浸没的球面各向同性球壳的自由振动

本文引入三个们移函数并用球面调和函数展开，可将球面各向同性弹性力学的基本方程转化成一个独立的二阶常微分方程和另一个耦合的二阶常微分方程组，采用液动压力表示流体与壳的相互作用，可以把无限大不可压缩流体中任意厚度球面各向同性球壳的自由振动频率计算归结为一个代数循征值问题，文中计算了若干种情况下球壳的频率，在各向同性情形与有关文献作了比较。

ON THE FREE VIBRATIONS OF A SUBMERGED SPHERICALLY ISOTROPIC HOLLOW SPHERE

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.