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郑攀攀,赵珧冰,吴先强.考虑损伤效应的悬索非线性共振响应分析[J].计算力学学报,2022,39(4):420~426
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考虑损伤效应的悬索非线性共振响应分析
Nonlinear resonant response of suspended cables considering damage effects
投稿时间:2021-01-22  修订日期:2021-06-24
DOI:10.7511/jslx20210122004
中文关键词:  悬索  损伤效应  共振响应  多尺度法  稳态解
英文关键词:suspended cable  damage effect  resonant response  multiple scales method  steady-state solution
基金项目:国家自然科学基金(11602089);华侨大学中青年教师科研提升资助计划(ZQN-YX505)资助项目.
作者单位E-mail
郑攀攀 华侨大学 土木工程学院, 厦门 361021  
赵珧冰 华侨大学 土木工程学院, 厦门 361021 Ybzhao@hqu.edu.cn 
吴先强 华侨大学 土木工程学院, 厦门 361021  
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中文摘要:
      悬索在其施工、运营和维护阶段会不可避免地遭受损伤,导致振动特性发生改变。本文基于哈密顿变分原理,引入与损伤程度、范围和位置相关的三个无量纲参数,建立损伤效应影响下悬索面内动力学模型,并推导其无穷维的非线性动力学微分方程。利用高阶多尺度法得到系统发生主共振响应时的幅频响应方程及稳态解。数值算例表明,悬索线性和非线性共振响应特性与损伤效应密切相关。悬索一旦发生损伤,其张力减小,垂跨比增加,将形成新的静力构形。受损悬索的固有频率将下降,且随着损伤程度增加而进一步减小。损伤会导致悬索正/反对称模态频率的交点发生偏移,影响系统内共振响应特性;损伤会引发系统振动特性发生明显定量和定性改变,但是垂跨比不同,其共振响应特性受损伤影响会有明显区别;损伤甚至会直接改变系统稳态响应幅值以及稳定解的数量,导致系统产生明显大幅振动,影响结构安全。
英文摘要:
      Suspended cables are inevitably damaged during construction,operation and maintenance,which leads to changes in vibration characteristics.Based on the Hamilton’s principle,three dimensionless parameters of damage intensity,extent and position are introduced here.The in-plane nonlinear dynamic model of the suspended cables considering the damage is established,and the infinite dimensional dynamic differential equation can be obtained.The amplitude-frequency response equation and steady-state solutions are obtained by using the higher-order multi-scale method.Numerical examples show that the linear and nonlinear resonance response characteristics of the suspended cables are closely related to damage effects.Once a suspended cable is damaged,its tension decreases and the sag increases,and a new static configuration is generated.The natural frequencies of the damaged cable decreases with the increase of the damage intensity.Damage effects make the crossover point between the symmetric and antisymmetric mode frequencies shift and the internal resonant responses could be affected.The vibration characteristics of the system are changed quantitatively and qualitatively due to the damage effects,and the resonant response characteristics are significantly affected by damage with different sag-to-span ratios.The damage effect can even directly change the amplitude of the steady-state response and the number of stable solutions,causing large amplitude and endangering the safety of the structures.
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