This paper is the first work on the vibration of a high-speed rotating spherical shell that rotates about its symmetric axis by developing a set of motion governing equations with consideration of both the Coriolis and centrifugal accelerations as well as the hoop tension arising in the rotating shell due to the angular velocity. To the author's understanding, no such work has so far been published on the rotating spherical shell with the Coriolis and centrifugal accelerations as well as the hoop tension, although there have been the works published on the rotating hemispherical shell with consideration of the Coriolis and centrifugal forces. A thin rotating isotropic truncated circular spherical shell with the simply supported boundary conditions at both the ends is taken as an example for the free vibrational analysis. In order to validate the present formulation, comparisons are made with a nonrotating isotropic spherical shell, and a good agreement is achieved since no published data results from open literature are available for comparison on the dynamics of rotating spherical shell. By the Galerkin method, several case studies are conducted for investigation of the influence of the important parameters on the frequency characteristics of the rotating spherical shell. The parameters studied include the circumferential wave number, the rotational angular velocity, Young's modulus of the shell material, and the geometric ratio of the thickness to radius of the spherical shell.

References

References
1.
Bryan
,
G. H.
,
1890
, “
On the Beats in the Vibration of Revolving Cylinder or Bell
,”
Proc. Cambridge Philos. Soc.
,
7
, pp.
101
111
.
2.
Li
,
H.
,
Lam
,
K. Y.
, and
Ng
,
T. Y.
,
2005
,
Rotating Shell Dynamics
,
Elsevier
,
Oxford, UK
.
3.
Chang
,
C. O.
,
Hwang
,
J. J.
, and
Chou
,
C. S.
,
1996
, “
Modal Precession of a Rotating Hemispherical Shell
,”
Int. J. Solid Struct.
,
33
, pp.
2739
2757
.10.1016/0020-7683(95)00177-8
4.
Gulyaev
,
V. I.
,
Kirichuk
,
A. A.
, and
Yasinskii
,
V.A.
,
1991
, “
Stability of Kinematically Excited Oscillations of a Rotating Spherical Shell
,”
Int. Appl. Mech.
,
27
, pp.
858
864
.10.1007/BF00887976
5.
Kobayashi
,
Y.
, and
Yamada
,
G.
,
1991
, “
Free Vibration of a Spinning Polar Orthotropic Shallow Spherical Shell
,”
JSME Int. J. Vib. Contr. Eng. Eng. Ind.
,
34
, pp.
233
238
.10.1299/jsmec1988.34.233
6.
Gulyaev
,
V. I.
,
Lugovoi
,
P. Z.
,
Solov'ev
,
I. L.
, and
Belova
,
M. A.
,
2002
, “
On the Bifurcational States of Rotating Spherical Shells
,”
Int. Appl. Mech.
,
38
, pp.
1131
1137
.10.1023/A:1021723917298
7.
Watts
,
A. L.
,
Andersson
,
N.
,
Beyer
,
H.
, and
Schutz
,
B. F.
,
2003
, “
The Oscillation and Stability of Differentially Rotating Spherical Shells: The Normal-Mode Problem
,”
Mon. Not. R. Astron. Soc.
,
342
, pp.
1156
1168
.10.1046/j.1365-8711.2003.06612.x
8.
Watts
,
A. L.
,
Andersson
,
N.
, and
Williams
,
R. L.
,
2004
, “
The Oscillation and Stability of Differentially Rotating Spherical Shells: The Initial-Value Problem
,”
Mon. Not. R. Astron. Soc.
,
350
, pp.
927
938
.10.1111/j.1365-2966.2004.07695.x
9.
Flügge
,
W.
,
1960
,
Stresses in Shells
,
Springer
,
Berlin
.
10.
Chen
,
Y.
,
Zhao
,
H. B.
,
Shen
,
Z. P.
,
Grieger
,
I.
, and
Kröplin
,
B. H.
,
1993
, “
Vibrations of High Speed Rotating Shells With Calculations for Cylindrical Shells
,”
J. Sound Vib.
,
160
, pp.
137
160
.10.1006/jsvi.1993.1010
11.
Dong
,
S. B.
,
1977
, “
A Block-Stodola Eigensolution Technique for Large Algebraic Systems With Non-Symmetrical Matrices
,”
Int. J. Numer. Meth. Eng.
,
11
, pp.
247
267
.10.1002/nme.1620110204
12.
Kalnins
,
A.
,
1964
, “
Effect of Bending on Vibrations of Spherical Shells
,”
J. Acoust. Soc. Am.
,
36
, pp.
74
81
.10.1121/1.1918916
13.
Kalnins
,
A.
,
1964
, “
Free Vibration of Rotationally Symmetric Shells
,”
J. Acoust. Soc. Am.
,
36
, pp.
1355
1365
.10.1121/1.1919208
14.
Chao
,
C. C.
, and
Chern
,
Y. C.
,
1988
, “
Axisymmetric Free-Vibration of Orthotropic Complete Spherical-Shells
,”
J. Compos. Mater.
,
22
, pp.
1116
1130
.10.1177/002199838802201203
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