变截面Timoshenko梁动力反应的半解析法  

Semi-Analytical Solution on Dynamic Response of Timoshenko Beams with Varying Cross-Section

作　　者：潘旦光[1] 郭泳[1,2] 

机构地区：[1]北京科技大学土木工程系,北京100083 [2]国核电力规划设计研究院,北京100095

出　　处：《力学季刊》2014年第3期522-530,共9页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(51078032);北京市自然科学基金(8143037);北京科技大学教改项目(JG2013M11)

摘　　要：为研究移动荷载下截面剪切变形和转动惯量影响,在推导变截面Timoshenko梁振型正交性的数学表达式的基础上,建立了任意荷载作用下Timoshenko梁动力响应的模态叠加法.然后,将模态摄动法和模态叠加法结合起来,提出了变截面Timoshenko梁动力反应计算的公式.在此基础上,基于矩形截面梁,比较分析了简支Timoshenko梁理论和Euler梁理论动力反应随移动荷载速度、长细比和截面衰减率的变化规律的区别.计算结果表明:由于剪切变形和转动惯量的影响,Timoshenko梁的动力反应将大于Euler梁.当长细比小于10时,Timoshenko梁跨中位移比Euler梁增加25%以上,当长细比大于30后,可采用Euler梁理论进行简化分析.For investigating the effect of the shear deformation and rotatory moment of inertia, the modal orthogonality of the Timoshenko beam with varying cross-section was formulated firstly. Then, a modal superposition method was developed to estimate dynamic response of a Timoshenko beam with varying cross-section under arbitrary excitations. Combining modal perturbation method with modal superposition method, an equation, which was easy to solve the dynamic response of Timoshenko beam with varying cross-section, was proposed. Then, considering the rectangle section, the response differences between simply-supported Timoshenko beams and Euler beams were investigated in cases of the speed of moving load, slenderness ratio and section decay rate. Numerical results show that the dynamic responses of Timoshenko beams are larger than that of Euler ones due to the effect of the shear deformation and rotatory moment of inertia. The middle-span displacements increase more than 25% for beams with slenderness ratio less than 10. It is reasonable to estimate the dynamic responses by Euler beam theory when slenderness ratio of beam exceed 30.

关 键 词：TIMOSHENKO梁 Euler梁 模态摄动法 模态叠加法 移动荷载 

分 类 号：TU311.3[建筑科学—结构工程] O32[理学—一般力学与力学基础]