Free Vibrations of Shallow Spherical Shells On Elastic Foundation

The main object of this paper is to investigate the natural frequencies and model shapes offree vibrations of shallow spherical shells on the two-parameter elastic foundation. The goveming equa-tion which includes the influence of inertia force of the soil is derived.The exact solutions of govemingeqation are deduced explicitly in terms of Bassel functions. In order to espress arbitrary boundary conditions, the meridional, circumferential and transversedisplacement component is given, respectively. From these solutions,the frequency equation of a shal-low spherical shell with the clamped edge is derived. Then the natrral frequencies are calcrlated numer-ically for various wave numbers. The transverse displacement amplitudes corresponding to the first threenatural frequencies are determined for n=0,1,2.