Research On The Characteristics Of Multi-Mode Vibration Of The Stay Cable-Viscous Damper System

Since many cable-stayed bridges have been built and under operation over the world, how to effectively mitigate the cable vibrations becomes a key technology and research hot in bridge engineering. Viscous dampers attached transversely near to one cable anchor have been widely used for suppressing large-amplitude vibrations of stay-cables. Considering one specific mode, a lot of research suggested the additional modal damping ratio supplied by the damper. As the discrete damper may cause the cable vibrates in multi-mode, the following research are conducted through numerical and theoretical analysis:Firstly, based on the taut cable-linear viscous damper model, the response of free vibration of the system is numerically calculated with the initial condition of the first three un-damped mode shapes. The characteristics of the multi-mode vibration of the cable are analyzed by the frequency spectra. The effects of the damper constant and location are investigated also. Under multi-mode vibration, the additional modal damping ratio is identified and compared to the results gotten from one specific mode.Secondly, the steady-state solution of the cable-damper system is derived under modal harmonic excitation load and concentrated harmonic load. The coupling due to the non-classical damping matrix is analyzed from the mode coordinate and vibration energy. Based on the energy method, the additional modal damping ratio is deduced, relating with the damper size and attached location. The corresponding optimal damper constant and the optimal damping ratio are given and verified.Thirdly, based on the analytical solution of the two-mode harmonic excitation, an index that characterizes the ratio of the exhausted energy of the damper in a fundamental period and the total energy of the cable is introduced. The performance and the design of the damper are investigated. Two numerical examples are given to prove the results, and the effectiveness of the coupling modal is analyzed also.Finally, considering the power-law nonlinear viscous damper, the free responses of the cable-damper system is numerically calculated to investigate the multi-mode character caused by the nonlinearity of the damper. The energy transfer caused by the damper is also analyzed according to the responses of free vibration.