摘要
悬索桥缆索在长期服役状态下损伤很难避免,单侧主缆刚度损伤会使系统出现主梁竖弯与扭转自由度间的耦合,这可能会进一步对悬索桥的模态和大振幅下的非线性响应造成影响.为此,建立了考虑单侧主缆刚度受损的七自由度悬索桥横截面模型,模态分析发现单侧主缆刚度损伤会使得系统前两阶固有频率曲线由交叉变为跃迁,导致两个本身相互独立的模态发生耦合.以此为基础,考虑悬索桥主缆刚度有损伤和未损伤两种工况,运用拓展的增量谐波平衡法(EIHB)计算系统在内共振条件下的非线性振动.研究结果表明:单侧主缆刚度有损伤的悬索桥在外部简谐激励下发生1∶1内共振,系统能量表现出明显的转移现象;竖向和扭转简谐激励下,有损伤的悬索桥较未损伤工况响应幅值有所减小,但出现了两个共振响应峰值,对激励频率更为敏感.数值结果与利用Runge-Kutta法计算得到的结果吻合一致,验证了EIHB法的准确性.
During the long period service,it is difficult to avoid damages on the cable system of a suspension bridge.The damage of the stiffness of one side of the main cable will cause the coupling between the vertical bending and torsional degrees of freedom of the main girder,which may further affect the modal property and nonlinear response of the cable bridge under big vibration.Therefore,7-DoFs cross section model of suspension bridge is established,considering the damage of single-side main cable stiffness.Modal analysis found that the damage of single-side main cable stiffness changed the first two natural frequency curves of the system from crossover to veering,resulting in the coupling of two independent modes.Based on this,the nonlinear vibration of the suspension bridge under internal resonance condition is calculated by the extended incremental harmonic balance method(EIHB)considering the two working conditions of damaged and undamaged main cable stiffness.The results show that the suspension bridge with damage to the stiffness of one side main cable will have 1∶1 internal resonance under external harmonic excitation,and the system energy will show obvious transfer phenomenon.Under vertical and torsional harmonic excitation,the response amplitude of damaged suspension bridge is smaller than that of non-damaged suspension bridge.However,the damaged suspension bridge has two resonant response peaks,which are more sensitive to the excitation frequency.The numerical results are in good agreement with those calculated by Runge-Kutta method,which verifies the accuracy of EIHB.
作者
夏超
回忆
李珂
Xia Chao;Hui Yi;Li Ke(School of civil engineering,Chongqing University,Chongqing 400045,China)
出处
《动力学与控制学报》
2023年第2期66-74,共9页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(52078087)。
关键词
悬索桥
截面模型
增量谐波平衡方法
模态分析
内共振
非线性响应
suspension bridge
section model
incremental harmonic balance method
modal analysis
internal resonance
nonlinear response
作者简介
通信作者:回忆,E-mail∶alihui@cqu.edu.cn。
