拉索-弹簧系统的振动特性研究

Free vibration of taut cable with a spring

将拉索简化为一根张紧弦,并将辅助索对拉索的刚度贡献简化为一根弹簧所提供的刚度,基于拉索-弹簧系统的动力学方程,采用分离变量法得到了拉索-弹簧系统的特征方程。研究了当弹簧刚度取极限值时特征值(振动频率)的极限解,由此确定了特征值的存在范围。当弹簧靠近锚固端时,由一阶泰勒展开得到了特征值的迭代解和近似解。分析了弹簧刚度和安装位置对拉索振动频率的影响,研究了针对提高低阶模态振动频率时弹簧的优化设置位置。研究结果为进一步研究辅助索减振设计问题提供基础理论依据,对辅助索减振设计也有一定的参考价值。

Cable vibration and its mitigation are major concern for cable-stayed bridges. The taut cable can be simplified as a tight string, and the stiffness contribution of the secondary cable as that of a spring. This paper tries to investigate the stiffness contribution effect of secondary cable to the stay cable by studying the vibration of cable-spring system. Based on dynamic equation of the taut cable with a spring, the characteristic equation was derived by separation of variables. In the case of ultimate spring stiffness, the limit solutions of eigenvalue were investigated and its existed range was determined too. The iterative solution and asymptotic one of the eigenvalue according to first order Taylor expansion were derived when spring was located near to cable anchorage. Parameter studies were conducted, influences of the stiffness of spring and its location on eigenvalues were analyzed, and further recommendation for optimization of spring location to improve first few modal frequencies of cable vibration was given. The studied results provide a theoretical base for further investigating the design of secondary cables for vibration reduction.