The free vibration analysis of rotating ring-stiffened cylindrical shells with arbitrary boundary conditions is investigated by employing the Rayleigh–Ritz method. Six sets of characteristic orthogonal polynomials satisfying six classical boundary conditions are constructed directly by employing Gram–Schmidt procedure and then are employed to represent the general formulations for the displacements in any axial mode of free vibrations for shells. Employing those formulations during the Rayleigh–Ritz procedure and based on Sanders' shell theory, the eigenvalue equations related to rotating ring-stiffened cylindrical shells with various classical boundary conditions have been derived. To simulate more general boundaries, the concept of artificial springs is employed and the eigenvalue equations related to free vibration of shells under elastic boundary conditions are derived. By adjusting the stiffness of artificial springs, those equations can be used to investigate the vibrational characteristics of shells with arbitrary boundaries. By comparing with the available analytical results for the ring-stiffened cylindrical shells and the rotating shell without stiffeners, the method proposed in this paper is verified. Strong convergence is also observed from convergence study. Further, the effects of parameters, such as the stiffness of artificial springs, the rotating speed of the ring-stiffened shell, the number of ring stiffeners and the depth to width ratio of ring stiffeners, on the natural frequencies are studied.

References

References
1.
Mikulas
,
M. M.
, and
McElman
,
J. A.
,
1965
,
On Free Vibrations of Eccentrically Stiffened Cylindrical Shells and Flat Plates
,
NASA TN D-3010
,
Washington, DC.
2.
Wah
,
T.
, and
Hu
,
W. C. L.
,
1968
, “
Vibration Analysis of Stiffened Cylinders Including Inter-Ring Motion
,”
J. Acoust. Soc. Am.
,
43
(
5
), pp.
1005
1016
.10.1121/1.1910933
3.
Zhao
,
X.
,
Liew
,
K. M.
, and
Ng
,
T. Y.
,
2002
, “
Vibrations of Rotating Cross-Ply Laminated Circular Cylindrical Shells With Stringer and Ring Stiffeners
,”
Int. J. Solids Struct.
,
39
(
2
), pp.
529
545
.10.1016/S0020-7683(01)00194-9
4.
Stanley
,
A. J.
, and
Ganesan
,
N.
,
1997
, “
Free Vibration Characteristics of Stiffened Cylindrical Shells
,”
Comput. Struct.
,
65
(
1
), pp.
33
45
.10.1016/S0045-7949(96)00115-0
5.
Forsberg
,
K.
,
1969
, “
Exact Solution for Natural Frequencies of Ring-Stiffened Cylinders
,”
AIAA/ASME 10th Structures, Structural Dynamics and Materials Conference, New Orleans, LA, ASME Volume on Structures and Materials
, pp.
18
30
.
6.
Wilken
, I
. D.
, and
Soedel
,
W.
,
1976
, “
The Receptance Method Applied to Ring-Stiffened Cylindrical Shells: Analysis of Modal Characteristics
,”
J. Sound Vib.
,
44
(
4
), pp.
563
576
.10.1016/0022-460X(76)90097-3
7.
Wilken
, I
. D.
, and
Soedel
,
W.
,
1976
, “
Simplified Prediction of the Modal Characteristics of Ring-Stiffened Cylindrical Shells
,”
J. Sound Vib.
,
44
(
4
), pp.
577
589
.10.1016/0022-460X(76)90098-5
8.
Huang
,
S. C.
, and
Soedel
,
W.
,
1988
, “
On the Forced Vibration of Simply Supported Rotating Cylindrical Shells
,”
J. Acoust. Soc. Am.
,
84
(
1
), pp.
275
285
.10.1121/1.396974
9.
Huang
,
S. C.
, and
Hsu
,
B. S.
,
1992
, “
Vibration of Spinning Ring-Stiffened Thin Cylindrical Shells
,”
AIAA J.
,
30
(
9
), pp.
2291
2298
.10.2514/3.11217
10.
Zhang
,
X. M.
,
Liu
,
G. R.
, and
Lam
,
K. Y.
,
2001
, “
Vibration Analysis of Thin Cylindrical Shells Using Wave Propagation Approach
,”
J. Sound Vib.
,
239
(
3
), pp.
397
403
.10.1006/jsvi.2000.3139
11.
Gan
,
L.
,
Li
,
X.
, and
Zhang
,
Z.
,
2009
, “
Free Vibration Analysis of Ring-Stiffened Cylindrical Shells Using Wave Propagation Approach
,”
J. Sound Vib.
,
326
(
3
), pp.
633
646
.10.1016/j.jsv.2009.05.001
12.
Galletly
,
G. D.
,
1954
, “
On the In-Vacuo Vibrations of Simply Supported, Ring-Stiffened Cylindrical Shells
,”
Proceedings of the 2nd U.S. National Congress of Applied Mechanics
, Ann Arbor, MI, June 14–18, pp.
225
231
.
13.
Lee
,
Y. S.
, and
Kim
,
Y. W.
,
1998
, “
Vibration Analysis of Rotating Composite Cylindrical Shells With Orthogonal Stiffeners
,”
Comput. Struct.
,
69
(
2
), pp.
271
281
.10.1016/S0045-7949(97)00047-3
14.
Lee
,
Y. S.
, and
Kim
,
Y. W.
,
1999
, “
Effect of Boundary Conditions on Natural Frequencies for Rotating Composite Cylindrical Shells With Orthogonal Stiffeners
,”
Adv. Eng. Softw.
,
30
(
9
), pp.
649
655
.10.1016/S0965-9978(98)00115-X
15.
Wang
,
R. T.
, and
Lin
,
Z. X.
,
2006
, “
Vibration Analysis of Ring-Stiffened Cross-Ply Laminated Cylindrical Shells
,”
J. Sound Vib.
,
295
(
3
), pp.
964
987
.10.1016/j.jsv.2006.01.061
16.
Jafari
,
A. A.
, and
Bagheri
,
M.
,
2006
, “
Free Vibration of Non-Uniformly Ring Stiffened Cylindrical Shells Using Analytical, Experimental and Numerical Methods
,”
Thin Wall. Struct.
,
44
(
1
), pp.
82
90
.10.1016/j.tws.2005.08.008
17.
Jafari
,
A. A.
, and
Bagheri
,
M.
,
2006
, “
Free Vibration of Rotating Ring Stiffened Cylindrical Shells With Non-Uniform Stiffener Distribution
,”
J. Sound Vib.
,
296
(
1
), pp.
353
367
.10.1016/j.jsv.2006.03.001
18.
Bagheri
,
M.
,
Jafari
,
A. A.
, and
Sadeghifar
,
M.
,
2011
, “
Multi-Objective Optimization of Ring Stiffened Cylindrical Shells Using a Genetic Algorithm
,”
J. Sound Vib.
,
330
(
3
), pp.
374
384
.10.1016/j.jsv.2010.08.019
19.
Bagheri
,
M.
,
Jafari
,
A. A.
, and
Sadeghifar
,
M.
,
2011
, “
A Genetic Algorithm Optimization of Ring-Stiffened Cylindrical Shells for Axial and Radial Buckling Loads
,”
Arch. Appl. Mech.
,
81
(
11
), pp.
1639
1649
.10.1007/s00419-011-0507-2
20.
Sharma
,
C. B.
, and
Johns
,
D. J.
,
1971
, “
Vibration Characteristics of a Clamped-Free and Clamped-Ring-Stiffened Circular Cylindrical Shell
,”
J. Sound Vib.
,
14
(
4
), pp.
459
474
.10.1016/0022-460X(71)90575-X
21.
Naeem
,
M. N.
,
Kanwal
,
S.
,
Shah
,
A. G.
,
Arshad
,
S. H.
, and
Mahmood
,
T.
,
2012
, “
Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells
,”
ISRN Mechanical Engineering
,
2012
, p.
232498
10.5402/2012/232498
22.
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
23.
Hua
,
L.
, and
Lam
,
K. Y.
,
1998
, “
Frequency Characteristics of a Thin Rotating Cylindrical Shell Using the Generalized Differential Quadrature Method
,”
Int. J. Mech. Sci.
,
40
(
5
), pp.
443
459
.10.1016/S0020-7403(97)00057-X
24.
Liew
,
K. M.
,
Ng
,
T. Y.
,
Zhao
,
X.
, and
Reddy
,
J. N.
,
2002
, “
Harmonic Reproducing Kernel Particle Method for Free Vibration Analysis of Rotating Cylindrical Shells
,”
Comput. Meth. Appl. Mech. Eng.
,
191
(
37
), pp.
4141
4157
.10.1016/S0045-7825(02)00358-4
25.
Civalek
,
Ö.
,
2007
, “
Numerical Analysis of Free Vibrations of Laminated Composite Conical and Cylindrical Shells: Discrete Singular Convolution (DSC) Approach
,”
J. Comput. Appl. Math.
,
205
(
1
), pp.
251
271
.10.1016/j.cam.2006.05.001
26.
Civalek
,
Ö.
,
2007
, “
A Parametric Study of the Free Vibration Analysis of Rotating Laminated Cylindrical Shells Using the Method of Discrete Singular Convolution
,”
Thin Wall. Struct.
,
45
(
7
), pp.
692
698
.10.1016/j.tws.2007.05.004
27.
Chung
,
H.
,
1981
, “
Free Vibration Analysis of Circular Cylindrical Shells
,”
J. Sound Vib.
,
74
(
3
), pp.
331
350
.10.1016/0022-460X(81)90303-5
28.
Sun
,
S.
,
Chu
,
S.
, and
Cao
,
D.
,
2012
, “
Vibration Characteristics of Thin Rotating Cylindrical Shells With Various Boundary Conditions
,”
J. Sound Vib.
,
331
(
18
), pp.
4170
4186
.10.1016/j.jsv.2012.04.018
29.
Sun
,
S.
,
Cao
,
D.
, and
Han
,
Q.
,
2013
, “
Vibration Studies of Rotating Cylindrical Shells With Arbitrary Edges Using Characteristic Orthogonal Polynomials in the Rayleigh–Ritz Method
,”
Int. J. Mech. Sci.
,
68
, pp.
180
189
.10.1016/j.ijmecsci.2013.01.013
30.
Liew
,
K. M.
, and
Lim
,
C. W.
,
1994
, “
Vibratory Characteristics of Cantilevered Rectangular Shallow Shells of Variable Thickness
,”
AIAA J.
,
32
(
2
), pp.
387
396
.10.2514/3.59996
31.
Bhat
,
R. B.
,
1985
, “
Natural Frequencies of Rectangular Plates Using Characteristic Orthogonal Polynomials in Rayleigh–Ritz Method
,”
J. Sound Vib.
,
102
(
4
), pp.
493
499
.10.1016/S0022-460X(85)80109-7
32.
Yuan
,
J.
, and
Dickinson
,
S. M.
,
1994
, “
The Free Vibration of Circularly Cylindrical Shell and Plate Systems
,”
J. Sound Vib.
,
175
(
2
), pp.
241
263
.10.1006/jsvi.1994.1326
33.
Basdekas
,
N. L.
, and
Chi
,
M.
,
1971
, “
Response of Oddly-Stiffened Circular Cylindrical Shells
,”
J. Sound Vib.
,
17
(
2
), pp.
187
206
.10.1016/0022-460X(71)90454-8
34.
Saito
,
T.
, and
Endo
,
M.
,
1986
, “
Vibration of Finite Length, Rotating Cylindrical Shells
,”
J. Sound Vib.
,
107
(
1
), pp.
17
28
.10.1016/0022-460X(86)90279-8
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