桥塔纵向作用下悬索桥主缆的非线性参数振动

研究特大悬索桥施工过程中主缆非线性参数振动问题.综合考虑主缆垂度、大变形引起的几何非线性等因素,将桥塔塔顶振动考虑为主缆的参数激励项,利用Newton定律建立的主缆参数振动控制方程,运用Galerkin和多尺度方法对主缆参数振动进行了理论分析,以某悬索桥中的主缆为例,运用有限元程序计算了桥塔的前20阶频率,通过桥塔与主缆的第一阶面内频率匹配,0号桥塔的第11,13阶振动及3号桥塔的第4阶振动激发主缆参数振动的可能性最大,数值分析了主缆发生参数振动时的位移时间历程和索力变化规律.研究结果表明,当桥塔的局部振动频率约为主缆振动频率的2倍左右时,主缆容易发生参数振动,发生参数振动时,位移响应显著,缆索张力增量很小.

Nonlinear parametric vibration of cables in suspension bridgeunder longitudinal vibration of tower

The nonlinear parametric vibration of main cable in suspension bridge was investigated. The local vibration of tower was considered the parametric excitation of main cable, the equation governing the parametric vibration of main cable was derived using Newton Law considering sag and geometric nonlinearity. Then the Galerkin and the multiple scales method were used to analyze the parametric vibration of main cable. A case study of main cable of a suspension bridge, the first 20 frequencies of the tower was calculated by means of the finite element program, through the frequency of tower and the first in-plane frequency of main cable matching, it was very possible that the 11th, 13th order vibration of No.0 tower and the 4th order vibration of No.3 tower excited the parameter vibration of main cable, the time history and the variation law of cable tension were examined. As a result, the main cable is prone to vibration parametric vibration when the local frequency of tower is about 2 times the frequency of main cable. The parametric vibration has a considerable effect on the displacement of main cable, and the increment of cable tension is small.