地面简谐运动作用下双自由度体系鞭梢效应的影响因素研究  

Study on Influencing Factors of Whiplash Effect of Two Degree of Freedom System Under Ground Simple Harmonic Motion

作　　者：李明瑧 郭长青[2] LI Mingzhen;GUO Changqing(School of Civil Engineering,University of South China,Hengyang,Hunan 421001,China;School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China)

机构地区：[1]南华大学土木工程学院,湖南衡阳421001 [2]南华大学数理学院,湖南衡阳421001

出　　处：《南华大学学报（自然科学版）》2022年第6期8-14,共7页Journal of University of South China：Science and Technology

基　　金：国家自然科学基金项目(51678286)。

摘　　要：为了更加全面准确地了解双自由度体系鞭梢效应发生的机理及影响因素,针对无阻尼和有阻尼两种情况,以上部结构与下部结构绝对位移的振幅比作为鞭梢效应的表征量,系统研究了外激励频率与上部结构自振频率之比、上部结构与下部结构的质量比和刚度比、结构阻尼比四种参数的影响。结果表明:对于无阻尼体系,鞭梢效应仅与频率比有关,当频率比为1时,振幅比为无穷大;对于有阻尼体系,若结构两阶振型阻尼比相等,随着阻尼比的增大,鞭梢效应减弱,质量比和刚度比不明显影响结构的鞭梢效应;若结构两阶振型阻尼比不相等,当刚度比远大于质量比时,二阶振型阻尼比对鞭梢效应影响更明显;当刚度比小于或等于质量比时,一阶振型阻尼比对鞭梢效应影响更明显。To gain a comprehensive understanding of the whip effect in a double-degree-of-freedom system,the study examined the ratio of upper to lower structure displacement amplitudes as a characterization of the effect,for both undamped and damped cases.It investigated four parameters,including the ratio of excitation frequency to the upper structure natural frequency,the mass and stiffness ratios between upper and lower structures,and the damping ratio of the structure.The results reveal that,for undamped systems,the whip effect depends solely on the frequency ratio,where the amplitude ratio becomes infinite at a ratio of 1.In damped systems,the whip effect weakens with increasing damping ratio,while mass and stiffness ratios have a negligible effect,provided the damping ratios of two-order vibration modes are equal.However,if the damping ratios are unequal and the stiffness ratio is greater than the mass ratio,the second-order vibration mode damping ratio has a more significant influence.When the stiffness ratio is less than or equal to the mass ratio,the first-order vibration mode damping ratio is more significant.

关 键 词：鞭梢效应 质量比 刚度比 模态分析 

分 类 号：TU311.3[建筑科学—结构工程]