支座激励下附加弹簧保护装置悬索的非线性动力分析  

Nonlinear dynamic analysis for suspended cables with additional spring-protection devices under support excitation

作　　者：张鹏[1,2] 卢文胜[1] 吕西林[1] ZHANG Peng;LU Wensheng;Lü Xilin(State Key Lab of Disaster Reduction in Civil Engineering,Tongji University,Shanghai 200092,China;School of Architectural and Surveying&Mapping Engineering,Jiangxi University of Science and Technology,Ganzhou 341000,China)

机构地区：[1]同济大学土木工程防灾国家重点实验室,上海200092 [2]江西理工大学建筑与测绘工程学院,江西赣州341000

出　　处：《振动与冲击》2020年第17期16-23,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金重点项目(51638012);国家重点研发计划项目(2016YFE0105600)。

摘　　要：索网幕墙常支承于两相邻结构,动力作用将激起相邻结构产生相对变形,其作为支座激励将引起索网产生约束次内力,进而导致索网幕墙失效。在索端附加弹簧保护装置,利用弹簧装置吸收支座相对变形,可以有效减小支座运动对索网幕墙的影响。建立支座激励下附加弹簧保护装置悬索振动的动力模型,引入边界条件,求解微分方程得到频率的特征方程和振型方程,并利用多尺度法求得简谐支座激励下主共振响应的近似解和幅频响应方程。分析了附加弹簧与悬索刚度比对不同垂度悬索前三阶频率、振型和幅频响应的影响规律。该模型可有助于合理选择附加弹簧与悬索刚度比,研究表明附加弹簧保护装置可同时降低悬索最大变形和最大索力响应,从而为相邻结构间索网幕墙的减震设计提供一定参考。Cable net curtain walls were usually supported by two adjacent structures to form a large public space.However,cable nets’constrained secondary internal forces generated due to dynamic support excitations caused by relative deformations of adjacent structures lead to failure of cable net curtain walls.Adding additional spring-protection devices at end of cable is an effective way to mitigate vibration of cable net curtain walls caused by dynamic support excitations.Here,the non-linear dynamic model for suspension cables with additional spring-protection devices under support excitations was established.Through introducing boundary conditions and solving the dynamic equations,the characteristic equation of the structure’s natural frequencies and modal shape equations were obtained.The multi-scale method was used to gain approximate solution to the system’s main resonance response and the amplitude-frequency response equation under simple harmonic support excitations.Effect laws of stiffness ratio of additional spring to suspended cable on the first three orders natural frequencies,modal shapes and amplitude-frequency responses of suspended cables with different suspensions were analyzed.It was shown that the proposed model can be helpful to reasonably choose the stiffness ratio of additional spring to suspended cable;additional spring protection devices can simultaneously reduce the maximum deformation of suspended cable and the maximum cable force response to provide a certain reference for vibration reduction design of cable net curtain walls supported by adjacent structures.

关 键 词：非线性振动 悬索 弹簧保护装置 支座激励 幅频响应 

分 类 号：TU382[建筑科学—结构工程]