Damper are the main measure for cable vibration control, and complex modal analysis is the main approach of cable-damper system analysis. The complex frequencies derived from complex modal analysis allow an accurate analysis of system’s damping ratio and frequency, which is of major interest of bridge researchers. There is few studies for investigating the complex mode shape of cable since it does not contain the key parameters for vibration suppression. This paper focuses on the analysis of cable′s phase contained in the complex modal shape. Firstly, the complex modal analysis is used to analysis the cable-damper system, and the physical meaning of complex mode shape is explained. Subsequently, based on its physical meanings, the real separating variable method is improved by adding phase function, thus it is possible to explain how the damping force is translated in the cable. In this process, a set of nonlinear equations are obtained and their general solutions are solved, and the results obtained are consistent with those by the complex modal analysis. Finally, the effect of the damper on the cable’s real modal shape and phase is analyzed based on the results obtained.
陈志,彭文林,禹见达,韩艳,田静莹.拉索-阻尼器系统的改进实模态分析方法[J].动力学与控制学报,2023,21(4):7~17; Chen Zhi, Peng Wenlin, Yu Jianda, Han Yan, Tian Jingying. An improved method to real modal analysis of cable-damper systems[J]. Journal of Dynamics and Control,2023,21(4):7-17.