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基于超细长弹性杆模型的斜拉索参数振动分析

Parametric Vibration Analysis of Stay Cables Using a Super-Thin Elastic Rod Model
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摘要 将超细长弹性杆力学模型应用于描述大跨度斜拉桥拉索的非线性振动行为.首先,在假设拉索静态位形为悬链线型的基础上,考虑斜拉索的几何非线性、垂度和抗弯刚度,推导了拉索在轴向激励作用下的多模态非线性振动方程.其次,通过多尺度法对该振动方程求解,得到拉索发生主共振、主参数共振和3∶1次共振的常解存在条件;再根据Lyapunov近似稳定性判据进一步揭示振幅稳态解的渐进稳定条件.最后,通过近似解与数值解的对比分析,研究频率比、激励幅值和拉索阻尼对拉索振动特性的影响关系.结果表明:基于弹性杆模型的拉索振幅值略大于弹性梁模型,且拉索发生主参数共振的最小起振幅值有所降低;增大阻尼可一定程度上减小拉索的振动,但抑制效果有限,故控制激励幅值是减小拉索振动的有效方法. The mechanical model of super-thin elastic rod is applied to describe the nonlinear vibration behavior of the cable of long-span cable-stayed bridge.Firstly,considering the geometric nonlinearity,sag and flexural stiffness of the cable,the multimodal nonlinear vibration equation of the cable under axial excitation is derived on the basis of assuming that the static configuration of the cable is catenary.Secondly,the vibration equation is solved by multiscale method,and the existence conditions of the constant solutions of primary resonance,primary parameter resonance and 3∶1 resonance are obtained.The sufficient conditions for the existence of the asymptotic steady solution are further obtained according to the Lyapunov's first approximate stability criterion.Finally,the effects of frequency ratio,excitation amplitude and cable damping on cable vibration characteristics are studied by comparing the approximate solution with the numerical solution.The results show that the amplitude of the cable based on the elastic rod model is slightly larger than that of the elastic beam model,and the minimum amplitude of the main parameter resonance of the cable is reduced.Increasing damping can reduce the vibration of the cable to some extent,but the suppression effect is limited,so controlling the excitation amplitude is an effective method to reduce the vibration of the cable.
作者 管永乐 王鹏 刘百强 Guan Yongle;Wang Peng;Liu Baiqiang(School of Civil Engineering and Architecture,University of Jinan,Jinan 250022,China)
出处 《动力学与控制学报》 2024年第9期37-44,共8页 Journal of Dynamics and Control
基金 国家自然科学基金资助项目(12272148,11772141),。
关键词 Kirchhoff弹性杆方程 斜拉索 轴向激励 参数振动 多尺度法 Kirchhoff elastic rod equation stay cable axial excitation parametric vibration multiscale method
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