Natural frequencies of an elastic spherically isotropic hollow sphere submerged in a compressible fluid medium

The non-axisymmetric free vibrations of a spherically isotropic spherical shell, which is submerged in a compressible fluid medium, are analyzed. A method based on three-dimensional elastic theory is developed. Two classes of frequency equations, which correspond to two classes of vibrations, respectively, are then obtained. It can be shown that for the first class of vibration there is no effect on the frequencies whether fluid exists outside or not. As numerical results show, the compressibility of the fluid has little effect on the real parts of the vibrational frequencies of the second class when compared with the incompressible case except for the breathing mode, n = 0. Various kinds of shell theory are also presented. It is found that the transverse normal strain has a great effect on the natural frequencies of a submerged spherical shell. (C) 1996 Academic Press Limited