In this paper,three displacement functions are introduced and expended in terms of spherical harmonic functions. It is found that the problem of a spherically isotropic elastic body is eventually reduced to an independent ordinary differential equation of second order and a set of coupled ordinary differential equations of second order. If we involve in the effect of the surrounding fluid by considering the fluid dynamic pressure, we should only solve an algebric eigenvalue problem and can easily calculate the... In this paper,three displacement functions are introduced and expended in terms of spherical harmonic functions. It is found that the problem of a spherically isotropic elastic body is eventually reduced to an independent ordinary differential equation of second order and a set of coupled ordinary differential equations of second order. If we involve in the effect of the surrounding fluid by considering the fluid dynamic pressure, we should only solve an algebric eigenvalue problem and can easily calculate the free vibration frequencies of the spherically isotropic hollow sphere of various thickness submerged in infinite incompressible ideal fluid. Finally, we give some examples on different conditions. Especially, when the original problem is inverted into an isotropic one, the results are comparedwith those in papers concerning this problem. |