Research On The Multi-Mode Composite Vibration Control Method Of Super-Long Stay Cables

The stay cables of the long-span cable-stayed bridge are prone to various of harmful vibrations under the external excitation.With the increase of the length of the stay cable,the natural frequency of the super-long stay cable decreases,and the target control mode order of the super-long stay cable increases further under the common wind speed.The installation position of the external mechanical damper is prone to be close to the node of the high-mode vibration mode shape of the stay cable,which makes the external mechanical damper unable to play the role of vibration reduction.Therefore,the vibration reduction measure by additional a single external mechanical damper is difficult to meet the requirements for the multi-mode vibration control of super-long stay cables.The composite vibration mitigation measures for multi-mode vibrations control of the cable are investigated in this paper,aiming at extending the control frequency range covering both lower and higher modes.Taking a 576.8 m long stay cable as the research object,the multi-mode vibrations control performance of the super-long stay cable with an external negative stiffness damper（NSD）and internal high damping rubber（HDR）dampers,NSD and Stockbridge dampers（SDs）,and NSD and viscous damper（VD）composite vibration reduction measures are investigated respectively.The main conclusions of this study are summarized as follows:（1）The cable-NSD-HDRs system can provide large supplemental modal damping ratios for both the lower and higher modes of the stay cable.For the single-mode vibration control,the negative stiffness of the NSD can increase the energy dissipation effects of the HDR dampers and the NSD.The stiffness effect and energy dissipation effects of the HDR dampers reduce the damping effect of the NSD and increase the optimal damping coefficient of the NSD.For the multi-mode vibration control,the reduction of damping coefficient of the NSD can bring larger modal damping ratios in the higher modes of the cable.When the dimensionless damping coefficient of NSD is 1,the installation of the HDR damper can increase the damping ratios of the lower modes.The effective mode range of vibration control becomes narrower with the increase of the negative stiffness coefficient of the NSD.However,the modal damping ratio of each mode of the cable can be significantly improved in the effective mode range.（2）The synergistic control measure of NSD and SDs significantly improves the high-order multi-mode vibration reduction performance of the cable.The change of the negative stiffness coefficient of the NSD has a significant effect on the optimal parameter selection of the SDs.Compared with the SDs installed in different positions,when the SDs are installed in the same position,similar multi-mode damping performance index can be obtained by using a smaller damping coefficient of the SDs.The optimal modal damping ratio of the SD₁ decreases by 40.57%,and the optimal modal damping ratio of the SD₂ decreases by 6.1%.The installation of the SDs can significantly enhance the damping ratios of the higher modes of the cable,and it seems not to affect the damping ratios of the lower modes.Compared with the cable-NSD system,the cable-NSD-SDs system has a significant advantage in controlling the acceleration responses of super-long stay cables,and the acceleration response is reduced by more than 30%.（3）The composite vibration reduction measure of NSD and VD can significantly improve the multi-mode vibration reduction performance of the cable,and the effective control mode range covers low-order modes and high-order modes.For the single-mode vibration control,when the VD is installed at the further distance from cable anchorage,increasing the negative stiffness coefficient of the NSD,the damping coefficient or the location of the VD can significantly improve the optimal mode damping ratio of single-mode of the cable,and can effectively reduce the damping design cost of the NSD.For the multi-mode vibration control,the reasonable parameter matching of the NSD-VD composite vibration reduction measure can effectively broaden the multi-mode vibration control range of the cable.Increasing the NSD location is more effective in suppressing the displacement responses of the cable,while the combined vibration reduction synergistic control of the NVD-VD has more advantageous in suppressing the acceleration responses of super-long cable,and the acceleration response is reduced by more than 35%.（4）Comparative analysis shows that the NSD-HDRs composite vibration reduction measure is more effective in suppressing the displacement responses of the stay cables,while the cable-NSD-VD composite vibration reduction system is more effective in suppressing the acceleration responses of the super-long stay cable.Compared with the composite vibration reduction measures of the NSD-HDRs and the NSD-SDs,the mid-span acceleration responses of the stay cable under the control of the NSD-VD composite vibration reduction measure are reduced by 57.7%and 11.4%,respectively.