基底隔震的多层建筑结构自振频率和振型解析  

Analysis of the natural frequencies and modes for multi-story structures with base isolation

作　　者：丁肇伟 陈龙珠[1] 李庆来 DING Zhaowei;CHEN Longzhu;LI Qinglai(Institute of Engineering Safety&Disaster Prevention,School of Naval Architecture,Ocean&Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;Shanghai Donghao Lansheng(Group)Co.,Ltd.,Shanghai 200040,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院安全与防灾工程研究所,上海200240 [2]上海东浩兰生(集团)有限公司,上海200040

出　　处：《哈尔滨工程大学学报》2020年第3期357-361,共5页Journal of Harbin Engineering University

基　　金：上海市科委资助项目(17DZ1201400);国家自然科学基金项目(51178267).

摘　　要：本文以基底隔震的7自由度建筑结构为研究对象,参考三对角Toeplitz矩阵特征值问题的数学解法,推导了2种特定隔震层刚度条件下的各阶自振圆频率和振型的解析解,由此构造了任意隔震层刚度条件下结构的各阶自振圆频率和振型的解析算式,并用数值解的结果进行了验证。结果表明:对基底隔震建筑结构地震响应具有重要影响的第1阶自振圆频率和振型,给出了精度良好的简化算式,可供工程设计选定隔震层刚度使用。To address the eigenvalue problem of a tridiagonal Toeplitz matrix,analytical solutions for the natural vibration frequencies and modes were derived for the base-isolated structure with seven degrees of freedom at two specific conditions using the recursive method.The analytical formulas for the natural vibration frequencies and modes under arbitrary stiffness of the base-isolated structure were then proposed and verified by numerical solutions.In addition,simplified formulas for the first natural vibration frequency and mode were established with high precision,which greatly influence the seismic response of the base-isolated structure and can be easily applied to the selection of stiffness of the base isolation in engineering design.

关 键 词：基底隔震 多层建筑 自振频率 振型 解析算式 近似算式 TOEPLITZ矩阵 三对角矩阵 

分 类 号：TU318[建筑科学—结构工程] TU352.1