考虑模态振型影响的斜拉桥非线性内共振能量转换研究  

Energy Transfer of Nonlinear Internal Resonances in Cable-stayed Bridges Considering the Influence of Global Modal Shapes

作　　者：陈柯帆 李源[1,3] 卢涛 贺拴海 宋一凡[1,3] 杨鹏 任祥伟[1] CHEN Ke-fan;LI Yuan;LU Tao;HE Shuan-hai;SONG Yi-fan;YANG Peng;REN Xiang-wei(School of Highway,Chang'an University,Xi'an 710064,Shaanxi,China;Department of Civil Engineering,Aalto University,Espoo 02150,Southern Finland,Finland;Key Laboratory of Bridge Detection&Reinforcement Technology Ministry of Communications,Chang'an University,Xi'an 710064,Shaanxi,China;Poly Changda Engineering Co.Ltd.,Guangzhou 510000,Guangdong,China)

机构地区：[1]长安大学公路学院,陕西西安710064 [2]阿尔托大学土木工程学院,南芬兰埃斯波02150 [3]长安大学旧桥检测与加固技术交通行业重点实验室,陕西西安710064 [4]保利长大工程有限公司,广东广州510000

出　　处：《中国公路学报》2024年第9期157-169,共13页China Journal of Highway and Transport

基　　金：国家自然科学基金项目(51978062);陕西省自然科学基础研究计划项目(2022JQ-415,2024JC-321)。

摘　　要：为研究斜拉桥面内局部模态与整体模态耦合激发非线性的振动复杂机理,针对索-梁耦合结构1∶1内共振进行了数值仿真和模型试验,分析了模态振型影响下的内共振能量转换进程及特点。首先,考虑了由拉索初始垂度引起的几何非线性,建立了由斜拉索与参数质量梁段构成的索-梁耦合动力学模型。然后,根据索-梁端动态耦合条件,基于达朗贝尔原理推导了索、梁动力控制方程,采用有限差分方法代数转换了梁段控制方程的二阶偏微分项以便进行数值求解,通过模态拖拽法和分离变量法得到了结构无穷维的常微分方程组和模态函数。最后,基于4阶Runge-Kutta方法建立了数值仿真程序,结合整体模态振型的影响,分析了1∶1内共振下的能量转换问题,并通过模型试验进行了验证。结果表明:内共振发生时,索-梁锚固点是系统能量进行周期性动态转换的通道,其对应的整体模态振型幅值对能量转换影响较大;锚固于某阶整体模态振型驻点处的拉索即使满足频率比例关系,亦无法被激励产生内共振;拉索的1阶与2阶内共振响应彼此独立,无明显干扰效应;局部与整体模态频率满足等比关系是引发内共振的前提,局部及整体模态间的周期性能量传递是产生内共振的根本原因,而索-梁锚点对应的模态有效参与系数是内共振下能量转换的重要量化指标。This study investigates the complex mechanism of nonlinear vibrations induced by local-global modal interactions in cable-stayed bridges.Through numerical simulations and experiments on a cable-beam coupled structure,we systematically examined the energy transfer processes and characteristics of 1∶1 internal resonance considering the influence of global modal shapes.First,a cable-beam coupled model was established using discrete parametric beam segments,considering the geometric nonlinearity caused by the cable's sag.Based on the cable-beam dynamic conditions,differential governing equations were obtained using the D'Alembert principle and algebraically reduced using the finite difference method.Moreover,ordinary differential governing equations of infinite dimensionality were derived using separation and modal drag methods.Subsequently,the mechanism of the resonance energy transfer was further analyzed based on the numerical simulations and laboratory experiments.The results show that when internal resonance occurs,the cable-beam anchorage particle is the main path for periodic resonance energy transfer.The amplitude of the global modal shape significantly influences the resonance energy transfer between the cable and the beam.Specifically,when the cables are anchored at global modal stagnation points and satisfy the proportional conditions of the modal frequency,the energy transmission between the cables and the beam is inhibited,preventing internal resonance in the structure.During multiple internal resonances,the first-and second-order cable vibrations remain independent of each other.The resonance frequency conditions are validated as the premise of the internal resonance,whereas the periodic energy transfer between the local and global modes is the fundamental cause.Furthermore,the proposed modal participation factor at the cable-beam anchor point is the critical factor that influences the energy transfer.

关 键 词：桥梁工程 1∶1内共振 模型试验 能量传递 面内模态振型 有限差分法 

分 类 号：U441.3[建筑科学—桥梁与隧道工程]