附加弹簧保护装置的悬索主共振响应分析  

Primary resonance responses study of suspended cables with supplemental spring-protection devices

作　　者：张鹏[1,2] 卢文胜[1] 吕西林[1] ZHANG Peng;LU Wensheng;LU Xi-lin(State Key Laboratory 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：《振动工程学报》2020年第3期550-558,共9页Journal of Vibration Engineering

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：在索端附加弹簧保护装置可以减少外部环境振动对索网幕墙正常使用的影响,然而,索端附加弹簧保护装置会显著改变其静力和动力特性。为分析该保护装置对索结构静力和动力特性的影响,通过建立附加弹簧保护装置悬索的静力和动力非线性方程,求得频率的特征方程和振型的闭合解,并利用多尺度法求解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的静力性能、前三阶频率和幅频响应的影响规律。结果表明:为将索变形控制在工程允许的范围内并同时降低最大索力响应,建议在工程上将附加弹簧刚度与悬索线刚度比取值在0.2到2之间。研究成果可以为索网幕墙附加弹簧保护装置的抗风和抗震的初步设计提供参考。Adding supplemental spring-protection devices at the end of cables has been identified as an effective way to mitigate the vibrations of cable net facades caused by variable environmental impacts.However,comparing with traditional cables,the static and dynamic characteristics of the cable with supplemental spring-protection devices are significantly affected by its distinct end boundary conditions.In order to analyze the effect of the variable amount of stiffness provided by the supplemental spring-protection devices on the static and dynamic characteristics of cables,static and dynamic non-linear equations of suspension cables with supplemental spring-protection devices are established in this paper.The characteristic equation of frequency and the closed-form solution of modal shapes are presented,and the approximate solution of the primary resonance response and the amplitude-frequency response equation are solved by the multi-scale method.Moreover,the effect ofγk(the stiffness ratio between supplemental spring and suspension cable)on the static performance,the first three order frequency and the amplitude-frequency response of suspension cables with different sags are also examined.It is suggested that when the stiffness ratioγkis within range of 0.2<γ_k<2,the cable with supplemental spring-protection devices can achieve reasonable amount of peak force reductions while controlling its deformation within the allowable range of engineering practice.Furthermore,this suggested range can be applied to the preliminary design of cable net facades with supplemental spring-protection devices to resist wind and earthquake.

关 键 词：非线性振动 主共振 悬索 弹簧保护装置 幅频响应 

分 类 号：O322[理学—一般力学与力学基础] TU382[理学—力学]