考虑索间作用的斜拉桥耦合振动研究

Coupled vibration of cable-stayed bridges considering cables’interaction

为了研究几何非线性条件下斜拉桥索梁耦合振动与索间作用问题,以两条斜拉索与简支梁组合体系为简化模型,利用D’Alembert原理建立考虑初始垂度的索梁体系非线性偏微分方程,设定索的前两阶复合振动模态与梁的基本模态,运用Galerkin方法将其离散为二阶常微分方程,并使用四阶—五阶Runge-Kutta方法对索与梁的振动响应进行了数值分析。结果表明:在双索单梁组合结构中,特定频率条件下一阶模态与主梁强烈耦合,二阶模态与主梁小程度耦合;与单梁单索结构相比,多索导致主梁频率增大,索间作用使得索振幅增大、拍频降低,面内一阶模态对索梁变化更敏感;当索梁频率不变时,索间作用对耦合振动产生的索大幅振动有明显抑制作用,且索梁结构对主梁初位移变化更敏感。

In order to study problems of cable-beam coupled vibration and cables’interaction under nonlinear geometric conditions,a two-cable and a single beam combined system was taken as a simplified model.D’Alembert principle was used to establish the cable-beam system’s dynamic partial differential equation considering cables’initial sag,and it was discretized into a two-order ordinary differential equation using Galerkin method after setting cables’first two vibration modes and beam’s first one.The 4-5 order Runge-Kutta method was used to solve and analyze the cable-beam system’s vibration responses.The results showed that in the 2-cable and a beam combined system,the first mode is strongly coupled with beam,and the second mode is coupled with beam at a lower level under specific frequency condition;compared with a single-beam and single-cable structure,multiple cables make beam frequencies increase,cables’interaction makes cable amplitude increase and beat frequency decrease;the system’s in-plane first mode is more sensitive to cables and beam changes;when cables and beam frequencies are unchanged,cables’interaction obviously suppresses cables’large amplitude vibration caused by coupled vibration;the system is more sensitive to beam initial displacement change.