KAV
(1978
), The role of meridian surface curvature in large amplitude flexural vibrations of thin shells
, J. Sound Vib.
60
, 119
–131
.24.
Gershtein
MS
(1985
), Vibrations of an elastic multilayer ring with large amplitudes (in Russian
), Prikl. Mekh.
21
, 119
–123
.25.
Maganty
SP
and Bickford
WB
(1987
), Large amplitude oscillations of thin circular rings
, ASME J. Appl. Mech.
54
, 315
–322
.26.
Maganty
SP
and Bickford
WB
(1988
), Influence of internal resonance on the non-linear oscillations of a circular ring under primary resonance conditions
, J. Sound Vib.
122
, 507
–521
.27.
Kovriguine
DA
and Potapov
AI
(1998
), Nonlinear oscillations in a thin ring; I. Three-wave resonant interactions
, Acta Mech.
126
, 189
–200
.28.
Kovriguine
DA
and Potapov
AI
(1998
), Nonlinear oscillations in a thin ring, II: Four-wave resonant interactions. Self-modulation
, Acta Mech.
126
, 189
–200
.29.
Natsiavas
S
and Theodossiades
S
(1998
), Regular and chaotic vibration of thin rotating rings
, Int. J. Non-Linear Mech.
33
, 843
–855
.30.
Grossman
PL
, Koplik
B
, and Yu
YY
(1969
), Nonlinear vibrations of shallow spherical shells
, ASME J. Appl. Mech.
36
, 451
–458
.31.
Varadan
TK
and Pandalai
KAV
(1978
), Nonlinear flexural oscillations of orthotropic shallow spherical shells
, Comput. Struct.
9
, 417
–425
.32.
Hui
D
(1983
), Large-amplitude vibrations of geometrically imperfect shallow spherical shells with structural damping
, AIAA J.
21
, 1736
–1741
.33.
Hui
D
(1990
), Accurate backbone curves for a modified-Duffing equation for vibrations of imperfect structures with viscous damping
, ASME J. Vib., Acoust., Stress, Reliab. Des.
112
, 304
–311
.34.
Yasuda
K
and Kushida
G
(1984
), Nonlinear forced oscillations of a shallow spherical shell
, Bull. JSME
27
, 2233
–2240
.35.
Coleby
JR
and Mazumdar
J
(1989
), Nonlinear forced vibrations of shallow shells on regular polygonal bases
, J. Acoust. Soc. Am.
85
, 1577
–1589
.36.
Karaesmen
E
, Ileri
L
, and Akkas
N
(1992
), Chaotic dynamic analysis of viscoelastic shallow spherical shells
, Comput. Struct.
44
, 851
–857
.37.
Chia
CY
and Chia
DS
(1992
), Nonlinear vibration of moderately thick antisymmetric angle-ply shallow spherical shell
, Comput. Struct.
44
, 797
–805
.38.
Xu
CS
and Chia
CY
(1992
), Nonlinear vibration of symmetrically laminated spherical caps with flexible supports
, Acta Mech.
94
, 59
–72
.39.
Xu
CS
and Chia
CY
(1992
), Non-linear analysis of unsymmetrically laminated moderately thick shallow spherical shells
, Int. J. Non-Linear Mech.
29
, 247
–259
.40.
Li
D
(1993
), A time-mode approach to nonlinear vibrations of orthotropic thin shallow spherical shells
, Int. J. Solids Struct.
30
, 3113
–3128
.41.
Sathyamoorthy
M
(1994
), Vibrations of moderately thick shallow spherical shells at large amplitudes
, J. Sound Vib.
172
, 63
–70
.42.
Sathyamoorthy
M
(1995
), Nonlinear vibrations of moderately thick orthotropic shallow spherical shells
, Comput. Struct.
57
, 59
–65
.43.
Cheung
YK
and Fu
YM
(1995
), Nonlinear static and dynamic analysis for laminated, annular, spherical caps of moderate thickness
, Nonlinear Dyn.
8
, 251
–268
.44.
Gonc¸alves
PB
(1993
), Jump phenomena, bifurcations, and chaos in a pressure loaded spherical cap under harmonic excitation
, Appl. Mech. Rev.
46
, (supplement), S279–S288
S279–S288
.45.
Gonc¸alves
PB
(1994
), Axisymmetric vibrations of imperfect shallow spherical caps under pressure loading
, J. Sound Vib.
174
, 249
–260
.46.
Gonc¸alves PB (1999), The complex non-linear dynamics of imperfection sensitive shells, Proc of IUTAM Symp on New Applications of Non-Linear and Chaotic Dynamics and Mechanics, Kluwer, 173–180.
47.
Ramachandran
J
(1976
), Large amplitude vibrations of shallow spherical shell with concentrated mass
, ASME J. Appl. Mech.
43
, 363
–365
.48.
Nath
Y
, Mahrenholtz
O
, and Varma
KK
(1987
), Non-linear dynamic response of a doubly curved shallow shell on an elastic foundation
, J. Sound Vib.
112
, 53
–61
.49.
Xu
CS
(1992
), Multi-mode nonlinear vibration and large deflection of symmetrically laminated imperfect spherical caps on elastic foundations
, Int. J. Mech. Sci.
34
, 459
–474
.50.
Paliwal
DA
and Bhalla
V
(1993
), Large amplitude free vibration of shallow spherical shell on a Pasternak foundation
, J. Vibr. Acoust.
115
, 70
–74
.51.
Mandal
UK
and Biswas
P
(1999
), Nonlinear thermal vibrations on elastic shallow spherical shell under linear and parabolic temperature distributions
, ASME J. Appl. Mech.
66
, 814
–815
.52.
Zhou
YH
and Tzou
HS
(2000
), Active control of nonlinear piezoelectric circular shallow spherical shells
, Int. J. Solids Struct.
37
, 1663
–1677
.53.
Liu
RH
and Li
J
(1995
), Non-linear vibration of shallow conical sandwich shells
, Int. J. Non-Linear Mech.
30
, 97
–109
.54.
Xu
CS
, Xia
ZQ
, and Chia
CY
(1996
), Non-linear theory and vibration analysis of laminated truncated, thick, conical shells
, Int. J. Non-Linear Mech.
31
, 139
–154
.55.
Fu
YM
and Chen
CP
(2001
), Non-linear vibration of elastic truncated conical moderately thick shells in large overall motion
, Int. J. Non-Linear Mech.
36
, 763
–771
.56.
Ye
ZM
(1997
), The non-linear vibration and dynamic instability of thin shallow shells
, J. Sound Vib.
202
, 303
–311
.57.
Wang
YG
, Wang
XZ
, and Song
HF
(1997
), Nonlinear free vibration of orthotropic shallow shells of revolution under the static loads
, Appl. Math. Mech.
18
, 585
–591
.58.
Singh
AV
(2000
), Linear and geometrically nonlinear vibrations of fiber reinforced laminated plates and shallow shells
, Comput. Struct.
76
, 277
–285
.59.
Ohnabe
H
(1995
), Non-linear vibration of heated orthotropic sandwich plates and shallow shells
, Int. J. Non-Linear Mech.
30
, 501
–508
.60.
Nie
G
(1994
), Non-linear vibration of rectangular reticulated shallow shell structures
, Appl. Math. Mech.
15
, 525
–535
.61.
Goodier
JN
and McIvor
IK
(1964
), The elastic cylindrical shell under nearly uniform radial impulse
, ASME J. Appl. Mech.
31
, 259
–266
.62.
McIvor
IK
and Lovell
EG
(1968
), Dynamic response of finite-length cylindrical shells to nearly uniform radical impulse
, AIAA J.
6
, 2346
–2351
.63.
Lovell
EG
and McIvor
IK
(1969
), Nonlinear response of a cylindrical shell to an impulsive pressure
, ASME J. Appl. Mech.
36
, 277
–284
.64.
Hsu CS (1974), On parametric excitation and snap-through stability problems of shells, Thin-Shell Structures: Theory, Experiment and Design, YC Fung and EE Sechler (eds), Prentice-Hall, Englewood Cliffs, NJ, 103–131.
65.
Lam
KY
and Ng
TY
(1997
), Dynamic stability of cylindrical shells subjected to conservative periodic axial loads using different shell theories
, J. Sound Vib.
207
, 497
–520
.66.
Babcock
CD
(1983
), Shell stability
, ASME J. Appl. Mech.
50
, 935
–940
.67.
Teng
JG
(1996
), Buckling of thin shells: Recent advances and trends
, Appl. Mech. Rev.
49
(4
), 263
–274
.68.
Hutchinson
J
(1974
), Plastic buckling
, Adv. Appl. Mech.
14
, 67
–143
.69.
Le Grognec P and Le Van A (2000), Buckling and post-buckling of thin elastoplastic cylindrical shells with finite rotations, Nonlinear Dynamics of Shells and Plates, MP Paı¨doussis, M Amabili, and PB Gonc¸alves (eds), ASME, New York, AMD 238, 137–146.
70.
Ross
CTF
, Gill-Carson
A
, and Little
APF
(2000
), The inelastic buckling of varying thickness circular cylinders under external hydrostatic pressure
, Structural Engineering and Mechanics
9
, 51
–68
.71.
Yao
JC
(1963
), Dynamic stability of cylindrical shells under static and periodic axial and radial loads
, AIAA J.
1
, 1391
–1396
.72.
Yao
JC
(1965
), Nonlinear elastic buckling and parametric excitation of a cylinder under axial load
, ASME J. Appl. Mech.
32
, 109
–115
.73.
Roth
RS
and Klosner
JM
(1964
), Nonlinear response of cylindrical shells subjected to dynamic axial load
, AIAA J.
2
, 1788
–1794
.74.
Vijayaraghavan
A
and Evan-Iwanowski
RM
(1967
), Parametric instability of circular cylindrical shells
, ASME J. Appl. Mech.
34
, 985
–990
.75.
Kan˜a
DD
and Craig
Jr. RR
(1968
), Parametric oscillations of a longitudinally excited cylindrical shell containing liquid
, J. Spacecr. Rockets
5
, 13
–21
.76.
Obraztsova
EI
(1976
), Nonlinear parametric oscillations of cylindrical shell with liquid under longitudinal excitation
, Soviet Aeronautics
19
(3
), 63
–67
.77.
Vol’mir
AS
and Ponomarev
AT
(1973
), Nonlinear parametric vibrations of cylindrical shells made of composite materials (in Russian
), Mekh. Polim.
3
, 531
–539
.78.
Tamura
YS
and Babcock
CD
(1975
), Dynamic stability of cylindrical shells under step loading
, ASME J. Appl. Mech.
42
, 190
–194
.79.
Nagai
K
and Yamaki
N
(1978
), Dynamic stability of circular cylindrical shells under periodic compressive forces
, J. Sound Vib.
58
, 425
–441
.1.
Bogdanovich
AE
and Feldmane
EG
(1980
), Nonlinear parametric vibrations of viscoelastic orthotropic cylindrical shells (in Russian
), Prikl. Mekh.
16
(4
), 49
–55
2.
(English version in
Soviet Applied Mechanics
16
, 305
–309
).1.
Bondarenko
AA
and Galaka
PI
(1977
), Parametric instability of cylindrical glass-plastic cylindrical shells (in Russian
), Prikl. Mekh.
13
(4
), 124
–128
2.
(English version in
Soviet Applied Mechanics
13
, 411
–414
).1.
Bondarenko
AA
, and Telalov
AI
(1982
), Dynamic instability of cylindrical shells subjected to longitudinal kinematic perturbations (in Russian
), Prikl. Mekh.
18
(1
), 57
–61
2.
(English version in
Soviet Applied Mechanics
18
(1
), 45
–49
).1.
Gotsulyak
EA
, Gulyaev
VI
, Dekhtyaryuk
ES
, and Kirichuk
AA
(1982
), Stability of nonlinear vibrations of shells of revolution (in Russian
), Prikl. Mekh.
18
, 50
–56
2.
(English version in
Soviet Applied Mechanics
18
, 526
–532
).1.
Birman
V
(1988
), Parametric vibrations of long cylindrical shells subject to transverse static load
, Int. J. Mech. Sci.
30
, 613
–623
.2.
Kovtunov
VB
(1993
), Dynamic stability and nonlinear parametric vibration of cylindrical shells
, Comput. Struct.
46
, 149
–156
.3.
Kubenko VD, Koval’chuk PS, and Krasnopol’skaya TS (1984), Nonlinear Interaction of Modes of Flexural Vibration of Cylindrical Shells (in Russian), Naukova Dumka, Kiev.
4.
Baumgarten
R
, Kreuzer
E
, and Popov
AA
(1997
), A bifurcation analysis of the dynamics of a simplified shell model
, Nonlinear Dyn.
12
, 307
–317
.5.
Popov
AA
, Thompson
JMT
, and Croll
JGA
(1998
), Bifurcation analyses in the parametrically excited vibrations of cylindrical panels
, Nonlinear Dyn.
17
, 205
–225
.6.
Gonc¸alves PB and Del Prado ZJGN (2000), The role of modal coupling on the non-linear response of cylindrical shells subjected to dynamic axial loads, Nonlinear Dynamics of Shells and Plates, MP Paı¨doussis, M Amabili, and PB Gonc¸alves (eds), ASME, New York, AMD 238, 105–116.
7.
Ng
CF
(1989
), Nonlinear and snap-through responses of curved panels to intense acoustic excitation
, J. Aircr.
26
, 281
–288
.8.
Koval
LR
(1974
), Effect of longitudinal resonance on the parametric stability of an axially excited cylindrical shell
, J. Acoust. Soc. Am.
55
, 91
–97
.9.
Greenberg
JB
and Stavsky
Y
(1980
), Buckling and vibration of orthotropic composite cylindrical shells
, Acta Mech.
36
, 15
–29
.10.
Bert
CW
and Birman
V
(1988
), Parametric instability of thick, orthotropic, circular cylindrical shells
, Acta Mech.
71
, 61
–76
.11.
Argento
A
and Scott
RA
(1993
), Dynamic instability of layered anisotropic circular cylindrical shells, Part I: Theoretical developments
, J. Sound Vib.
162
, 311
–322
.12.
Argento
A
and Scott
RA
(1993
), Dynamic instability of layered anisotropic circular cylindrical shells, Part II: Numerical results
, J. Sound Vib.
162
, 323
–332
.13.
Argento
A
(1993
), Dynamic stability of a composite circular cylindrical shells subjected to combined axial and torsional loading
, J. Compos. Mater.
27
, 1722
–1738
.14.
Bhatia
P
and Babcock
CD
(1974
), Axial buckling of cylindrical shells with prismatic imperfections
, ASME J. Appl. Mech.
41
, 731
–736
.15.
Ovenshire
LJ
and McIvor
IK
(1971
), On the dynamic snap-through of a shallow cylindrical shell subjected to nearly symmetric impulsive loading
, Int. J. Solids Struct.
7
, 585
–601
.16.
Ovenshire
LJ
and McIvor
IK
(1972
), Conditions for the existence of dynamic snap-through of a shallow cylindrical shell under impulsive loading
, Int. J. Non-Linear Mech.
7
, 19
–29
.17.
Mente
LJ
(1973
), Dynamic nonlinear response of cylindrical shells to asymmetric pressure loading
, AIAA J.
11
, 793
–800
.18.
Simitses GJ (1990), Dynamic Stability of Suddenly Loaded Structures, Springer-Verlag, Berlin.
19.
Jiang
EJ
and Olson
MD
(1991
), Nonlinear dynamic analysis of blast loaded cylindrical shell structures
, Comput. Struct.
41
, 41
–52
.20.
Witmer
EA
, Balmer
HA
, Leech
JW
, and Pian
THH
(1963
), Large dynamic deformations of beams, rings, plates and shells
, AIAA J.
1
, 1848
–1857
.21.
Leech
JW
, Witmer
EA
, and Pian
THH
(1968
), Numerical calculation technique for large elastic-plastic transient deformations of thin shells
, AIAA J.
6
, 2352
–2359
.22.
Morino
L
, Leech
JW
, and Witmer
EA
(1971
), An improved numerical calculation technique for large elastic-plastic transient deformations of thin shells. Part 1—Background and theoretical formulation
, ASME J. Appl. Mech.
38
, 423
–428
.23.
Morino
L
, Leech
JW
, and Witmer
EA
(1971
), An improved numerical calculation technique for large elastic-plastic transient deformations of thin shells. Part 2—Evaluation and applications
, ASME J. Appl. Mech.
38
, 429
–436
.24.
Clough
RC
and Wilson
EL
(1971
), Dynamic finite element analysis of arbitrary thin shells
, Comput. Struct.
1
, 33
–56
.25.
Belytschko
T
and Marchertas
AH
(1974
), Nonlinear finite element method for plates and its application to the dynamic response of reactor fuel subassemblies
, ASME J. Pressure Vessel Technol.
96
, 251
–257
.26.
Bathe
KJ
, Ramm
E
, and Wilson
EL
(1975
), Finite element formulations for large deformation dynamic analysis
, Int. J. Numer. Methods Eng.
9
, 353
–386
.27.
Saigal
S
and Yang
TY
(1985
), Nonlinear dynamic analysis with a 48 DOF curved thin shell element
, Int. J. Numer. Methods Eng.
21
, 1115
–1128
.28.
Wu
YC
, Yang
TY
, and Saigal
S
(1987
), Free and forced nonlinear dynamics of composite shell structures
, J. Compos. Mater.
21
, 898
–909
.29.
Gendy
AS
and Saleeb
AF
(2000
), Nonlinear dynamics for mixed shells with large rotation and elastoplasticity
, International Journal of Computational Engineering Science
1
, 1
–31
.30.
Chien
LS
and Palazotto
AN
(1992
), Nonlinear snapping considerations for laminated cylindrical panels
, Composites Engineering
2
, 631
–639
.31.
Greer
JM
and Palazotto
AN
(1995
), Nonlinear dynamics of simple shell model with chaotic snapping behavior
, J. Eng. Mech.
121
, 753
–761
.32.
Greer
JM
and Palazotto
AN
(1994
), Some nonlinear response charac-teristics of collapsing composite shells
, AIAA J.
32
, 1935
–1938
.33.
Forral
AE
and Palazotto
AN
(1994
), A finite element model considering nonlinear dynamically loaded composite plates and shells
, International Journal for Engineering Analysis and Design
1
, 379
–393
.34.
Palazotto AN and Dennis ST (1992), Nonlinear Analysis of Shell Structures, AIAA, Washington DC.
35.
Palazotto
AN
, Perry
R
, and Sandhu
R
(1992
), Impact response of graphite/epoxy cylindrical panels
, AIAA J.
30
, 1827
–1832
.36.
Raouf
RA
and Palazotto
AN
(1996
), Nonlinear analysis of pressurized spinning fiber-reinforced tori
, AIAA J.
34
, 2596
–2603
.37.
Raouf
RA
and Palazotto
AN
(1996
), Nonlinear dynamics of unidirectional, fiber-reinforced tori
, J. Eng. Mech.
122
, 271
–276
.38.
Naboulsi
SK
, Palazotto
AN
, and Greer
JM
(2000
), Static-dynamic analyses of toroidal shells
, Journal of Aerospace Engineering
13
, 110
–121
.39.
Byun
C
and Kapanaia
RK
(1992
), Nonlinear transient response of imperfect hyperbolic shells using a reduction method
, Comput. Struct.
44
, 255
–262
.40.
Simo
JC
and Tarnow
N
(1994
), A new energy and momentum conserving algorithm for the non-linear dynamics of shells
, Int. J. Non-Linear Mech.
37
, 2527
–2549
.41.
Belytschko
T
, Lin
JI
, and Tsay
CS
(1984
), Explicit algorithms for the nonlinear dynamics of shells
, Comput. Methods Appl. Mech. Eng.
42
, 225
–251
.42.
Kuhl
D
and Ramm
E
(1996
), Constraint energy momentum algorithm and its application to non-linear dynamics of shells
, Comput. Methods Appl. Mech. Eng.
136
, 293
–315
.43.
Brank
B
, Briseghella
L
, Tonello
N
, and Damjani
FB
(1998
), On non-linear dynamics of shells: implementation of energy-momentum conserving algorithm for a finite rotation shell model
, Int. J. Non-Linear Mech.
42
, 409
–442
.44.
Belytschko
T
, Wong
BLL
, and Plaskacz
EJ
(1989
), Fission-fusion adaptivity in finite elements for nonlinear dynamics of shells
, Comput. Struct.
33
, 1307
–1323
.45.
Lee
SH
and Belytschko
T
(1995
), H-adaptive methods for nonlinear dynamic analysis of shell structures
, Shock and Vibration
2
, 193
–204
.46.
El Damatty
AA
, Korol
RM
, and Mirza
FA
(1997
), Large displacement extension of consistent shell element for static and dynamic analysis
, Comput. Struct.
62
, 943
–960
.47.
Chang
TP
and Chang
HC
(2000
), Nonlinear vibration analysis of geometrically nonlinear shell structures
, Mech. Res. Commun.
27
, 173
–180
.48.
Meek
JL
and Wang
Y
(1998
), Nonlinear static and dynamic analysis of shell structures with finite rotation
, Comput. Methods Appl. Mech. Eng.
162
, 301
–315
.49.
Lau
SL
and Cheung
YK
(1986
), Incremental Hamilton’s principle with multiple time scales for nonlinear aperiodic vibrations of shells
, ASME J. Appl. Mech.
53
, 465
–466
.50.
Kumar
V
and Singh
AV
(1997
), Geometrically non-linear dynamic analysis of laminated shells using Be´zier functions
, Int. J. Non-Linear Mech.
32
, 425
–442
.51.
Goncharenko
VM
(1962
), Investigation of probability of snapping through of long cylindrical shell under random pressure (in Russian
), Prikl. Mat. Mekh.
26
, 740
–744
.52.
Vol’mir AS and Kil’dibekov IG (1968), Probabilistic characteristics of behavior of shallow shells in an acoustic field, (in Russian), Proc of 2nd USSR Conf on the Reliability Problems in Structural Mechanics, 169–174.
53.
Vol’mir
AS
and Kul’terbaev
KP
(1974
), Stochastic stability of forced nonlinear shell vibrations
, J. Appl. Math. Mech.
38
, 840
–846
.1.
Kil’dibekov
IG
(1978
), Nonlinear vibrations and bulging of a cylindrical shell upon strong acoustical excitations (in Russian
), Prikl. Mekh.
14
, 43
–48
2.
(English version in
Soviet Applied Mechanics,
(1979
) 14
, 704
–708
).1.
Kil’dibekov IG (1971), Vibrations of circular cylindrical shell under axial compression and acoustic pressure, (in Russian), Proc of 3rd USSR Conf on the Reliability Problems in Structural Mechanics, 58–63.
2.
Dogan
V
and Vaicaitis
R
(1999
), Nonlinear response of cylindrical shells to random excitation
, Nonlinear Dyn.
20
, 33
–53
.3.
Dogan
V
and Vaicaitis
R
(1999
), Active control of nonlinear cylindrical shell vibrations under random excitation
, J. Intell. Mater. Syst. Struct.
10
, 422
–429
.4.
Shkenev S (1964), The dynamics of an elastic and elastoplastic shell filled with an ideal liquid, Proc of IV All-Union Conf on the Theory of Shells and Plates, Nauka, Moscow, 997–1007.
5.
Abramson HN and Kan˜a DD (1966), Some recent research on the vibrations of elastic shells containing liquids, Proc of Symp on the Theory of Shells, Univ of Houston, TX, 253–310.
6.
Chu
WH
and Kan˜a
D
(1967
), A theory for nonlinear transverse vibrations of a partially filled elastic tank
, AIAA J.
5
, 1828
–1835
.7.
Vol’mir AS (1976), Shells in Flow of Liquid and Gas: Problems of Hydroelasticity (in Russian), Academy of Sciences (Nauka), Moscow.
8.
Vol’mir AS (1979), Shells in Flow of Gas and Liquid: Problems of Hydroelasticity (in Russian), Academy of Sciences (Nauka), Moscow.
9.
Ramachandran
J
(1979
), Non-linear vibrations of cylindrical shells of varying thickness in an incompressible fluid
, J. Sound Vib.
64
, 97
–106
.10.
Geers
TL
and Yen
CL
(1981
), Nonlinear response of an elastic cylindrical shell to a transient acoustic wave
, ASME J. Appl. Mech.
48
, 15
–24
.11.
Boyarshina
LG
(1984
), Resonance effects in the nonlinear vibrations of cylindrical shells containing a liquid
, Soviet Applied Mechanics
20
, 765
–770
.12.
Boyarshina
LG
(1988
), Nonlinear wave modes of an elastic cylindrical shell partially filled with a liquid under conditions of resonance
, Soviet Applied Mechanics
24
, 528
–534
.13.
Chiba
M
, Tani
J
, Hashimoto
H
, and Sudo
S
(1986
), Dynamic stability of liquid-filled cylindrical shells under horizontal excitation, Part I: Experiment
, J. Sound Vib.
104
, 301
–319
.14.
Chiba
M
, Tani
J
, and Yamaki
N
(1987
), Dynamic stability of liquid-filled cylindrical shells under vertical excitation, Part I: Experimental results
, Earthquake Eng. Struct. Dyn.
15
, 23
–36
.15.
Chiba
M
and Tani
J
(1987
), Dynamic stability of liquid-filled cylindrical shells under vertical excitation, Part II: Theoretical results
, Earthquake Eng. Struct. Dyn.
15
, 37
–51
.16.
Gonc¸alves PB (1987), Non-linear dynamic interaction between fluid and thin shells. PhD Thesis, COPPE-Federal Univ of Rio de Janeiro, Brasil (in Portuguese).
17.
Krasnopol’skaya
TS
and Lavrov
KA
(1988
), Nonlinear oscillations of a cylindrical shell with a fluid subject to bounded excitations
, Soviet Applied Mechanics
24
, 1079
–1086
.18.
Sivak
VF
and Telalov
AI
(1991
), Experimental investigation of vibrations of a cylindrical shell in contact with a liquid
, Soviet Applied Mechanics
27
, 484
–488
.19.
Chiba
M
(1993
), Non-linear hydroelastic vibration of a cantilever cylindrical tank, II Experiment (Liquid-filled case
), Int. J. Non-Linear Mech.
28
, 601
–612
.20.
Chiba
M
(1993
), Experimental studies on a nonlinear hydroelastic vibration of a clamped cylindrical tank partially filled with liquid
, ASME J. Pressure Vessel Technol.
115
, 381
–388
.21.
Sivak
VF
(2000
), Experimental investigation of the nonlinear resonance properties of cylindrical shells (in Russian
), Prikl. Mekh.
36
(2
), 111
–114
.22.
Selmane
A
and Lakis
AA
(1997
), Non-linear dynamic analysis of orthotropic open cylindrical shells subjected to a flowing fluid
, J. Sound Vib.
202
, 67
–93
.23.
Lakis
AA
and Selmane
A
(2000
), Hybrid finite element analysis of large amplitude vibration of orthotropic open and closed cylindrical shells subjected to a flowing fluid
, Nucl. Eng. Des.
196
, 1
–15
.24.
Lakis
AA
and Laveau
A
(1991
), Non-linear dynamic analysis of anisotropic cylindrical shells containing a flowing fluid
, Int. J. Solids Struct.
28
, 1079
–1094
.25.
Amabili
M
, Pellicano
F
, and Paı¨doussis
MP
(2001
), Non-linear stability of circular cylindrical shells in annular and unbounded axial flow
, ASME J. Appl. Mech.
68
, 827
–834
.26.
Amabili
M
, Pellicano
F
, and Paı¨doussis
MP
(2002
), Non-linear dynamics and stability of circular cylindrical shells conveying flowing fluid
, Comput. Struct.
80
, 899
–906
.27.
Kubenko
VD
and Lakiza
VD
(2000
), Vibration effects of the dynamic interaction between a gas-liquid medium and elastic shells
, International Applied Mechanics
36
, 896
–902
.28.
Koval’chuk
PS
and Kruk
LA
(2000
), Nonlinear energy interchange between natural modes of freely vibrating circular cylindrical shells filled with liquid
, International Applied Mechanics
36
, 103
–110
.29.
Heil
M
and Pedley
TJ
(1995
), Large axisymmetric deformations of a cylindrical shell conveying a viscous flow
, J. Fluids Struct.
9
, 237
–256
.30.
Heil
M
(1996
), The stability of cylindrical shells conveying viscous flow
, J. Fluids Struct.
10
, 173
–196
.31.
Greffet N and Combescure A (2000), Coupled fluid-structure simulation: instability problems under viscous flows, Proc of 7th Int Conf on Flow-Induced Vibrations, Balkema, Rotterdam, The Netherlands, 311–318.
32.
Bathe M and Kamm RD (2001), Fluid-structure interaction analysis in biomechanics, Proc of 1st MIT Conf on Computational Fluid and Solid Mechanics, Elsevier, Amsterdam, The Netherlands, 2, 1068–1072.
33.
Librescu
L
(1965
), Aeroelastic stability of orthotropic heterogeneous thin panels in the vicinity of the flutter critical boundary, Part I: Simply supported panels
, J. Mec.
4
, 51
–76
.34.
Librescu
L
(1967
), Aeroelastic stability of orthotropic heterogeneous thin panels in the vicinity of the flutter critical boundary, Part II
, J. Mec.
6
, 133
–152
.35.
Librescu L (1975), Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Noordhoff, Leiden, The Netherlands.
36.
Olson
MD
and Fung
YC
(1967
), Comparing theory and experiment for the supersonic flutter of circular cylindrical shells
, AIAA J.
5
, 1849
–1856
.37.
Evensen DA and Olson MD (1967), Nonlinear flutter of a circular cylindrical shell in supersonic flow, NASA TN D-4265.
38.
Evensen
DA
and Olson
MD
(1968
), Circumferentially travelling wave flutter of a circular cylindrical shell
, AIAA J.
6
, 1522
–1527
.39.
Olsson
U
(1978
), Supersonic flutter of heated circular cylindrical shells with temperature-dependent material properties
, AIAA J.
16
, 360
–362
.40.
Carter
LL
and Stearman
RO
(1968
), Some aspects of cylindrical shell panel flutter
, AIAA J.
6
, 37
–43
.41.
Barr
GW
and Stearman
RO
(1969
), Aeroelastic stability characteristics of cylindrical shells considering imperfections and edge constraint
, AIAA J.
7
, 912
–919
.42.
Barr
GW
and Stearman
RO
(1970
), Influence of a supersonic flowfield on the elastic stability of cylindrical shells
, AIAA J.
8
, 993
–1000
.43.
Bolotin VV (1963), Nonconservative Problems of the Theory of Elastic Stability, MacMillan, New York.
44.
Dowell
EH
(1966
), Nonlinear oscillations of a fluttering plate
, AIAA J.
4
, 1267
–1275
.45.
Dowell
EH
(1967
), Nonlinear oscillations of a fluttering plate II
, AIAA J.
5
, 1856
–1862
.46.
Ventres
CS
and Dowell
EH
(1970
), Comparison of theory and experiment for non-linear flutter of loaded plates
, AIAA J.
8
, 2022
–2030
.47.
Dowell
EH
(1969
), Nonlinear flutter of curved plates
, AIAA J.
7
, 424
–431
.48.
Dowell
EH
(1970
), Nonlinear flutter of curved plates, II
, AIAA J.
8
, 259
–261
.49.
Anderson WJ (1962), Experiments on the flutter of flat and slightly curved panels at Mach number 2.81, AFOSR TN 2996, Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, California.
50.
Vol’mir
AS
and Medvedeva
SV
(1973
), Investigation of the flutter of cylindrical panels in a supersonic gas flow
, Sov. Phys. Dokl.
17
, 1213
–1214
.51.
Vol’mir
AS
, Nisht
MI
and Ponomarev
AT
(1976
), Nonlinear vibrations of a plate and cylindrical panel during stalled nonsteady flow
, Soviet Applied Mechanics
12
(1
), 8
–12
.52.
Krause H and Dinkler D (1998), The influence of curvature on supersonic panel flutter, Proc of 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf, Long Beach, CA, (AIAA paper 98-1841), 1234–1240.
53.
Amabili
M
and Pellicano
F
(2001
), Nonlinear supersonic flutter of circular cylindrical shells
, AIAA J.
39
, 564
–573
.54.
Amabili
M
and Pellicano
F
(2002
), Multi-mode approach to nonlinear supersonic flutter of imperfect circular cylindrical shells
, ASME J. Appl. Mech.
69
, 117
–129
.55.
Olson
MD
and Fung
YC
(1966
), Supersonic flutter of circular cylindrical shells subjected to internal pressure and axial compression
, AIAA J.
4
, 858
–864
.56.
Dowell EH (1975), Aeroelasticity of Plates and Shells, Noordhoff Int, Leyden.
57.
Dowell EH and Ilgamov M (1988), Studies in Nonlinear Aeroelasticity, Springer-Verlag, New York.
58.
Bein T, Friedmann PP, Zhong X, and Nydick I (1993), Hypersonic flutter of a curved shallow panel with aerodynamic heating, Proc of 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf, April 19–22, La Jolla, CA, 1–15 (AIAA paper 93-1318).
59.
Nydick I, Friedmann PP, and Zhong X (1995), Hypersonic panel flutter studies on curved panels, Proc of the 36th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf, April 10–13, New Orleans, (AIAA paper 95-1485-CP), 5, 2995–3011.
60.
Heyman
W
and Lasiecka
I
(1999
), Asymptotic behavior of solutions to nonlinear shells in a supersonic flow
, Numerical Functional Analysis and Optimization
20
, 279
–300
.61.
Engineer
JC
and Abrahams
ID
(1994
), The radiation of sound waves from a lightly loaded finite elastic shell II: non-linear shell resonances
, J. Sound Vib.
174
, 353
–377
.62.
Horn
W
, Barr
GW
, Carter
L
, and Stearman
O
(1974
), Recent contributions to experiments on cylindrical shell panel flutter
, AIAA J.
12
, 1481
–1490
.63.
El Chebair
A
, Paı¨doussis
MP
, and Misra
AK
(1989
), Experimental study of annular-flow-induced instabilities of cylindrical shells
, J. Fluids Struct.
3
, 349
–364
.64.
Paı¨doussis
MP
and Denise
JP
(1972
), Flutter of thin cylindrical shells conveying fluid
, J. Sound Vib.
20
, 9
–26
.65.
Nguyen
VB
, Paı¨doussis
MP
, and Misra
AK
(1993
), An experimental study of the stability of cantilevered coaxial cylindrical shells conveying fluid
, J. Fluids Struct.
7
, 913
–930
. Copyright © 2003
by ASME
You do not currently have access to this content.
