正弦行波激励下单层对称框架结构扭转响应的解析解  

Analytical solutions for torsional response of single-story symmetric frame structure subjected to sinusoidal wave passage excitation

作　　者：刘铁林[1] 张世玉 李文博 LIU Tielin;ZHANG Shiyu;LI Wenbo(School of Civil Engineering,Shenyang Jianzhu University,Shenyang 110168,China)

机构地区：[1]沈阳建筑大学土木工程学院

出　　处：《地震工程与工程振动》2019年第5期67-77,共11页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(11672190)~~

摘　　要：本文以单层对称框架结构为研究对象,利用正弦行波激励研究对称结构扭转响应的频率影响因素。建立了行波激励下单层对称框架结构的运动方程。采用相对运动法求解运动方程,给出了正弦行波激励下楼板扭矩和柱剪力的解析解。计算了正弦行波激励下一个单层对称钢筋混凝土框架结构的楼板扭矩和柱剪力,并与一致激励的计算结果进行了对比。结果表明:正弦行波激励下对称结构楼板产生扭转振动,柱子产生非激励方向的振动,并且结构产生扭转共振。与一致激励相比,正弦行波激励下对称结构楼板扭矩稳态振幅既与地面运动视波速有关,又与激励频率有关,柱剪力稳态振幅不但与地面运动视波速和激励频率有关,还与结构固有频率和激励频率比值的平方有关。除视波速外,激励频率也是对称结构行波效应的主要影响因素,在激励频率低于结构固有频率的一定范围内,激励频率越低,柱剪力行波效应越显著。In this paper,frequency influencing factors have been studied for the torsional response of single-story symmetric frame structure subjected to sinusoidal wave passage excitation.The equation of motion is established for the symmetric structure subjected to wave passage excitation.The analytical solutions of floor torque and column shear are presented by solving the equation of motion.The floor torque and column shear are calculated for a single-story symmetric reinforced concrete frame structure subjected to sinusoidal wave passage excitation,and are also compared with the corresponding results of uniform excitation.The analytical solutions and the calculating results show that the torsional vibration of floor and lateral vibration of columns in the unexcited direction as well as torsional resonance occur for the symmetric structure subjected to sinusoidal wave passage excitation.The steady-state amplitude of floor torque is related to the ground motion apparent velocity as well as the excitation frequency.The steady-state amplitudes of column shear are not only related to the ground motion apparent velocity and excitation frequency,but also related to the square of the ratio of natural frequency of structure to excitation frequency.Besides the apparent velocity,the excitation frequency is also the main influencing factor on wave passage effect of symmetric structure.The lower excitation frequency shows more remarkable wave passage effect on the column shears for the excitation frequency within a certain range less than the natural frequency of structure.

关 键 词：扭转响应 对称结构 正弦行波激励 柱剪力 解析解 

分 类 号：TU311.3[建筑科学—结构工程]