拉索-双弹簧系统的自由振动特性分析

辅助索减振措施是常见的拉索减振方法之一，但拉索-辅助索的减振机理尚不清楚，优化设计方法尚未建立。该文将辅助索对拉索的刚度贡献简化为弹簧对拉索的支撑作用，进行了附加两根弹簧的拉索自由振动特性分析。由位移的连续条件和力的平衡条件建立了拉索-双弹簧系统的频率方程；由一阶泰勒展开得到了当弹簧安装位置靠近拉索锚固端时频率方程的近似解。以弹簧刚度为零时对应的拉索自由振动频率和弹簧刚度趋向于极限时拉索振动频率极限值为基础，讨论分析了不同安装位置和不同弹簧刚度下拉索低阶振动模态的特点，得到了其振动模态分布随弹簧安装位置和刚度变化的内在规律；研究结果可供辅助索减振优化设计参考。

FREE VIBRATION OF TAUT CABLE WITH TWO SPRINGS

Secondary cables are one of counter-measures for cable vibration mitigation, but the mechanism of vibration mitigation in a cable-net system has not fully understood yet, and the optimal design method of secondary cables is still not well established. In this paper, the stiffness contribution of secondary cables to cable is simplified to be two spring supports attached to a taut cable, and then the free vibration of a taut cable with two springs is investigated. The frequency equation of the taut cable with two springs is obtained by means of displacement compatibility and force equilibrium conditions. An asymptotic solution is given by using the first-order Taylor expansion when locations of springs are close to the cable ends. More detail investigations on lower mode vibration frequencies and mode shapes are studied based on the limiting solutions while the spring stiffness is zero or infinite. The variation pattern of frequencies and mode shapes with the changes of spring locations and stiffness is studied and given. The research results can be used as a reference for the optimal design of secondary cables.