漂浮式斜拉桥全局模态对CFRP索的敏感性研究

ANALYSIS ON SENSITIVITY OF GLOBAL MODE OF FLOATING CABLE-STAYED BRIDGE TO CFRP CABLE

斜拉桥复杂动力学问题中的一个关键问题是局部模态频率与全局模态频率成倍数匹配关系时可能导致的斜拉索大幅振动.本文针对这个问题,基于传递矩阵法,研究CFRP索对斜拉桥全局模态频率的敏感性.将斜拉桥的桥面梁和桥塔分别视为多离散弹性支承欧拉伯努利梁,建立其动力学控制微分方程,基于传递矩阵法对其特征频率进行求解.以长沙某独塔斜拉桥作为算例,对结构主要构件:斜拉索、塔和桥面梁的刚度变化对全局模态频率变化的敏感性问题进行了分析.结果表明,桥面梁和桥塔全局模态频率对斜拉索刚度变化非常敏感,并且用CFRP索替换钢质拉索可能避开拉索局部模态与斜拉桥全局模态的倍频关系,从而控制斜拉索的大幅振动.

One of the key problems in the complex dynamics of cable-stayed bridge is the large vibration of cables resulting from the matching relation between the local and global modal frequencies. In this paper,based on the transfer matrix method,the sensitivity of global modal frequency to CFRP cable was investigated. The deck and tower of cable-stayed bridge are regarded as Euler-Bernoulli beam with discrete elastic supports,respectively. Their corresponding differential equations governing the motion of deck and beam are obtained. Then,the eigen frequencies of global modes are obtained by transfer matrix method. A cable-stayed bridge with single tower in Changsha is taken as an example,and the sensitivity of the stiffness of cable,tower and deck to global modal frequencies was studied. The results shows that the global modal frequency is considerably sensitive to the stiffness of cables and the CFRP cable can be used to replace steel cable in order to reduce and control the vibration of cables.