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基于部件模态综合理论,将拉索和阻尼器看作两个子结构,则安装阻尼器的拉索振动可以表示为静态约束模态和低频主模态的线性组合。考虑拉索抗弯刚度,推导结构的约束模态和主模态函数,并利用Galerkin方法得到以模态坐标为未知量的常微分运动方程。当仅考虑约束模态和1阶主模态时,根据复模态理论研究线性粘滞阻尼器参数与拉索-阻尼器系统的1阶模态参数的关系。通过与精确解的比较证明该降阶模型的有效性。此外,当忽略拉索抗弯刚度时,仿真分析表明,与目前常用的Johnson降阶模型相比,文中给出的降阶模型更为简便,计算的精度也略高些。
Based on the component modal synthesis theory, considering the cable and the damper as two substructures, the cable vibration of the installed damper can be expressed as a linear combination of the static constraint mode and the low-frequency main mode. Considering the flexural rigidity of the cable, the constrained mode and the main mode function of the structure are deduced. The ordinary differential equations of motion whose modal coordinates are unknown are obtained by Galerkin method. When only the constrained mode and the first order mode are considered, the relationship between the parameters of the linear viscous damper and the first order modal parameters of the cable-damper system is studied according to the complex mode theory. The validity of the reduced order model is proved by comparison with exact solutions. In addition, when the bending stiffness of cable is ignored, the simulation analysis shows that the reduced-order model presented in this paper is simpler and the precision of calculation is slightly higher than that of Johnson’s reduced-order model.