Analytical solutions for the three displacements are obtained, in the form of power series, directly from the three governing equations for free vibration of laminated conical shells under axial load. Numerical results are presented for free vibration of axially loaded laminated conical shells with different geometric parameters and under two types of boundary conditions. It is found that an axial tension increases the frequencies while an axial compression decreases the frequencies. For the shells studied, the effect of axial load on the lowest frequency of the shell is found to be not sensitive to change in semivertex angle when the applied axial load is kept as a constant fraction of the critical buckling load. However, the axial load effect becomes very sensitive to variation in semivertex angle when a constant axial load is applied.

1.
Garnet
H.
, and
Kempner
J.
,
1964
, “
Axisymmetric Free Vibrations of Conical Shells
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
31
, pp.
458
466
.
2.
Goldberg
J. E.
,
Bogdanoff
J. L.
, and
Marcus
L.
,
1960
, “
On the Calculation of the Axisymmetric Modes and Frequencies of Conical Shells
,”
Journal of Acoustical Society of America
, Vol.
32
, p.
738
738
.
3.
Irie
T.
,
Yamada
G.
, and
Kaneko
Y.
,
1982
, “
Free Vibration of a Conical Shell With Variable Thickness
,”
Journal of Sound and Vibration
, Vol.
82
, pp.
83
94
.
4.
Irie
T.
,
Yamada
G.
, and
Kaneko
Y.
,
1984
, “
Natural Frequencies of Truncated Conical Shells
,”
Journal of Sound and Vibration
, Vol.
92
, pp.
447
453
.
5.
Kalnins
A.
,
1964
, “
Free Vibration of Rotationally Symmetric Shells
,”
Journal of Acoustical Society of America
, Vol.
36
, pp.
1355
1365
.
6.
Saunders
H.
,
Wisniewski
E. J.
, and
Pasley
P. R.
,
1960
, “
Vibration of Conical Shells
,”
Journal of Acoustical Society of America
, Vol.
32
, pp.
765
772
.
7.
Seide
P.
,
1956
, “
Axisymmetrical Buckling of Circular Cones Under Axial Compression
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
23
, p.
626
626
.
8.
Siu
C. C.
, and
Bert
C. W.
,
1970
, “
Free Vibration Analysis of Sandwich Conical Shells With Free Edges
,”
Journal of Acoustical Society of America
, Vol.
47
, p.
943
943
.
9.
Tong
L.
,
1993
, “
Free Vibration of Composite Laminated Conical Shells
,”
International Journal of Mechanical Science
, Vol.
35
, pp.
47
61
.
10.
Tong
L.
,
1994
, “
Buckling Load of Composite Conical Shells Under Axial Compression
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
61
, pp.
718
719
.
11.
Tong, L., 1998, “Buckling of Filament Wound Composite Conical Shells Under Axial Compression,” Proceedings of the 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Apr. 20–23, Long Beach, CA, AIAA paper no. 98–1769, pp. 585–594.
12.
Tong
L.
, and
Wang
T. K.
,
1992
, “
Simple Solutions for Buckling of Laminated Conical Shells
,”
International Journal of Mechanical Science
, Vol.
34
, pp.
93
111
.
13.
Wilkins
D. J.
,
Bert
C. W.
, and
Egle
D. M.
,
1970
, “
Free Vibration of Orthotropic Sandwich Conical Shells With Various Boundary Conditions
,”
Journal of Sound and Vibration
, Vol.
13
, p.
211
211
.
14.
Yang
C. C.
,
1974
, “
On Vibration of Orthotropic Conical Shells
,”
Journal of Sound and Vibration
, Vol.
34
, p.
552
552
.
This content is only available via PDF.
You do not currently have access to this content.