非均匀变截面梁动力响应的一般解

The General Solution for Dynamic Response of Nonhomogeneous Beam with Variable Cross Section

本文利用精确解析法￣［１］给出非均匀变截面梁在任意谐振荷载和边界条件下的动力响应的一般解。问题最后归结为求解一个非正定微分方程。对于这一问题用一般变分法求解失败，利用本文的方法，这个问题的一般解可以写成解析的形式。因此对优化特别方便。本文给出收敛性证明。文末给出的算例表明本文的方法可获得满意的结果。

In this paper, by means of the exact analytic method￣[1] the general solution for dynamic response of nonhomogeneous beam with variable cross section is obtained under arbitrary resonant load and boundary conditions. The problem is reduced to solve a non-positive differential equation. Generally, it is not solved by variational method. By the present method, the general solution for this problem may be written as an analytic form. Hence, it is convenient for struc-ture optimizing problem. In this paper, its convergence is proved. Numerical examples are given at the end of the paper, which indicates satisfactory results can be obtained.