弹性地基上扁球壳的自由振动

本文研究双参数弹性地基上扁球壳的自由振动频率和振型，推导了计及地基惯性力影响的扁壳自由振动控制方程。方程的精确解以贝塞尔函数表达。同时，分别导出了壳的经向、环向和横向位移分量的表示式。根据所得的解，文中给出了固定边扁球壳的频率方程和数值结果。同时。还给出了对应于前三个频率的振型变化曲线。

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.