支座激励下附加弹簧保护装置悬索的非线性动力分析

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (17) : 16-23.

论文

张鹏1,2，卢文胜1，吕西林1

作者信息 +

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

ZHANG Peng1,2, LU Wensheng1, LV Xilin1

Author information +

文章历史 +

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。

Abstract

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.

导出引用

张鹏1,2，卢文胜1，吕西林1. 支座激励下附加弹簧保护装置悬索的非线性动力分析[J]. 振动与冲击, 2020, 39(17): 16-23

ZHANG Peng1,2, LU Wensheng1, LV Xilin1. Nonlinear dynamic analysis for suspended cables with additional spring-protection devices under support excitation[J]. Journal of Vibration and Shock, 2020, 39(17): 16-23

参考文献

[1]崔娟, 杨霄, 蒋炳丽, 等. 连体结构中连体桁架选型和幕墙索网的地震响应分析 [J]. 建筑结构, 2018, 48(24): 41-46.
CUI Juan, YAO Xiao, JIANG Bingli, et al. Structural scheme selection of connected truss and seismic response analysis of curtain wall cable net in connected structure [J]. Building Structure, 2018, 48(24): 41-46.
[2]李明, 王元清, 陶伟, 等. 单层平面索网玻璃幕墙抗震性能研究进展 [J]. 地震工程与工程振动, 2014, 34(S1): 523-528.
LI Ming, WANG Yuanqing, TAO Wei, et al. Research progress on seismic performance of cable net facade [J]. Earthquake Engineering and Engineering dynamics, 2014, 34(S1): 523-528.
[3]李丽, 范重, 刘学林, 等. 天津国际金融会议酒店超大弧形幕墙结构设计 [J]. 建筑结构, 2015, 45(S1): 290-296.
LI Li, FAN Zhong, LIU Xuelin, et al. Design on large curve curtain structure of Tianjin International Financial Conference Hotel [J]. Building Structure, 2015, 45(S1): 290-296.
[4]丁洁民, 何志武. 上海中心大厦悬挂式幕墙结构设计 [M]. 中国建筑工业出版社, 2015.
DING Jiemin, HE Zhijun. Shanghai Tower curtain wall structure [M]. Beijing: China Architecture & Building Press, 2015.
[5]丁洁民, 何志军, 李久鹏. 上海中心大厦幕墙支撑结构与主体结构协同工作分析与控制 [J]. 建筑结构学报, 2014, 35(11): 1-9.
DING Jiemin, HE Zhijun, LI Jiupeng. Analysis on properties of cooperative work and control of curtain wall support structure with main structure of Shanghai Tower [J]. Journal of Building Structures, 2014, 35(11): 1-9.
[6]何志军，丁洁民，李久鹏. 上海中心大厦悬挂式幕墙支撑结构竖向地震作用反应分析 [J]. 建筑结构学报, 2014, 35(1): 34-40.
HE Zhijun, DING Jiemin, LI Jiupeng. Analysis on vertical seismic response of curtain wall support structure of the Shanghai Tower [J]. Journal of Building Structures, 2014, 35(1): 34-40.
[7]石永久, 李勇, 王元清. 点支式幕墙单层索网谐波地震响应的几何非线性研究 [J]. 振动与冲击, 2009, 28(10): 31-35.
SHI Yongjiu, Li Yong, WANG Yuanqing. Nonlinearity in seismic response of a cable net in point-supporting glass wall [J]. Journal of vibration and shock, 2009, 28(10): 31-35.
[8]吴丽丽, 石永久, 王元清. 单层平面索网幕墙结构的实用抗风设计方法研究 [J]. 工程力学, 2008, 25(2): 102-109.
WU Lili, SHI Yongjiu, WANG Yuanqing. Research on practical wind-resistant design methodology of monolayer cable net for glass facades [J]. Engineering Mechanics, 2008, 25(2): 102-109.
[9]REGA G. Nonlinear vibrations of suspended cables---Part I: Modeling and analysis [J]. Applied Mechanics Reviews, 2004, 57(6): 443-478.
[10]IBRAHIM R A. Nonlinear vibrations of suspended cables---Part III: Random excitation and interaction with fluid flow [J]. Applied Mechanics Reviews, 2004, 57(6): 504-506.
[11]IRVINR H M, CAUGHEY T K . The Linear Theory of Free Vibrations of a Suspended Cable [J]. Proceedings of the Royal Society of London, 1974, 341(1626): 299-315.
[12]BENEDETTITI F, REGA G. Non-linear dynamics of an elastic cable under planar excitation [J]. International Journal of Non-Linear Mechanics, 1987, 22(6): 497-509.
[13]NAYFEH A H, ARAFAT H N, Chin C. M., et al. Multimode interactions in suspended cables [J]. Journal of Vibration and Control, 2002, 8(3): 337-387.
[14]GUO T D, KANG H J, Wang L H, et al. An investigation into cables’ in-plane dynamics under multiple support motions using a boundary modulation approach [J]. Archive of Applied Mechanics, 2017, 87(6): 1-18.
[15]GUO T D, KANG H J, Wang L H, et al. Cable’s mode interactions under vertical support motions: boundary resonant modulation [J]. Nonlinear Dynamics, 2016, 84(3): 1259-1279.
[16]GUO T D, KANG H J, Wang L H, et al. Cable dynamics under non-ideal support excitations: Nonlinear dynamic interactions and asymptotic modelling [J]. Journal of Sound & Vibration, 2016, 384: 253-272.
[17]GUO T D, KANG H J, Wang L H, et al. An asymptotic expansion of cable–flexible support coupled nonlinear vibrations using boundary modulations [J]. Nonlinear Dynamics, 2016, 88(1): 33-59.
[18]Arafat H N, Nayfeh A H. Nonlinear Responses of Suspended Cables to Primary Resonance Excitations[J]. Journal of Sound & Vibration, 2003, 266(2): 325-354.
[19]李胜利, 张帅, 王东炜, 等.大跨悬索桥吊索阻尼比影响因素分析 [J]. 振动与冲击, 2017, 36(16): 79-84.
Li Sheng-li, Zhang Shuai, Wang Dong-wei, et al. Analysis of factors influencing galloping on the straddle sling damping ratio of long-span suspended bridges [J]. Journal of vibration and shock, 2017, 36(16): 79-84.