梁横向振动方程解的Ritz方法

考虑计算梁横向振动方程解的Ritz方法.主要结果的证明运用变分法.首先,证明变分问题（2）与问题（1）等价;其次,采用坐标函数系来构造适当的近似解;最后,将问题（1）的解的近似计算问题离散化为线性方程组解的计算问题,获得了计算问题（1）解的近似值的Ritz方法,而且可以用第n次近似值来估计第n-1次的近似值的精确度.随着n的增大,解的精确度逐步提高,只要适当选取n,就可以求得所要精确度解的近似值,这个算法具有广泛的实用价值和理论价值.

Ritz method for the solutions of horizontal vibration equations of beam

This paper presents the Ritz method for the approximate solutions of horizontal vibration equations of beam. The results are proved by variational method. First of all, variational problem （2） and problem （ 1 ） were proved equivalent. Secondly, the appropriate approximate solutions were constructed by the system of coordinate functions. At last, we obtained the Ritz method for approximate value of solutions of problem （1） by dispersing the calculation of the solutions for approximate value of problem （1） into that of linear equations. The accuracy of （n-1）-th approximate value was estimated by n-th approximate value. When n was increased, the degree of accuracy of solutions was increased. When n was appropriately selected, the accuracy of solutions for approximate value needed could be obtained. This Ritz method is significant in practice and theory.