Vibration Control Of Stay Cable Using Inerter-Damping System

Stay cables in cable-stayed bridges are often susceptible to a variety of harmful vibrations under various environmental excitations.The effective vibration control technology of stay-cables is very important for the safe operation of the cable-stayed bridge.Transversely attaching passive dampers have solved the vibration problem of stay cables to a certain extent.However,with the application of long cables with large flexibility,the location of the damper should be further reduced and the range of the cable vibrations mode orders is greatly widened.How to use passive method to solve the problem that traditional passive dampers may not provide enough damping to cables,has been greatly concerned by engineers and researchers.To improve the control performance of passive dampers,relies on the project of the National Natural Science Foundation of China “The theory and technology of three-element passive mitigation of structural vibration and its performance improvement for vibration control of stay cables”(51878274)and combined with the latest theoretical achievement in the field of structural vibration control——“inerter”,cable vibration control using the parallel “inerter-damping” system(PVMD),the series “inerter-damping” system and tuned “inerter-damping” system(TID)are carried out in this study,respectivelyBased on complex modal theory and finite difference method,parametric analysis of the PVMD,the SVMD and the TID on the supplemental modal damping ratio of stay cables are investigate.On the basis,the optimal parameters of these dampers and the maximum supplemental modal damping ratio of stay cable are obtained.The effects of the cable sag and flexural stiffness on the optimum parameters of the three dampers and the maximum modal damping ratio of stay cables are evaluated.Compared with conventional viscous dampers(VD),the superiority of the PVMD,the SVMD and the TID in controlling stay cables is illustrated by comparing the maximum modal damping ratio,the displacement amplitude and the vibration energy in the first mode under the same load.The energy dissipation mechanism of the “inerter-damping” system are investigated.Furthermore,the superior control performance such dampers are illustrated from the perspective of energy dissipation capacity of the dampers.The application scope of different “inerter-damping” systems in controlling cable vibrations is pointed out by comparing the control performance of the PVMD,the SVMD and the TID.The main conclusions of this study are summarized as follows:(1)Compared with the VD,the PVMD,the SVMD and the TID can provide more modal damping ratio to stay cables.In addition,the displacement amplitude and vibration energy of stay cables under the same loads can also be significantly reduced.The better control performance of the PVMD and the SVMD can be attributed to their negative stiffness behaviour induced by the inerter element,which can enlarge the displacement of the damping element and improve the energy dissipation capacity of dampers.The better control performance of the TID can be attributed to the negative stiffness effect and the tuning effect of the TID,both of which can significantly amplify the displacement of the damping element in the TID.(2)When the dimensionless inertance is close to “1”,the control performance of the PVMD is best.The maximum supplemental modal damping ratio of the stay cable increases with the increase of the inertance,while the optimal damping coefficient of the PVMD decreases with the increase of the inertance when the inertance is less than its optimal value.The optimum modal damping ratios provided by the PVMD are basically the same for all modes of stay cables,while both the optimal inertance and damping coefficient decrease with the increase of the modal order of stay cables.The combine effects of the cable sag and flexural stiffness will decrease the performance of the PVMD.(3)The performance of the SVMD is better than the VD when the dimensionless inertance of the SVMD is larger than 0.5.And the control performance of the SVMD is best when the dimensionless inertance is close to “1”.Both the maximum supplemental modal damping ratio of the cable and the optimal damping coefficient of the SVMD are increase with the increase of the inertance when the inertance is less than its optimal value.The optimal modal damping ratios provided by the SVMD are basically the same for each mode of stay cables,while both the optimal inertance and damping coefficient decrease with the increase of the modal order of stay cables.The combine effects of cable sag and flexural stiffness will decrease performance of the SVMD.(4)The maximum modal damping ratio provided by the TID for each mode of the cable is basically the same.The optimal inertance ratio decreases with the increase of the mode order of the cable,while the optimal frequency ratio and the optimal damping ratio increase with the increase of the mode order of the cable.The combined effect of the cable sag and the flexural stiffness of cable will reduce the maximum modal damping ratio added to cable,and the inertance of the TID tends to enlarge the adverse effect.The tuning effect of the TID can enlarge its equivalent negative stiffness coefficient and equivalent damping coefficient,which will significantly reduce the inertance and damping coefficient of the TID for cable vibration control.(5)Compared with the PVMD and the SVMD,the TID can provide more supplemental damping to cable in a specific mode and multi-modes.The control performance of PVMD is better than SVMD in a specific mode,while is not performed as well as SVMD in multi-modes.