正弦行波激励下单层偏心框架结构扭转响应的解析解  

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

作　　者：刘铁林[1] 杨越 李文博 LIU Tielin;YANG Yue;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,辽宁沈阳110168

出　　处：《地震工程与工程振动》2022年第1期46-55,共10页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(11672190)。

摘　　要：文中针对单层偏心框架结构,利用正弦行波激励研究了质量偏心率和激励频率对偏心框架结构行波扭转响应的影响规律。建立了行波激励下单层偏心框架结构的振动方程,采用相对运动法求解给出了正弦行波激励下单层偏心框架结构楼板的质心平动位移和转角位移以及楼板扭矩和柱剪力的解析解。计算了一个钢筋混凝凝土单层偏心框架结构的峰值楼板扭矩和峰值柱剪力,并分析了不同偏心率和激励频率情况下的峰值楼板扭矩和峰值柱剪力。研究表明:行波激励下偏心结构峰值楼板扭矩在结构的2个固有频率处各存在1个共振区,而对称结构峰值楼板扭矩只存在第2个共振区。各共振区随着偏心率增大都向低频方向偏移且范围逐渐增大。行波激励下偏心和对称结构的激励方向峰值柱剪力于极低激励频率处都存在1个突升陡降区域,在结构的2个固有频率处各存在1个共振区。突升陡降区域的峰值位置与偏心率无关,而2个共振区都随偏心率增大向低频方向偏移。无论偏心结构还是对称结构,当激励频率在低于基频的一定范围时,激励频率越低,柱剪力的行波效应越显著。对于偏心结构,无论行波激励还是一致激励,靠近质心一侧柱子的峰值柱剪力大,远离质心一侧柱子的峰值柱剪力小。The influences of mass eccentricity ratio and excitation frequency on the torsional response of the single-story eccentric frame structure to sinusoidal wave passage excitation are studied in this paper.The dynamic equilibrium equation for the single-story eccentric frame subjected to wave passage excitation is established,and the relative motion method is used to solve the equation.The analytical solutions are respectively given for the mass center displacement and torsional displacement of the floor,and for floor torque and column shears with sinusoidal wave passage excitation.The peak floor torque and peak column shear of a single-story eccentric reinforced concrete frame are calculated,and the peak floor torque and peak column shear in terms of different eccentricity ratio and excitation frequency are analyzed.Studies show that there are resonance regions at two natural frequencies of structure for the peak floor torque of eccentric structure with wave passage excitation,there is only one resonance region at second natural frequency for symmetric structure.With the increase of eccentricity ratio,resonance regions of peak floor torque shift to low frequency and their ranges gradually increase.There exists a steep region at very low excitation frequency for the peak column shears in the excitation direction of both eccentric and symmetric structures subjected to wave passage excitation,and there are resonance regions at the two natural frequencies of structure.The position of the steep region is independent of eccentricity ratio,while the two resonance regions shift to low frequency with the increase of eccentricity ratio.Regardless of the eccentric or symmetric structure,when the excitation frequency is in a certain range below the fundamental frequency,the lower the excitation frequency,the more significant the wave passage effect on column shear.The peak column shears of columns near the center of mass are large,while the peak column shears of columns away from the center of mass are small for eccentric stru

关 键 词：扭转响应 偏心结构 行波 解析解 激励频率 

分 类 号：TU311.[建筑科学—结构工程]