Natural frequencies of a fluid-filled anisotropic spherical shell

In this paper, the general nonaxisymmetric free vibration of a spherically isotropic elastic spherical shell filled with a compressible fluid medium is investigated. To this end, the three-dimensional elasticity solution method recently developed by the authors [H. J. Ding and W. Q. Chen, Int. J. Solids Struct. 33, 2575-2590 (1996)] is employed. The effect of fluid is considered by introducing a relation between the normal displacement and the normal stress of the shell at the inner spherical surface. It is shown that the coupled vibration can be divided into two independent classes as in the case of empty spherical shell. The exact three-dimensional frequency equations are then derived. As the exact elasticity solution can serve as a benchmark to check various approximate theories, frequency equations of three typical shell theories are also presented. Numerical examples are given and comparisons between four theories are made. (C) 1999 Acoustical Society of America. [S0001-4966(99)03801-1].