拉索-阻尼器-弹簧系统的阻尼特性分析

DAMPING OF TAUT CABLE WITH A DAMPER AND SPRING

该文研究得到了拉索-阻尼器-弹簧系统的复特征频率方程。在阻尼器和弹簧安装点距拉索锚固点长度与拉索长度之比远远小于1的假设条件下,得到了拉索-阻尼器-弹簧系统模态阻尼比的近似解析解,该近似解析解与数值计算得到的精确解对比吻合良好。当弹簧和阻尼器处于同一侧时将会减小拉索所能获得的最大模态阻尼值,而当阻尼器与弹簧在拉索两端时弹簧对阻尼的影响几乎可以忽略。当阻尼器仍处于拉索锚固点附近而弹簧位置向中间移动时由阻尼器引起的频率变化量仍是小量的条件下,得到了结合数值频率解的拉索-阻尼器-弹簧系统模态阻尼比近似解析式。此时拉索所能获得最大模态阻尼比、对应的最优阻尼系数、无量纲频率与弹簧位置、刚度之间存在明确的变化关系。该文研究成果对于拉索端部同时附加橡胶减振器和阻尼器、附加阻尼器的索网结构减振设计具有重要的参考价值。

The damping and frequency of cable-damper-spring system was studied. The complex trequency equation of taut cable with a discrete damper and spring was derived. Asymptotic approximate solutions for the damper and spring was both close to the cable ends were developed as the frequency shifts between free cable and damped cable was small. The comparison between accurate numerical results and approximate formulations showed that they were close to each other. It was found that the spring would reduce the maximum attainable damping as the damper and spring were located at the same end of cable; but the spring would not affect the damping as the damper and spring were located at the two ends of cable. The hybrid numerical and approximate formulations were also given for the case of spring was not close to cable anchorage. The effects of spring stiffness and location to maximum modal damping, the corresponding frequency and the optimum damping parameter were also investigated. The main founding of this paper could provide design basis for cables with both rubber bushing and damper or cable networks with dampers.