变截面Timoshenko固端梁和简支梁的模态特性  

Modal Characteristics of Timoshenko Fixed and Simply Supported Beams with Variable Cross Section

作　　者：韩博宇[1] 楼梦麟[1] 

机构地区：[1]同济大学土木工程防灾国家重点实验室,上海200092

出　　处：《力学季刊》2010年第4期610-617,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金项目(90915011)

摘　　要：Timoshenko梁的振动方程一般较为复杂,很难给出解的解析形式,尤其对于梁为变截面的情况。采用直接模态摄动法可将Timoshenko梁的振动微分方程组转化为一组非线性代数方程组,不仅可以简化计算过程,而且计算结果具有较高的精度。本文应用直接模态摄动法研究了变截面Timoshenko固端及简支梁的自由振动特性,并通过算例,讨论了这两种支撑条件下梁高的斜率及长细比对梁各阶主频率的影响,得到了相同条件下深梁效应对固端梁的影响要大于对简支梁的影响,且其影响随梁高的斜率增加而增大的结论。Since the motion equation of Timoshenko beam is very complex,its analytic solution is obtained difficultly,especially for the beam with variable cross section.The set of differential equations of Timoshenko beams with variable cross-section were transferred as a set of nonlinear algebraic equations with the application of direct modal perturbation method.This method predigests the process of calculation and the result of calculation also owns good precision.The direct modal perturbation method was applied to analyze the characteristics of free vibration of variable cross-section Timoshenko beams with two ends fixed and two ends simply supported.From several numerical examples,the effects of slope of beam depth,slenderness were discussed on the natural frequencies of beams with these two kinds of supporting conditions and it is proved to be simple and accurate in calculation.

关 键 词：变截面Timoshenko梁 直接模态摄动 

分 类 号：TU311.3[建筑科学—结构工程]