辅助索接地的简化索网-阻尼器系统的阻尼和频率

Damping and Frequency of Simplified Cable-Network-Damper System with Cross-Tie Fixed to Ground

索网-阻尼器-接地辅助索系统的振动特性研究对于拉索减振问题具有重要的工程应用价值.本文建立了由2根水平拉索和1根锚固于桥面的辅助索组成的简化索网系统,将辅助索简化为线性弹簧单元,基于弦理论,由拉索锚固端的位移边界条件和阻尼器、辅助索安装位置处位移及力的连续条件,推导得索网系统的复特征值方程,并由此求得阻尼和频率的数值解.以3、4阶振动模态为例,讨论了弹簧刚度、安装位置对最大模态阻尼比、阻尼器的最优阻尼系数和相应振动频率的影响.研究结果表明,索网系统的各阶模态存在奇数阶和偶数阶两种模态,两种振动模态具有不同的振动特性.随着辅助索与桥面连接段刚度的增加,最大模态阻尼比可能的取值上限将增加至单索-阻尼器系统的最大模态阻尼比值的2.0～2.4倍,但辅助索可选择的优化安装区间则变得更为狭窄和分散。

The dynamics of cable network with both cross-ties and dampers are important for cable vibration mitigation. A simplified cable-network-damper system was proposed. It is comprised of two parallel cables and a cross-tie fixed on ground. The cross-tie was simplified as linear spring elements. Based on the string theory, the complex frequency equation of the system was deduced according to the boundary conditons at the fixed end of the cables and displacement continuity and force equilibrium equations at the mounting position of the cross-tie. Then the damping and frequency values were derived by numerical iteration. In the cases of the third and fourth vibration modes, effects of spring stiffness and location on the maximum damping ratio, the optimal damping coefficient and the corresponding frequency were analyzed. It is found that there are odd and even modes in the system vibration; and these two modes have different vibration characteristics. With the increasing in the stiffness of the cross-tie fixed on ground, the upper limit of maximum damping value is increased 2.0 - 2.4 times of the maximum modal damping ratio of a single cable-damper system ; however, the optimal cross-tie locations become less and separated.