Theoretical Research On Application Of External Damping Devices To Mitigate Stay Cable Vibration

Nowadays,as a result of the economic growth and the developments in material studies,design theories and construction technologies,the number of cable-stayed bridges as well as their span lengths are increasing rapidly to carry large volumes of vehicle traffic and railways.As the stay cables in cable-stayed bridges become lighter and more flexible,their intrinsic damping ratio decreases and induces large amplitude of vibration due to dynamic excitations such as traffic vehicles,wind,and rain-wind combination.Many stay cables of bridges around the world have exhibited excessive and unanticipated vibration which result in increasing frequency of maintenance and disruption to normal operations of the entire bridges.Therefore,studies on cable vibration control have been keenly interested by researchers and engineers in designing new bridges and assessing in-service bridges.In general,mitigation of undesired cable vibration can be achieved by attaching a damping device near the anchorage such as a Viscous Damper(VD),High-Damping Rubber(HDR)damper,Friction Damper(FD),Magneto-rheological(MR)damper etc.Although there have been many studies in this field,understanding of the behavior of cable-damper system and design guidelines on dampers are still incomplete and further research is needed.The following main works and novelties are proposed,developed,demonstrated and carried out in this study:Firstly,research on application of HDR damper for cable vibration reduction are conducted as below:(1)HDR material has the capability to dissipate energy significantly.Thus,it has been widely utilized in buildings and bridges to resist earthquake and reduce vibrations.HDR damper has a wide application on stay cables because it brings many advantages such as compact size,better aesthetics,easy maintenance,temperature stability,and low cost compared to other types of damper.However,the theoretical study on cable vibration reduction with a HDR damper is still incomplete.Therefore,in this study,oscillation parameters of the cable-HDR damper system are investigated in detail by modeling the cable as a taut string and the HDR damper as complex-valued impedance and by using an analytical formulation of the complex eigenvalue problem.Some HDR damper parameters which affect the dynamic characteristics of the cable are considered and discussed.(2)The use of two HDR dampers to improve effectiveness and robustness in suppressing cable vibration are also proposed and investigated in this research.Vibration and damping ratio of a taut cable with two attached HDR dampers are investigated in detail by using theory of the complex eigenvalue problem.The problem of two HDR dampers arbitrarily located along a cable is solved and the solution is discussed.Asymptotic formulas to calculate the damping ratios of the first few modes when two HDR dampers are installed near the anchorage(s)are proposed and compared with the exact solutions.Further,a design example is presented in order to justify the methodology.The results of this study show that when the two HDR dampers are installed close to each other on the same end of the cable,some interaction between the dampers leads to reduced damping ratio.When the dampers are on the opposite ends of the cable,they effectively increase damping ratio and provide better vibration reduction to multiple modes.(3)Traditional mechanical dampers have been demonstrated effective in reducing cable vibrations.However,their efficiency is limited due to the fact that they are often attached to the cables near the anchorages because of practical reasons.Unlike traditional dampers,a Tuned Mass Damper(TMD)has been used to overcome the deficiency of the traditional mechanical damper since it can be mounted anywhere along a cable.However,installation and maintenance of TMD are very difficult.This dissertation proposes a new type of damper,which is named the Tuned Mass-High-Damping Rubber(TM-HDR)damper for increasing damping ratio of the cable.The proposed damper can be practically manufactured and installed.Oscillation parameters of cable-damper system are investigated in detail using an analytical formulation of the complex eigenvalue problem.The effects of TM-HDR damper are demonstrated by numerical parametric study and by using a design example.Secondly,research on application of passive viscoelastic damper to mitigate cable vibrations reduction is attended with the following major works:(4)Based on the passive control methodology,viscous damping devices are commonly used for bridge stay cables of medium length.However,the optimal VD can only be selected for each mode of vibration.In this study,to obtain a profound understanding and provide more insights into the dynamics of cable-VD system,its oscillation parameters are analysed by finding the exact values of complex eigenvalue.As a result,optimal parameters of VD can be evaluated and selected in order to reduce vibrations of cable.(5)Based on VD mechanism,Viscous Mass Damper(VMD)is composed of arranging VD and inertial mass element in parallel.Although this device has been used to control seismic in many buildings in Japan,it has not been studied to apply in the field of cable vibration control.This study proposes the application of VMD to improve the damping ratio of the cable.The vibration of a cable with an attached VMD are investigated using analytical formulation of the complex eigenvalue problem and compared with the case of VD.Some VMD parameters that affect dynamic characteristics of the cable are considered in detail through finding the exact values of the complex eigenvalue.Asymptotic formulas for the calculation of damping ratios of a cable when VMD is installed near the end of the cable are also presented.Their accuracy is compared with the exact solution.Further,the effects of elastic support on the VMD effectiveness of a cable-VMD system are also considered.In addition,a design example is presented in order demonstrate the methodology.(6)Finally,a hybrid dampers system combining a VD and a TMD are proposed and studied for their potential applications to overcome the shortcoming of each single type of dampers in suppressing cable vibration of cable-stayed bridges.The results of this study provide insights into the dynamic of the cable with attached damper(s).The research proposes useful methods for selecting optimal type and parameters of the damper for a given cable.Furthermore,it provides guidelines and recommendations in reducing cable vibration in cable-stayed bridges.