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

作　　者：纪振义[1] 叶开沅[1] 

机构地区：[1]安徽建筑工业学院,兰州大学

出　　处：《应用数学和力学》1994年第5期381-388,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金

摘　　要：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.

关 键 词：变截面梁 动力响应 稳态谐振动 梁 

分 类 号：TU323.301[建筑科学—结构工程]