Feasibility Study On Vibration Reduction Of The Long Stay-cable Using TMD

The length of the stay cable serving as a main load-bearing component of the cable-stayed bridge increases gradually with the main span.The vibration control of the long stay cable is an important factor affecting the safety and durability of the cable-stayed bridge.The TMD(Tuned Mass Damper)is widely used in the bridge vibration control,but less used in the cable vibration control.Compared with commonly used viscous dampers,the TMD is not affected by the install position in the vibration control of stay cables,but there are relatively few related studies.Therefore,it is very necessary to carry out the feasibility study on the TMD application to vibration reduction of the long stay cable.Consequently,the parametric vibration of the stay cable without the TMD,the dynamic characteristics of the stay-cable considering the influence of the TMD and the temperature effect in the damping performance of the stay cables-TMD system are studied in this paper.The main elements and conclusions are as follows:(1)The parametric vibration model of the stay cable subjected to the periodic displacement of the support is estabilished and its motion equations considering the first two modes were derived.The multi-scale method and the fourth-order Runge-Kutta method are employed to obtain the resonance characteristics and the numerical solutions,respectively.The results show that as for short cables,medium cables and long cables,the main resonance and parametric resonance of the first-order mode occur at the internal resonance frequency ratio of points 1 and 2.The parametric vibration of the second-order mode occurs when the internal resonance frequency is higher than points 2and 4.(2)The analytical solution of the stay-cable-TMD system subjected to the support excitation was derived in order to perform the vibration reducing analysis.The results show that the stay-cable-TMD system exhibts the best performance of vibration reduction for the first-order frequency modulation.The cable amplitude gradually decreases with the increasing damping ratio with the same mass ratio.However,if the TMD damping ratio becomes too larger,it will amplify the system vibration.Every mass ratio corresponds to its own optimal TMD damping ratio.If the installation position of the TMD approaches the middle of the span,the vibration reducing performance will be the best.(3)A finite element model of a cable-stayed bridge was established to analyze the influence of temperature on both the internal force of the cable and the displacement of the support.On this basis,the influence of the temperature effect on the parametric vibration of the stay cable is looked into.The results show that both the internal force of the cable and the displacement of the support are roughly in proportion to the temperature variantion.The overall rise and drop of temperature have little implication on the parametric vibration of the stay cable.The gradient rise of temperature has a greater impact on the parametric vibration.The gradient drop of temperature has little influence on the first-order mode but has a greater impact on the second-order mode.(4)The results of the temperature effect on the vibration reducing performance of the stay cable-TMD system show that the overall rise and gradient rise e have improve the damping effect and the overall drop and gradient drop will amplify the vibration of the system.