A new analytical and numerical method is presented for modeling and analysis of cylindrical shells stiffened by circumferential rings. This method treats the shell and ring stiffeners as individual structural components, and considers the ring eccentricity with respect to the shell middle surface. Through use of the distributed transfer functions of the structural components, various static and dynamic problems of stiffened shells are systematically formulated. With this transfer function formulation, the static and dynamic response, natural frequencies and mode shapes, and buckling loads of general stiffened cylindrical shells under arbitrary external excitations and boundary conditions can be determined in exact and closed form. The proposed method is illustrated on a Donnell-Mushtari shell, and compared with finite element method and two other modeling techniques.

Issue Section:
Technical Papers
Topics:
Pipes, Shells, Modeling, Structural elements (Construction), Transfer functions, Boundary-value problems, Buckling, Dynamic response, Excitation, Finite element methods, Mode shapes, Numerical analysis, Stress
1.
Al-Najafi
A. M.
, and
Warburton
G. B.
,
1970
, “
Free Vibration of Ring-Stiffened Cylindrical Shells
,”
Journal of Sound and Vibration
, Vol.
13
, No.
1
, pp.
9
–
25
.
2.
Deskos
D. E.
, and
Oates
J. B.
,
1981
, “
Dynamic Analysis of Ring-Stiffened Circular Cylindrical Shells
,”
Journal of Sound and Vibration
, Vol.
75
, No.
1
, pp.
1
–
15
.
3.
Egle
D. M.
, and
Sewall
J. L.
,
1968
, “
An Analysis of Free Vibration of Orthogonally Stiffened Cylindrical Shells with Stiffeners Treated as Discrete Elements
,”
AIAA Journal
, Vol.
6
, No.
3
, pp.
518
–
526
.
4.
Frosberg, K., 1969, “Exact Solution For Natural Frequencies of Ring-Stiffened Cylinders,” AIAA/ASME 10th Structures, Structural Dynamics and Materials Conference, Volume on Structures and Materials, pp. 18–30.
5.
Garnet, H., and Goldberg, M. A., 1962, “Free Vibrations of Ring-Stiffened Shells,” RE-156, Grumman Aircraft Research.
6.
Godzevich, V. G., and Ivanova, O. V., 1965, “Free Oscillations of Circular Conical and Cylindrical Shell Reinforced by Rigid Circular Ribs,” TTF-291, NASA.
7.
Huntington
D. E.
, and
Lyrintzis
C. S.
,
1992
, “
Dynamics of Skin-Stringer Panels Using Modified Wave Methods
,”
AIAA Journal
, Vol.
30
, No.
11
, pp.
2765
–
2773
.
8.
Markus, S., 1989, The Mechanics of Vibrations of Cylindrical Shells, Elsevier, Amsterdam.
9.
Mead
D. J.
, and
Bardell
N. S.
,
1987
, “
Free Vibration of a Thin Cylindrical Shell with Periodic Circumferential Stiffeners
,”
Journal of Sound and Vibration
, Vol.
115
, No.
3
, pp.
499
–
520
.
10.
Reddy
B. D.
,
1980
, “
Buckling of Elastic-Plastic Discretely Stiffened Cylinders in Axial Compression
,”
International Journal of Solid and Structures
, Vol.
16
, pp.
313
–
328
.
11.
Rigo
P.
,
1992
, “
Stiffened Sheathings of Orthotropic Cylindrical Shells
,”
Journal of Structural Engineering
, Vol.
118
, No.
4
, pp.
926
–
943
.
12.
Schnell, W., and Heinrichsbauer, F. J., 1964, “The Determination of Free Vibrations of Longitudinally Stiffened Thin-Walled Circular Shells,” TTF-8856, NASA.
13.
Soedel, W., 1981, Vibrations of Shells and Plates, Marcel Dekker, New York.
14.
Sridharan
S.
,
Zeggane
M.
, and
Starnes
J. H.
,
1992
, “
Postbuckling Response of Stiffened Composite Cylindrical Shells
,”
AIAA Journal
, Vol.
30
, No.
12
, pp.
2897
–
2905
.
15.
Wang
J. T. S.
,
1970
, “
Orthogonally Stiffened Cylindrical Shells Subjected to Internal Pressure
,”
AIAA Journal
, Vol.
8
, No.
3
, pp.
455
–
461
.
16.
Wang
J. T. S.
, and
Lin
Y. J.
,
1973
, “
Stability of Discretely Stringer-Stiffened Cylindrical Shells
,”
AIAA Journal
, Vol.
11
, No.
6
, pp.
810
–
813
.
17.
Wang
J. T. S.
, and
Rinehart
S. A.
,
1974
, “
Free Vibrations of Longitudinally Stiffened Cylindrical Shells
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
41
, No.
4
, pp.
1087
–
1093
.
18.
Wang
J. T. S.
, and
Hsu
T. M.
,
1985
, “
Discrete Analysis of Stiffened Composite Cylindrical Shells
,”
AIAA Journal
, Vol.
23
, No.
11
, pp.
1753
–
1761
.
19.
Wilken
I. D.
, and
Soedel
W.
,
1976
, “
The Receptance Method Applied to Ring-Stiffened Cylindrical Shells: Analysis of Model Characteristics
,”
Journal of Sound and Vibration
, Vol.
44
, No.
4
, pp.
563
–
576
.
20.
Yang
B.
,
1992
, “
Transfer Functions of Constrained/Combined One-Dimensional Continuous Dynamic Systems
,”
Journal of Sound and Vibration
, Vol.
156
, No.
3
, pp.
425
–
443
.
21.
Yang
B.
, and
Tan
C. A.
,
1992
, “
Transfer Functions of One Dimensional Distributed Parameter Systems
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
59
, No.
4
, pp.
1009
–
1014
.
22.
Yang
B.
,
1994
, “
Distributed Transfer Function Analysis of Complex Distributed Parameter Systems
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
61
, No.
1
, pp.
84
–
92
.
23.
Zhou
J.
, and
Yang
B.
,
1995
, “
A Distributed Transfer Function Method for Analysis of Cylindrical Shells
,”
AlAA Journal
, Vol.
33
, No.
9
, pp.
1698
–
1708
.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.