The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential wave numbers for clamped (C), and simply supported (SS) boundary conditions.

References

References
1.
Lam
,
K.
, and
Hua
,
L.
,
1999
, “
On Free Vibration of a Rotating Truncated Circular Orthotropic Conical Shell
,”
Composites Part B
,
30
(
2
), pp.
135
144
.10.1016/S1359-8368(98)00049-3
2.
Civalek
,
O.
,
2006
, “
An Efficient Method for Free Vibration Analysis of Rotating Truncated Conical Shells
,”
Int. J. Press. Vessels Pip.
,
83
(
1
), pp.
1
12
.10.1016/j.ijpvp.2005.10.005
3.
Hua
,
L.
,
2000
, “
Influence of Boundary Conditions on the Free Vibrations of Rotating Truncated Circular Multi-Layered Conical Shells
,”
Composites Part B
,
31
(
4
), pp.
265
275
.10.1016/S1359-8368(00)00012-3
4.
Liu
,
M.
,
Liu
,
J.
, and
Cheng
,
Y. S.
,
2014
, “
Free Vibration of a Fluid Loaded Ring-Stiffened Conical Shell With Variable Thickness
,”
ASME J. Vib. Acoust.
(in press).10.1115/1.4027804
5.
Wang
,
Y.
,
Liu
,
R.
, and
Wang
,
X.
,
1999
, “
Free Vibration Analysis of Truncated Conical Shells by the Differential Quadrature Method
,”
Int. J. Sound Vib.
,
224
(
2
), pp.
387
394
.10.1006/jsvi.1999.2218
6.
Qu
,
Y.
,
Chen
,
Y.
,
Chen
,
Y.
,
Long
,
X.
,
Hua
,
H.
, and
Meng
,
G.
,
2013
, “
A Domain Decomposition Method for Vibration Analysis of Conical Shells With Uniform and Stepped Thickness
,”
ASME J. Vib. Acoust.
,
135
(
1
), p.
011014
.10.1115/1.4006753
7.
Lakis
,
A.
,
Dyke
,
P. V.
, and
Ouriche
,
H.
,
1992
, “
Dynamic Analysis of Anisotropic Fluid-Filled Conical Shells
,”
J. Fluids Struct.
,
6
(
2
), pp.
135
162
.10.1016/0889-9746(92)90042-2
8.
Sabri
,
F.
, and
Lakis
,
A.
,
2010
, “
Hybrid Finite Element Method Applied to Supersonic Flutter of an Empty or Partially Liquid-Filled Truncated Conical Shell
,”
J. Sound Vib.
,
329
(3), pp.
302
316
.10.1016/j.jsv.2009.09.023
9.
Liew
,
K. M.
,
Ng
,
T. Y.
, and
Zhao
,
X.
,
2005
, “
Free Vibration Analysis of Conical Shells Via the Element-Free kp-Ritz Method
,”
J. Sound Vib.
,
281
(
35
), pp.
627
645
.10.1016/j.jsv.2004.01.005
10.
Amabili
,
M.
,
2008
,
Nonlinear Vibrations and Stability of Shells and Plates
,
Cambridge University
,
New York
.
11.
Leissa
,
A. W.
,
1973
, “
Vibration of Shells
,”
National Aeronautics and Space Administration
,
Washington, DC
, Paper No. NASA SP-288.
12.
Kayran
,
A.
, and
Vinson
,
J. R.
,
1990
, “
Free Vibration Analysis of Laminated Composite Truncated Circular Conical Shells
,”
AIAA J.
,
28
(
7
), pp.
1259
1269
.10.2514/3.25203
13.
Valathur
,
M.
, and
Albrecht
,
B.
,
1971
, “
On Axisymmetric Free Vibrations of Thin Truncated Conical Shells
,”
J. Sound Vib.
,
18
(
1
), pp.
9
16
.10.1016/0022-460X(71)90626-2
14.
Tong
,
L.
,
1993
, “
Free Vibration of Orthotropic Conical Shells
,”
Int. J. Eng. Sci.
,
31
(
5
), pp.
719
733
.10.1016/0020-7225(93)90120-J
15.
Tong
,
L.
,
1993
, “
Free Vibration of Composite Laminated Conical Shells
,”
Int. J. Mech. Sci.
,
35
(
1
), pp.
47
61
.10.1016/0020-7403(93)90064-2
16.
Tong
,
L.
,
1994
, “
Free Vibration of Laminated Conical Shells Including Transverse Shear Deformation
,”
Int. J. Solids Struct.
,
31
(
4
), pp.
443
456
.10.1016/0020-7683(94)90085-X
17.
Amabili
,
M.
, and
Reddy
,
J.
,
2010
, “
A New Non-Linear Higher-Order Shear Deformation Theory for Large-Amplitude Vibrations of Laminated Doubly Curved Shells
,”
Int. J. Non Linear Mech.
,
45
(
4
), pp.
409
418
.10.1016/j.ijnonlinmec.2009.12.013
18.
Amabili
,
M.
,
2012
, “
A New Nonlinear Higher-Order Shear Deformation Theory With Thickness Variation for Large-Amplitude Vibrations of Laminated Doubly Curved Shells
,”
J. Sound Vib.
,
332
(
19
), pp.
4620
4640
.10.1016/j.jsv.2013.03.024
19.
Novozhilov
,
V. V.
,
1999
,
Foundations of the Nonlinear Theory of Elasticity
,
Courier Dover Publications
, Mineola, NY.
20.
Irie
,
T.
,
Yamada
,
G.
, and
Tanaka
,
K.
,
1984
, “
Natural Frequencies of Truncated Conical Shells
,”
J. Sound Vib.
,
92
(
3
), pp.
447
453
.10.1016/0022-460X(84)90391-2
21.
Loy
,
C.
, and
Lam
,
K.
,
1999
, “
Vibration of Thick Cylindrical Shells on the Basis of Three-Dimensional Theory of Elasticity
,”
J. Sound Vib.
,
226
(
4
), pp.
719
737
.10.1006/jsvi.1999.2310
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