摘要
为估计模态叠加法中模态截断对结构地震作用下位移、速度、加速度反应的影响,对比分析了累积振型参与质量误差、静荷载参与比误差、质量相关荷载作用下的位移误差、累积振型贡献系数误差、累积振型加速度贡献系数误差和单位阵误差等模态截断指标随模态数目增加的变化规律。以一个5层剪切框架、一个单向不对称的4层框架和一个框架支撑结构的地震反应为例,讨论了结构位移、速度和加速度反应的模态截断误差与模态截断指标的关系。算例分析结果表明,静荷载参与比误差高估了低阶模态的影响而使模态截断数目偏少;质量相关荷载作用下的位移误差所得模态数目不稳定,这两个指标不适合作为模态截断的依据。对于悬臂类结构,模态截断所产生的累积误差以加速度的最大,速度的次之,位移的最小;对于位移反应,首层平动位移的累积振型贡献系数误差和累积振型参与质量误差可作为位移反应模态截断的依据;高阶模态对结构加速度反应的贡献大于对位移反应的贡献,应采用累积振型加速度贡献系数误差作为加速度反应模态截断的依据。
To estimate the effect of modal truncation on seismic response of displacement,velocity and acceleration in modal superposition method,the modal truncation indexes,including accumulated modal participation mass error,static load participation ratio error,displacement error of mass dependent load,accumulated modal contribution factor error,modal contribution factor error of acceleration and unit matrix error,were investigated considering the increasing of modal numbers.Then the relationship between the modal truncation error of displacement,velocity,acceleration and the modal truncation indexes was analyzed using a five-story building,a one-way asymmetry four-story building and a frame-supported structure under three different seismic excitations.The numerical results show that both the static load participation ratio error and the displacement error of mass dependent load are not suitable for modal truncation because the former overestimates the effect of low mode and the latter is instability.Due to the modal truncation,the cumulative error of acceleration response is the largest,followed by velocity and the cumulative error of displacement is the smallest for cantilever-type structures.For the displacement response,the accumulated modal participation mass error and the accumulated modal contribution factor error of the horizontal displacement of the first story can be used as the modal truncation indexes.The contribution of higher modes to acceleration response is greater than that of the displacement,therefore,the modal contribution factor error of acceleration is suggested to be used as the modal truncation index for the acceleration time history analysis.
作者
潘旦光
李雪菊
谭晋鹏
陈清军
鲁文艳
PAN Danpiang;LI Xueju;TAN Jinpeng;CHEN Qingjun;LU Wrnyan(Department of Civil Engineering,University of Science and Technology Beijing,Beijing 100083,China;Stale Key laboratory of Disaster Reduction in Civil Engineering,Tongji University,Shanghai 200092,China)
出处
《建筑结构学报》
EI
CAS
CSCD
北大核心
2020年第2期55-62,共8页
Journal of Building Structures
基金
土木工程防灾国家重点实验室开放基金(SLDRCE15-01)
关键词
悬臂类结构
模态截断
模态叠加法
地震响应
截断误差
cantilever-type structure
modal truncation
modal superposition method
seismic response
truncation error
