The Investigation On Cable-Beam Vibration Of The Cable In Cable-Stayed Bridge

Inclined cables are most easily prone to exhibit vibration of large amplitude that may be excited by external excitation, because of the small mass, large flexibility and small damping. And the vibration may influence the safety of the bridge. In this thesis, the characteristics of Cable-Beam vibration of cable-stayed bridges under external excitation were investigated based on the theory of non-linear vibration of cables and FEM(Finite Element Method), taking the actual project as the background. The conclusions of this investigation can provide a reference for the design and analysis of cable-stayed bridges.In chapter 2, in order to study the vibration characteristics of a single cable, the equations of large amplitude vibration of a cable with a sag in three-dimensional space were derived, considering the coupled effect of cable-modals of large amplitude vibration. The characteristics of equations of cable-vibration were discussed by multi-scale method. According to the theory of nonlinear vibration, the characteristics of vibration of large amplitude of cables were analyzed. The computer program was developed, and the nonlinear vibration equations of a cable were solved by numerical method to verify the results of theory analysis.In chapter 3, the nonlinear static algorithm and dynamic time-history integral algorithm based on the theory of Co-Rotational formulation of the element in FEM was developed. The program of FEM was developed, and the correctness and reliability of this program was verified by ANSYS. The program is applicable to the study of nonlinear vibration of cables.In chapter 4, based on the parameters of a cable in a real Cable-Stayed bridge, the effects on the cable-vibration of the sag, bending stiffness and the vibration state were discussed, and the nonlinear vibration time-history of the cable under the displacement-excitation at its end was calculated by the FEM program of this paper. Comparing the results of FEM and the results of numerical calculation of the equation, the reliability and applicability of the cable vibration equations were verified. The calculation and analysis results show that the theoretical equations which describe the vibration of the cable are reasonable for the real cables in Cable-stayed bridges. This laid the theoretical foundations for the development of the dynamic element of cables.In chapter 5. the concept of "Cable-Beam vibration" was defined, and it is believed that the cable-beam vibration mainly include two kinds in cable-stayed bridge, the forced vibration and parametric vibration. The Cable-dynamic element was developed, through combining the theory of cable vibration equation and FEM. A simple FEM model for the investigation of Cable-beam vibration was built. The essential rules of Cable-Beam in Cable-Stayed bridges were summarized through analyzing the results of calculation. This investigation could provide key theoretical and technological foundations for the investigation of the Cable-Beam vibration in global bridge.In chapter 6&7, the algorithm of Vehicle-Bridge coupling vibration used in this paper was discussed. The dynamic characteristics of Cable-Beam vibration of a long span Cable-stayed bridge under the train excitation was investigated, based on the nonlinear vibration theory of cables, FEM, and the algorithm of Vehicle-Bridge coupling vibration. A real Cable-Stayed bridge FEM model was built by the program of this thesis the cables were simulated by Cable-Dynamic elements. Firstly, the natural frequency of each cable and the natural frequency of global bridge were compared, and the possibility of resonance of each cable was analyzed. Secondly, the characteristic of Cable-Beam vibration in the cable-stayed bridge was analyzed in the conditions of free vibration and vibration excited by ideal external excitation. Based on the results of the analysis in the thesis, the characteristics of Cable-Beam vibration in Cable-Stayed bridge were discussed, under the influence of different working conditions of a train. The investigation results indicate that, as to the large span cable-stayed bridge, the possibility of the large vibration caused by the Cable-Beam vibration is very low, when trains go through the bridge. Finally, the research results of this thesis were summarized, and general principles were put forward to avoid the large amplitude vibration of cables in the design of Cable-Stayed bridges by Cable-Beam vibration.