基于虚拟激励法的人⁃桥⁃MTMD竖向耦合振动分析及其减振优化设计  

Analysis of human-footbridge-MTMD coupled system and MTMD optimization design based on the pseudo-excitation method

作　　者：温金龙 李阳 汪志昊 陈爱玖 胡明祎 WEN Jinlong;LI Yang;WANG Zhihao;CHEN Aijiu;HU Mingyi(College of Civil Engineering and Communication,North China University of Water Resources and Electric Power,Zhengzhou 450045,China;Faculty of Civil Engineering and Mechanics,Kunming University of Science and Technology,Kunming 650000,China;Henan Engineering Research Center for Structural Vibration Control and Health Monitoring,Zhengzhou 450045,China;Engineering Vibration Control Technology Research Center of State Machinery Group Science and Technology Research Institute Co.,Ltd.,Beijing 100083,China)

机构地区：[1]华北水利水电大学土木与交通学院,河南郑州450045 [2]昆明理工大学建筑工程学院,云南昆明650000 [3]河南省结构振动控制与健康监测工程技术研究中心,河南郑州450045 [4]国机集团科学技术研究院有限公司工程振动控制技术研究中心,北京100083

出　　处：《振动工程学报》2025年第4期794-802,共9页Journal of Vibration Engineering

基　　金：国家自然科学基金面上项目(52378300);河南省杰出青年科学基金资助项目(242300421014)。

摘　　要：为建立考虑人⁃结构竖向相互作用的人行桥MTMD减振优化设计方法,通过模拟行人单自由度质量⁃弹簧⁃阻尼(MSD)模型参数的随机性,基于虚拟激励法求解了随机人群⁃人行桥⁃MTMD耦合系统的竖向振动响应;分析了人⁃结构竖向相互作用对人行桥TMD减振效果的影响规律;基于随机人群⁃人行桥⁃MTMD耦合系统的加速度传递函数H2范数与响应面优化,建立了考虑人⁃结构竖向相互作用的人行桥MTMD减振优化设计方法。结果表明:本文计算方法避免了大量非线性时程分析,可高效获得耦合系统振动响应的功率谱和均方根值;人⁃结构竖向相互作用使得TMD失谐效应显著,人群密度由0.25人/m^(2)增至1.25人/m^(2),TMD(质量比为3%)减振率下降37.19%;考虑人⁃结构竖向相互作用的人行桥MTMD优化设计方法对人行桥加速度响应减振率均值达到70%以上。To establish the optimal design method of multiple tuned mass damper(MTMD)for the footbridge considering the vertical human-structure interaction,the parameters randomness of the mass-spring-damper(MSD)pedestrian model is simulated,and the vertical dynamic response of the random crowd-footbridge-MTMD system is calculated based on the pseudo-excitation method.Then,the effect of vertical human-structure interaction on the dynamic response of the footbridge-TMD system is demonstrated.Finally,based on the H2 performance of the acceleration transfer function and response surface methodology of the coupled system,an optimal design method of MTMD for footbridge vibration control considering vertical human-structure interaction is established.The results show that the dynamic response calculation method of the coupled system avoids a large number of nonlinear time history analyses,and the power spectrum and root mean square of the coupled system response can be obtained efficiently.The vertical human-structure interaction makes the TMD detuning effect significant,and the reduction rate of TMD with 3%mass ratio decreases by 37.19%when the crowd density increases from 0.25 person/m2 to 1.25 person/m2.The proposed MTMD optimization design method for footbridge has an average mitigation rate of over 70%for footbridge acceleration response.

关 键 词：人⁃结构竖向相互作用 人行桥 随机人群 MTMD减振 虚拟激励法 

分 类 号：TU311.3[建筑科学—结构工程] U448.11[建筑科学—桥梁与隧道工程]