旋转薄壳自由振动的精确解法

AN EXACT SOLUTION FOR FREE VIBRATION OF TOROIDAL THIN SHELL

提出一种计算具有齐次边界条件的旋转薄壳的特征值和特征函数的精确解法。这一方法仍需借用数值法求解８阶行列式所对应的频率方程。其精确意义是与用数值法求解梁的超越频率方程而获得梁振动频率精确解意义等同的。用此方法，本文给出了两端简支（ｓｓ）、一端固定一端自由（ｃｆ）以及一端固定一端简支（ｃｓ）柱壳的自振频率随柱壳长细比的变化，并与解析解（ｓｓ）、试验值（ｃｓ）及其它方法进行了比较。

A new exact solution is developed which enables to determine the free vibration characteristics of toroidal thin shell with homogeneous boundary conditions.But the solution requires numerical evaluation of an eight order complex determinant to find its eigenvalues.The results are exact in the same sense as the numerical solution of the transcendental frequency equation for a beam yields an exact solution of its vibration frequency.The eigenvalues of cylindrical shell with the boundary conditions corresponding to simple-simple support(SS),clamped-free support(CF)and clamped-simple support(CS)have been calculated and their dependences on the slenderness of the shell have been found out yet.The results are compared with those obtained by other investigators using different methods and experiments.