斜拉索-三单元Maxwell阻尼器系统的复模态分析

Complex Modal Analysis of a Taut Cable with Three-Element Maxwell Damper

针对拉索-三单元Maxwell阻尼器系统的自由振动,运用复模态方法分析得到系统最优模态阻尼比和阻尼器最优阻尼系数的近似解析解.采用三单元Maxwell阻尼器模型模拟粘滞阻尼器、阻尼器内刚度和支架,得到拉索-三单元Maxwell阻尼器系统的运动方程.通过复模态分析得到以超越方程形式表达的系统自由振动阻尼特性的解析形式.对于阻尼器安装位置接近索端的情况,给出了有理函数形式的近似解析式.采用迭代法对解析形式的复特征频率方程进行了数值分析,结果表明近似解析式具有良好的精度.研究表明,阻尼器内刚度和支架柔度的耦合作用将显著削弱阻尼器的减振效果;阻尼器的最优阻尼系数随阻尼器内刚度的增大而增大,但随支架柔度的增大而减小.

Free vibrations of a taut cable with an attached three-element Maxwell damper were investigated by using an analytical formulation of the complex eigenvalue problem. As the viscous damper, its inherent stiffness and supporter were represented as a three-element Maxwell model, the equations of motion of the cable and the three-element Maxwell damper system were obtained. The damping properties in the free vibration of the system were extracted by complex-mode analysis technique. An explicit analytical approximation was obtained, when the damper was installed near the cable anchorage. The full solution was evaluated numerically by iteration, and the results showed that the approximate explicit formulae were rather accurate. This study shows that the interaction between the inherent stiffness of the damper and the flexibility of the supporter in the viscous damper reduces the damper effectiveness. The optimum damping coefficient of the three-element Maxwell damper increases when the inherent stiffness of the damper increases, but decreases when the flexibility of the supporter increases.