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]
Issue Section:
Brief Notes
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
. Copyright © 2000
by ASME
You do not currently have access to this content.