Model Damping Of Long-Span Cable-Stayed Bridges With CFRP Cables

Carbon Fiber Reinforced Polymer(CFRP) cable is a new material and has potential application to long-span cable-stayed bridges because of its light weight,high strength,good corrosion resistance and fatigue resistance.Since its quality,Young's modulus and damping are very different from those of steel cable,the vibration characteristics and modal damping of CFRP cable need to be studied first before its broad application.Complex eigenvalue method based on non-proportional damping model,one of most commonly used methods for structural damping calculation,has been widely applied to seismic analysis,wind resistance analysis of long-span cable-stayed bridge.However,the applicability of this method to different bridge structures and loadings needs to be further discussed.Stain energy proportional damping theory, another calculation method for model damping,is introduced recently and has shown some advantages and reasonability for damping calculation for long-span cable-stayed bridge by calculating the structural modal damping ratio from energy.Therefore,based on the long-span cable-stayed bridges with 600～1400m spans,we analyzed the modal damping of CFRP cables and cable-stayed bridges with CFRP cables by two different calculation methods(complex eigenvalue method and stain energy proportional damping method) and compared the values of modal damping calculated by these two different methods.Firstly,the modal damping of CFRP cable-stayed bridge was calculated by complex eigenvalue method and stain energy proportional damping theory and its value was compared with that of steel cable.Furthermore,by comparing the calculated values with measured values of steel cable in Tatara bridge,the difference and applicability of these two methods were discussed.Secondly,the air damping of CFRP cable of free vibrationg and forced vibration induced by lateral forces of the wind was analyzed and the effect of vibration amplitude as well as wind speed on the damping of CFRP cable was discussed based on the comparison with that of steel cable.Thirdly,the modal damping of CFRP cable with oil dampers was calculated by complex eigenvalue method and the applicability of complex eigenvalue method to calculation of non-proportional viscous damping system was evaluated.Fourthly,the non-proportional viscous damping and strain energy proportional damping of substructures(such as girder,tower,cable,support and so on) of cable-stayed bridge with CFRP cable were analyzed.The calculated damping value of steel cable-stayed bridge was compared with the measured damping value,so the applicability of these two methods to calculation of modal damping of long-span cable-stayed bridge was discussed.Lastly,the coupled vibration of moving vehicle and bridge for cable-stayed bridge with CFRP cable was calculated and compared with that of steel cable-stayed bridge,so the effect of new cable material on vibration response due to moving vehicles was assessed.Results from the study showed that the nature vibration frequency of CFRP cable was higher than that of steel cable and was affected greatly by air damping.Air damping of CFRP cable increased with the increase of vibration amplitude and wind speed.The vibration of CFRP cable with oil damper is reduced more obviously than that of steel cable.The main vibration modes and modal damping of cable-stayed bridge with CFRP cable were similar to those of steel cable-stayed bridge.The girder deformation of cable-stayed bridge with CFRP cable due to moving vehicles was larger than that of steel cable-stayed bridge.Compared with viscous damping theory,the modal damping calculated based on stain energy proportional damping theory fit better with the field test value,indicating that stain energy proportional damping theory is more applicable for damping calculation of cable-stayed bridge.