弹性地基上扁球壳自由振动的级数解

Free vibration of shallow spherical shells on elastic foundations

采用Fourier-Bessel级数解法,对弹性地基上周边夹支扁球壳的自由振动进行分析.壳体的挠度被展为第一类Fourier-Bessel级数,进而导出了频率方程.计算了壳体的前三阶频率,给出了n分别取0和1时的前三阶振型变化曲线,且将本文所得的级数解与精确解进行比较.数值计算表明,本文的求解方法能够满足实际工程要求.

The free vibration of shallow spherical shell with clamped edges on the elastic founda- tion, is analyzed here using Fourier-Bessel series. The deflection of shallow spherical shell is expressed in Fourier-Bessel series of the first kind, and the frequency equation is derived. The natural frequencies are calculated numerically for the first three orders. The first three corresponding modal shape change curves are given for n=0, 1. Then the solutions here are compared with the exact solutions. In the end, the numerical calculation indicates that the method used in this paper is satisfying in practical engineering.