Wave based method (WBM) is presented to analyze the free and forced vibration of cylindrical shells with discontinuity in thickness. The hull is first divided into multiple segments according to the locations of thickness discontinuity and/or driving points, and then the Flügge theory is adopted to describe the motion of cylindrical segments. The dynamic field variables in each segment are expressed as wave function expansions, which accurately satisfy the equations of motion and can be used to analyze arbitrary boundary conditions, e.g., classical or elastic boundary conditions. Finally, the boundary conditions and interface continuity conditions between adjacent segments are used to assemble the final governing equation to obtain the free and forced vibration results. By comparing with the results existing in open literate and calculated by finite element method (FEM), the present method WBM is verified. Furthermore, the influences of the boundary conditions and the locations of thickness discontinuity on the beam mode frequency and fundamental frequency are discussed. The effects of the direction of external force, location of external point force, and the structural damping on the forced vibration are also analyzed.

References

References
1.
Qatu
,
M. S.
,
2002
, “
Recent Research Advances in the Dynamic Behavior of Shells: 1989–2000, Part 2: Homogeneous Shells
,”
ASME Appl. Mech. Rev.
,
55
(
5
), pp.
415
434
.
2.
Zhang
,
X. M.
,
Liu
,
G. R.
, and
Lam
,
K. Y.
,
2000
, “
Vibration Analysis of Thin Cylindrical Shells Using Wave Propagation Approach
,”
J. Sound Vib.
,
293
(
3
), pp.
397
403
.
3.
Li
,
X. B.
,
2008
, “
Study on Free Vibration Analysis of Circular Cylindrical Shells Using Wave Propagation
,”
J. Sound Vib.
,
311
(
3–5
), pp.
667
682
.
4.
Gan
,
L.
,
Li
,
X. B.
, and
Zhang
,
Z.
,
2009
, “
Free Vibration Analysis of Ring-Stiffened Cylindrical Shells Using Wave Propagation Approach
,”
J. Sound Vib.
,
326
(
3–5
), pp.
633
634
.
5.
Mustate
,
B. A. J.
, and
Ali
,
R.
,
1989
, “
An Energy Method for Free Vibration Analysis of Stiffened Circular Cylindrical Shells
,”
Comput. Struct.
,
32
(
2
), pp.
355
363
.
6.
Wang
,
C. M.
,
Swaddiwuhipong
,
S.
, and
Tian
,
J.
,
1997
, “
Ritz Method for Vibration Analysis of Cylindrical Shells With Ring Stiffeners
,”
J. Eng. Mech.
,
123
(
2
), pp.
134
142
.
7.
Naeem
,
M. N.
, and
Sharma
,
C. B.
,
2000
, “
Prediction of Natural Frequencies for Thin Circular Cylindrical Shells
,”
Proc. Inst. Mech. Eng., Part C
,
214
(
10
), pp.
1313
1328
.
8.
Salahifar
,
R.
, and
Mohareb
,
M.
,
2012
, “
Finite Element for Cylindrical Thin Shells Under Harmonic Forces
,”
Finite Elem. Anal. Des.
,
52
, pp.
83
92
.
9.
Santos
,
H.
,
Soares
,
C. M. M.
,
Soares
,
C. A. M.
, and
Reddy
,
J. N.
,
2009
, “
A Semi-Analytical Finite Element Model for the Analysis of Cylindrical Shells Made of Functionally Graded Materials
,”
Compos. Struct.
,
91
(
4
), pp.
427
432
.
10.
Radhamohan
,
S. K.
, and
Maiti
,
M.
,
1977
, “
Vibrations of Initially Stressed Cylinders of Variable Thickness
,”
J. Sound Vib.
,
53
(
2
), pp.
267
271
.
11.
Wang
,
J. T. S.
,
Armstrong
,
J. H.
, and
Ho
,
D. V.
,
1979
, “
Axisymmetric Vibration of Prestressed Non-Uniform Cantilever Cylindrical Shells
,”
J. Sound Vib.
,
64
(
4
), pp.
529
538
.
12.
Ganesan
,
N.
, and
Sivadas
,
K. R.
,
1990
, “
Vibration Analysis of Orthotropic Shells With Variable Thickness
,”
Comput. Struct.
,
35
(
3
), pp.
239
248
.
13.
Ganesan
,
N.
, and
Sivadas
,
K. R.
,
1990
, “
Free Vibration of Cantilever Circular Cylindrical Shells With Variable Thickness
,”
Comput. Struct.
,
34
(
4
), pp.
669
667
.
14.
Sivadas
,
K. R.
, and
Ganesan
,
N.
,
1991
, “
Free Vibration of Circular Cylindrical Shells With Axially Varying Thickness
,”
J. Sound Vib.
,
147
(
1
), pp.
73
85
.
15.
Sivadas
,
K. R.
, and
Ganesan
,
N.
,
1992
, “
Vibration Analysis of Orthotropic Cantilever Cylindrical Shells With Axial Thickness Variation
,”
Compos. Struct.
,
22
(
4
), pp.
207
215
.
16.
Duan
,
W. H.
, and
Koh
,
C. G.
,
2008
, “
Axisymmetric Transverse Vibrations of Circular Cylindrical Shells With Variable Thickness
,”
J. Sound Vib.
,
317
(
3–5
), pp.
1035
1041
.
17.
E-Kaabazi
,
N.
, and
Kennedy
,
D.
,
2012
, “
Calculation of Natural Frequencies and Vibration Modes of Variable Thickness Cylindrical Shells Using the Wittrick–Williams Algorithm
,”
Comput. Struct.
,
104–105
, pp.
4
12
.
18.
Warburton
,
G. B.
, and
Al-Najafi
,
A. M.
,
1969
, “
Free Vibration of Thin Cylindrical Shells With a Discontinuity in the Thickness
,”
J. Sound Vib.
,
9
(
3
), pp.
373
382
.
19.
Stanley
,
A. J.
, and
Ganesan
,
N.
,
1995
, “
Dynamic Response of Cylindrical Shells With Discontinuity in Thickness Subjected to Axisymmetric Load
,”
J. Sound Vib.
,
184
(
4
), pp.
703
724
.
20.
Chang
,
S. D.
, and
Greif
,
R.
,
1979
, “
Vibrations of Segmented Cylindrical Shells by a Fourier Series Component Mode Method
,”
J. Sound Vib.
,
67
(
3
), pp.
315
328
.
21.
Zhou
,
J. P.
, and
Yang
,
B. G.
,
1995
, “
Distributed Transfer Function Method for Analysis of Cylindrical Shells
,”
AIAA J.
,
33
(
9
), pp.
1698
1708
.
22.
Zhang
,
L.
, and
Xiang
,
Y.
,
2007
, “
Exact Solutions for Vibration of Stepped Circular Cylindrical Shells
,”
J. Sound Vib.
,
299
(
4–5
), pp.
948
964
.
23.
Qu
,
Y. G.
,
Chen
,
Y.
,
Long
,
X. H.
,
Hua
,
H. X.
, and
Meng
,
G.
,
2013
, “
Free and Forced Vibration Analysis of Uniform and Stepped Circular Cylindrical Shells Using a Domain Decomposition Method
,”
Appl. Acoust.
,
74
(
3
), pp.
425
439
.
24.
Desemt
,
W.
,
1998
, “
A Wave Based Technique for Coupled Vibro-Acoustic Analysis
,” Ph.D. thesis, K. U. Leuven, Leuven, Belgium.
25.
Wah
,
T.
, and
Hu
,
W. C. L.
,
1967
, “
Vibration Analysis of Stiffened Cylinders Including Inter-Ring Motion
,”
J. Acoust. Soc. Am.
,
43
(
5
), pp.
1005
1016
.
26.
Chen
,
M. X.
,
Wei
,
J. H.
,
Xie
,
K.
,
Deng
,
N. Q.
, and
Hou
,
G. X.
,
2013
, “
Wave Based Method for Free Vibration Analysis of Ring Stiffened Cylindrical Shells With Intermediate Large Frame Ribs
,”
Shock Vib.
,
20
(
3
), pp.
459
479
.
27.
Wei
,
J. H.
,
Chen
,
M. X.
,
Hou
,
G. X.
,
Xie
,
K.
, and
Deng
,
N. Q.
,
2013
, “
Wave Based Method for Free Vibration Analysis of Ring Stiffened Cylindrical Shells With Non-Uniform Stiffener Distribution
,”
ASME J. Vib. Acoust.
,
135
(
6
), p.
061011
.
28.
Flügge
,
W.
,
1973
,
Stress in Shells
,
Springer
,
Berlin
.
You do not currently have access to this content.