This note presents exact frequency equations of two independent classes of vibrations of a spherically isotropic solid sphere with fixed boundary conditions. Numerical calculations are performed and comparison between two different materials is made. Some useful observations are obtained. [S0021-8936(00)00102-1]

1.
Maiti
,
M.
,
1975
, “
Stress in Anisotropic Nonhomogeneous Sphere
,”
J. Eng. Mech.
,
101
, pp.
101
108
.
2.
Montagner
,
J. P.
, and
Anderson
,
D. L.
,
1989
, “
Constrained Reference Mantle Model
,”
Phys. Earth Planet. Inter.
,
54
, pp.
205
227
.
3.
Chen, W. Q., 1996, Coupled Free Vibrations of Spherically Isotropic Hollow Spheres, Ph.D. dissertation, Zhejiang University, Hangzhou, China (in Chinese).
4.
Hu
,
H. C.
,
1954
, “
On the General Theory of Elasticity for a Spherically Isotropic Medium
,”
Acta Sci. Sin.
,
3
, pp.
247
260
.
5.
Chen
,
W. T.
,
1966
, “
On Some Problems in Spherically Isotropic Elastic Materials
,”
ASME J. Appl. Mech.
,
33
, pp.
539
546
.
6.
Cohen
,
H.
,
Shah
,
A. H.
, and
Ramakrishnan
,
C. V.
,
1972
, “
Free Vibrations of a Spherically Isotropic Hollow Sphere
,”
Acustica
,
26
, pp.
329
333
.
7.
Ding
,
H. J.
, and
Chen
,
W. Q.
,
1996
, “
Nonaxisymmetric Free Vibrations of a Spherically Isotropic Spherical Shell Embedded in an Elastic Medium
,”
Int. J. Solids Struct.
,
33
, pp.
2575
2590
.
8.
Schafbuch
,
P. J.
,
Rizzo
,
F. J.
, and
Thompson
,
R. B.
,
1992
, “
Eigenfrequencies of an Elastic Sphere With Fixed Boundary Conditions
,”
ASME J. Appl. Mech.
,
59
, pp.
458
459
.
9.
Ding
,
H. J.
,
Chen
,
W. Q.
, and
Liu
,
Z.
,
1995
, “
Solutions to Equations of Vibrations of Spherical and Cylindrical Shells
,”
Appl. Math. Mech.
,
16
, pp.
1
15
.
10.
Silbiger
,
A.
,
1962
, “
Non-axisymmetric Modes of Vibrations of Thin Spherical Shell
,”
J. Acoust. Soc. Am.
,
34
, p.
862
862
.
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