悬索桥刚度、阻尼和风载参数对风致涡激振动的影响  

Effects of stiffness, damping and wind loads on suspension bridges vortex vibration

作　　者：李天鹏 黄坤 许蔚[1] 黄晓敏 LI Tianpeng;HUANG Kun;XU Wei;HUANG Xiaomin(Department of Engineering Mechanics,Faculty of Civil Engineering and Mechanics,Kunming University of Science and Technology,650500 Kunming,China)

机构地区：[1]昆明理工大学建筑工程学院工程力学系,昆明650500

出　　处：《应用力学学报》2024年第5期1160-1167,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.11562009,12050001)。

摘　　要：悬索桥较低刚度使得其风致涡激振动较容易被激发,并产生复杂的异常运动。使用悬索桥竖向弯曲运动偏微分方程,定性的探究了悬索桥结构刚度、阻尼和风载参数对涡激振动影响。首先,使用伽辽金法把非线性偏微分方程在前两阶竖向正对称弯曲模态截断,得到两个二阶非线性常微分方程。之后,使用多尺度法对该常微分方程组进行摄动求解,得到悬索桥在前两阶竖向正对称弯曲模态主共振时的近似解析解。最后,通过近似解析解分析了虎门大桥风致涡激振动的特点。研究结果显示:悬索桥数学模型中的三次非线性项对结构的非线性振动行为有显著影响;当风的涡激频率小于悬索桥固有频率时,伴随风载的变化,振动幅值将产生跳跃现象;结构阻尼和刚度对悬索桥的涡激振动均有明显影响,伴随阻尼和刚度的增加振动的幅值显著减小。The low stiffness of the suspension bridge makes it sensitive to wind-induced vortex vibrations,and wind loads may induce its complex abnormal motions.We use the partial differential equation,which models the vertical bending motion of suspension bridges to qualitatively research the effects of stiffness,damping,and wind loads on the vortex-induced vibrations of suspension bridges.First,the Galerkin method truncates the nonlinear partial differential equations in the first two-order symmetric bending modes and obtains two second-order nonlinear ordinary differential equations.Then,the multi-scale method is used to obtain the approximate analytical solution of the primary resonance.Finally,the characteristics of wind-induced vortex vibrations of the Humen Bridge are analyzed through approximate analytical solutions.The research results show that:The cubic nonlinear term of the mathematical model significantly impacts the nonlinear vibrations of the structure;When the vortex-induced load frequency is less than the modal frequency of the suspension bridge,vibrational amplitude’s jump phenomenon may occur with the change of the wind load;Structural damping and stiffness have apparent effects on the vortex-induced vibrations of the suspension bridge,and the vibration amplitude may decrease significantly with the increase of damping and stiffness.

关 键 词：悬索桥 风致涡激振动 多尺度法 结构刚度 结构阻尼 

分 类 号：U448.25[建筑科学—桥梁与隧道工程]