矩阵迁移法收敛性的条件及其证明

THE CONVERGENTE CONDITION AND ITS PROOF OF THE TRANSITION MATRIX METHOD

摘要: 矩阵迁移法广泛用于工程力学的非均匀弹性力学问题,如求解变厚度梁,轴对称圆柱壳的静力、稳定和振动问题以及非均匀转轴的临界转速等。其特点是把一个非均匀的力学问题变成一个分段均匀的力学问题来求解。本文证明了矩阵迁移法求解这类问题的收敛法,并给出矩阵迁移法收敛的充分条件。文中还给出矩阵迁移法的误差估计。文末给出两个算例,以示用本文的理论可以得到矩阵迁移法的正确模式。

Abstract: The transition matrix method is used to solve non-uniform elastic mecha-nics problems widely.For examble,we can solve the stregth, vibration nd stability problems of the beam and cylindrical shell, as well as the crit-ical speeds of a rotating multiple span axis by the method.The transition ma-trix method's charac-teristic is that a non-uniform mechanics problem can be transformed a uniform problem on d:screte inteval by it. In this paper, the method's convergence is proved,and convergent condition as well as err-or estimate also is given out. Two numerical examples are given at the end of the paper which indicate that, using this paqptr's theory, the right mo-del can be obtain for the transition matrix method.