Analytical And Experimental Studies On Vibration Control Of Stay Cable

Stay cables are very sensitive to environmental excitations due to low internal damping. The wide exhibited vibrations may induce fatigue or broken up of stay cables. To mitigate cable vibration, mechanical viscous dampers have already been installed to stay cables of some cable-stayed bridges in practice. However, some stay cables still vibrate after damper installation and the damage of damper devices are reported. It is regarded as due to that the dynamics of cable-damper-system is still not fully understood yet. On the other hand, the span of cable stayed bridges become longer and longer, passive dampers may not be able to suppress these super long stay-cable vibrations effectively. The research and practice for semi-active control is needed.To further investigate the dynamics of cable-damper-system, the mechanical behaviour of different dampers are tested. It is found that different dampers own different mechanical behaviour. The force velocity relation of different damper may be near to fractional model, linear or bilinear model. It is also found that nearly all dampers own stiffness.To testify the damping effect of different types of dampers, full scale experiments are conducted by using two 215 meters long stay cables with eleven sets of dampers attached to. It is confirmed that the internal damping of free cable is very low, smaller than 0.5% in logarithmic decrement for most of cases, however, the damping of cable attached with damper is much larger and greater than 0.03 in logarithmic decrement in average. It is also found that the damping observed is changed by amplitude and modes number, which is totally different to the results predicted from the linear design method, which assume damper is linear and thus damping of cable will be rely on cable frequency only.The comparison of the test results of the viscous fluid damper to the analysis is made. It is found that the tested changing trends of the damping to amplitude are similar to the analysis; however, the tested maximum damping is far less than the maximum damping predicted from analysis, which is due to the effect of stiffness. It is also observed that the tested damping is not well accord to the damping predicted from analysis when amplitude is small, and the observed effect of small friction force of the damper is confirmed to be the reason. The effect of this small friction force is also observed during tests of other kinds of dampers. It was found that due to the supporter stiffness, the tested average damping of oil damper was the smallest compare to the other three kinds of dampers. It is concluded that the importance of damper supporter should be emphasized. It is found that the damping of cable with attached voltage strengthened MR damper could be divided into two parts, which is confirmed to be due to the binlinear mechanical behaviour of MR damper. The damping of cable-MR damper system will rely on strengthening voltage, mode number and amplitude.The maximum damping predicted from analysis is observed in the test of friction damper. The damping vs. amplitude curve of the theoretical is similar to the test. However, the starting amplitude of the test results is smaller than the analysis; the reason is thoutht to be due to the non rational assumption.The free vibration of a taut cable with linear viscous damper and spring in parallel is investigated. An approximate analytical solution is derived for the optimum damping constant. It is found that the stiffness will greatly reduce the maximum attainable damping of the cable with attached damper near to anchorage. It is also found that there are also universal design curve for viscous damper with stiffness. The influence of fractional damper with stiffness is investigated and verified by full scale experiment results of nonlinear viscous damper.The free vibration of a taut cable with attached bilinear damper is investigated. It is found that the damping vs. amplitude curve of cable could be divided into two parts. The part one is at larger amplitude, the damper works in bilinear states. The part two is at smaller amplitude, the damper works in linear state. It is found that the critical changing point of damping will depend on initial state of cable vibration. The theoretical study is verified by full scale experiment results of voltage strengthened MR damper. It is found that the changing trend of damping is well predicted.Semi-active control method of cable vibration is proposed by using Shape Memory Alloy (SMA) as actuator. The SMA actuator is in series with cable near cable anchorage. The control rule is Kobori's Switch/off control in separated time. A semi-active control experiment of model cable with SMA actuator is conducted. It is found that time delay of SMA actuator is only about 0.3s. This time is shorter than period of many stay-cable. The experiment found that the effect of control is not good for the free vibration of model cable vibration. The numerical simulation results also verified the experiment results. However, the numerical simulations find that the control effect will be much better when the control method is change SMA actuator according to phase of cable vibration, but this control method will need a much faster SMA actuator.