Nonlinear Coupled Vibration Analysis Of Long-span Cable-stayed Bridge

Because of the lightweight and prefabricated development direction of modern bridges,cable-stayed bridges occur large vibration under the circumstances of vehicle,wind,rain or earthquake excitation.If the system dynamic response is affected by the energy transfer between components,this phenomenon is called coupled vibration.The non-linear problem of cable-stayed cables with light weight,large flexibility and small damping becomes more and more prominent.The mechanism analysis of nonlinear coupled vibration of long-span cable-stayed bridge provides a reliable theoretical basis for the study of vibration reduction methods and measures.In this dissertation,the nonlinear dynamic response characteristics of the cable-stayed bridge simplified model under ideal conditions were studied based on the cable large vibration amplitudes observed in engineering cases.The coupled phenomena of different degrees at specific frequencies were found.The influence mechanism of the cable interaction and the in-plane first three modes on the coupled vibration were explained theoretically.In addition,the dynamic characteristics of multi-cable structures were preliminarily discussed.The main contributions of this dissertation are summarized as follows.1.A double cable,single beam and single pylon composite system model considering geometrical nonlinearity of cables was proposed.The partial differential equation of motion was obtained by dynamic methods.The in-plane first three modal truncation of cable and the basic modal truncation of beam and pylon were set up.The equation was discretized by Galerkin method,and then approximated by multi-scale perturbation method.It was found that there were high-order nonlinearities in the system,and the vibration functions of the components were interrelated.The resonance or coupled frequency conditions which might cause large-amplitude motion were explained.2.Based on the reasonable assumptions of structural parameters and vibration conditions,the Runge-Kutta method was used to simulate the nonlinear dynamic response of the composite system without considering the system damping.Under the specific frequency ratio condition,the structure vibration appeared beating phenomenon.Under different initial disturbance amplitudes,the coupled degree between the cable and pylon was different,and there was no similar relationship between the cable and beam.The cable vibration sensitivity to initial displacement and velocity of cable,beam and pylon was determined.In addition,the pyloncable coupled frequency ratio was given.3.For the cable high-order modal vibration of intensive-cable-stayed bridge,the time-history changes affected by the cable interaction and first three modes were investigated under the comparative working conditions,and the control variables were the number of cables and the in-plane modes.The comparison between single cable structure and double cable structure showed that the cable interaction restrained large vibration amplitudes of cables and made the structure stable.By comparing the vibration process of the first mode,the first two modes and the first three modes of single cable structure,it was shown that the first three modes of cables had long-term effects and affected the structure coupled forms.