斜拉索阻尼器减振参数优化局部刚度理论

Local Stiffness Theory of Damper Parameter Optimization for Cable Vibration Control

目前抑制拉索振动普遍采用的方法是在拉索锚固端附近安装黏滞阻尼器,提高拉索阻尼比。但阻尼器黏性系数过小会耗能不足,过大则会对拉索产生明显的钳固效应,使拉索产生过大的局部变形,减小阻尼器行程,同样降低阻尼器耗能效率。因此,对斜拉索-黏性阻尼器减振参数优化设计,提高拉索附加阻尼比,是保证阻尼器对拉索减振效果的重要环节。为此,采用局部刚度模拟阻尼器对拉索的钳固效应,提出了拉索附加阻尼比计算的局部刚度理论,由拉索长度、阻尼器安装位置、索力及拉索平均振幅计算出拉索局部刚度,以单模态振型推导了拉索-黏性阻尼器系统振动方程,获得了黏性阻尼器对拉索减振的附加阻尼比解析解。计算结果表明:对于小垂度拉索的前4阶模态附加阻尼比,局部刚度理论与经典理论吻合。以电涡流阻尼器作为耗能元件,进行了拉索-黏性阻尼器减振模型试验,在相差较大的3种索力条件下获得了拉索第1阶模态附加阻尼比。实测结果与解析解吻合良好,验证了局部刚度理论对不同垂度拉索附加阻尼比预测的准确性。局部刚度理论通过单模态分析获得不同垂度下的拉索任一模态最大附加阻尼比与阻尼器最优黏性系数,其物理意义明确、计算简便,为工程实际提供了一种实用的计算方法。

Currently,a common method for suppressing cable vibrations is installing a viscous damper near the anchor end of a cable to improve the cable damping ratio.However,a small damping coefficient cannot consume sufficient energy,and a large damping coefficient has an obvious clamping effect on the cable,causing the cable to produce excessive local deformation and reducing the damper stroke.Meanwhile,local deformation can reduce the energy consumption efficiency of the dampers.Therefore,optimization design of the damping parameters for the cable-viscous damper is an important step towards ensuring the damping effect,which can improve the additional damping ratio of the cable.To this end,local stiffness is used to simulate the clamp-tightening effect of the damper on the cable,and the local stiffness theory is proposed to calculate the additional damping ratio of the cable.The local stiffness of the cable was calculated considering the cable length,damper installation position,cable force,and average amplitude.In addition,the vibration equation of the cable-viscous damper system can be derived from the single-mode shape,and the analytical solution of the additional damping ratio of the viscous damper for the vibration damping of the cable can be obtained.The calculation results indicate that for the first four modal additional damping ratios of the small sag cable,the local stiffness theory is consistent with the classical theory.After considering the eddy-current damper as the energy-dissipating element,a damping model test of the cable-viscous damper was conducted,and the first modal additional damping ratio of the cable was obtained under the condition of three cable tensions with large differences.The measured results are in good agreement with the analytical solution,verifying the accuracy of the local stiffness theory for predicting the additional damping ratio of different sag cables.The maximum additional damping ratio and optimal viscosity coefficient of any mode of the cable with different sags can be obtained by single-mode analysis in the theory of local stiffness,which has the advantage of clear physical significance and easy calculation.This study provides a practical method for calculating the actual projects.