变截面Timoshenko简支梁动力特性的半解析解  

SEMI-ANALYTIC SOLUTION OF DYNAMIC CHARACTERISTICS OF NON-PRISMATIC TIMOSHENKO SIMPLY SUPPORTED BEAMS

作　　者：潘旦光[1] 楼梦麟[2] 

机构地区：[1]北京科技大学土木与环境工程学院,北京100083 [2]同济大学土木工程防灾国家重点实验室,上海200092

出　　处：《工程力学》2009年第8期6-9,25,共5页Engineering Mechanics

摘　　要：基于直接模态摄动法基本原理,建立一种求解变截面Timoshenko梁动力特性的近似分析方法。该方法在等效均匀Euler-Bernoulli梁的模态子空间内实施,将变截面Timoshenko梁特征方程的微分方程组转化为代数方程组求解。对于等截面Timoshenko简支梁情况,该方法可以得到精确的特征值和特征向量。对于变截面情况,数值分析结果表明这一方法简单适用,且具有良好的精度。Based on modal perturbation method, a novel approach is presented to analyze the free vibration of non-prismatic Timoshenko beams. In the method, the dynamic characteristics of non-prismatic Timoshenko beams are calculated approximately in the modal subspace spanned by several lower models of equivalent prismatic Euler-Bernoulli beams. As a result, the set of characteristic equations of non- prismatic Timoshenko beams is transformed into a set of algebraic equations. For prismatic Timoshenko simply supported beams, the exact eigenvalues and eigenfunctions can be obtained by using the method. For non- prismatic ones, the results of numerical examples show that the method is simple, practicable and accurate.

关 键 词：变截面Timoshenko梁 EULER-BERNOULLI梁 模态摄动法 动力特性 半解析解 

分 类 号：TU311.3[建筑科学—结构工程]