Theoretical And Experimental Studies On Higher Multi-mode Vibration Control Of Cables

Cables on cable-stayed bridges are prone to excessive vibrations under complex excitations due to their high flexibility,relatively-small mass and low damping.Installing a damper near the lower end of stay cables is one of the most common ways to suppress the large amplitude vibrations.It is believed that the threats of cable vibrations mainly result from lower modes in previous studies.Therefore,the parameter optimization theories of cable dampers mainly consider the first few modes,and the design of dampers often aims at controlling the first few mode vibrations only.However,with the continuous increase of cable length,more and more cable vibration events show that the harms of higher mode vibrations to cables and their connectors can not be ignored.The higher mode vibration event of the cables on the Sutong Bridge shows that it is unreasonable to ignore the higher mode vibrations of cables and their control.Aiming at the problems that the previous parameter optimization theories of cable dampers are not suitable for higher modes and the damper schemes can not effectively control the higher mode vibrations,a systematic and in-depth research are made in this study,and the main i nnovative achievements include: The classical parameter optimization theory of cable-viscous damper system is extended,the explicit solutions of the damping ratios and the optimal parameters which are not limited to the lower modes are obtained;A paramet er optimization scheme of viscous damper for controlling higher-multi mode vibrations of cables is proposed,which significantly expands the modal range of dampers for cable control;A scheme of installing an additional damper between the original damper and the anchorage is proposed to control the "node mode" vibrations,which exist on long cables with specific frequencies even under the control of dampers;A parameter optimization scheme of a cable with two dampers is proposed to solve the possible proble m that the first dozens modes all need to be controlled.Taking the method of verifications between theoretical analyses and experimental researches,the main works of this study are listed below:(1)The wind speed,wind direction and acceleration responses o f five selected cables on the Sutong Bridge were monitored between August to October in 2018.According to the lengths,the cables of the Sutong Bridge are divided into three types:short cables,medium cables and long cables.Based on the monitoring resul ts,the vibration characteristics and vibration types of the three types of the cables are respectively analyzed,the relationships between the cable vibrations and the wind speed are summarized,and the control effects of several original control measures of the Sutong Bridge are evaluated.(2)By establishing the dynamic equation of the cable-viscous damper system,the explicit solutions of the damping ratios,the optimal damping coefficients and the optimal installation positions are obtained.It is worth re minding that the applicability of the explicit solutions are not limited to lower modes.Based on the explicit solutions,the effects of modes,the damper positions and the damping coefficients on the modal damping ratios are studied.A three-dimensional diagram is used to systematically describe the laws of the modal damping ratios vary with the several parameters.These studies provide a comprehensive and clear theoretical basis for the parameter optimization design of the cable dampers.(3)Aiming at the problem that the previous control measures can not effectively suppress the higher mode vibrations of cables,a parameter optimization scheme of viscous dampers for controlling the higher-multi mode vibrations of cables is proposed.In order to verify the eff ectiveness of the parameter optimization scheme and establish a complete set of technology of the eddy current damper system(ECDS)applied to cable vibration control,7 cables on the Sutong Bridge are selected to test the parameter optimization scheme by using ECDS.Through the observations and tests of the working states and control effects of the ECDS in the trial operation stage,the design of ECDS are improved,and finally the first application of the ECDS in the cable vibration control is realized.The results of the cable excitation experiment and the long-term monitoring of the cable responses show that the ECDS achieve the desirable control effects.(4)Aiming at the problem that some in-plane vibrations with the specific frequencies still exist on the long cables of the Sutong Bridge in some cases,the monitoring data are analyzed and the relevant theories are studied.It is locked that the reason why this part of vibrations are not successfully controlled is that the installation position of the damper will inevitably coincide with a node of a certain mode on the cable,and this part of vibrations is called node mode vibrations.Based on the analysis,a control scheme of installing a Stockbridge damper between cable anchorage end and viscous damper to control the node mode vibrations is proposed.The design theory and parameter optimization method of using a Stockbridge dampers to control the node mode vibrations are completely established.In order to verify the effectiveness of Stockbridge dampers,exp eriments are carried out on a long cable with serious node mode vibrations on the Sutong Bridge.The monitoring results of 6months period show that the Stockbridge damper successfully control the node mode vibrations of the cable.(5)Aiming at the possible problem that all the first dozens of modes need to be controlled,a parameter optimization scheme of a cable with two dampers is proposed.According to the analysis results of the mode shapes of the cable-two dampers system,a simplified estimation method of the modal damping ratios is obtained.Based on the simplified estimation method,a flowchart of parameter design for cable-two dampers system is summarized.Taking a cable on the Sutong Bridge as an example,several different damper control schemes are d esigned.By comparing the modal damping ratios and response results of the cable under different control schemes,it is verified that the two-damper control scheme proposed in this study can significantly improve the damping ratios of the first several mod es and higher modes at the same time.The vibrations of the dozens of modes are effectively controlled.