Refined Modeling And Eigenvalue Analysis Of Cable-stayed Bridges Based On Variational Principle

Cable-stayed bridge is a structural system jointly stressed by cable-stayed cables,main girders and towers,and cable-stayed bridges are widely used due to their significant advantages in stress system,construction technology,and economic performance.However,with the development of span and the application of lightweight and high-strength materials,the large vibration problem of cable-stayed bridges has become increasingly prominent and has attracted widespread attention from scholars.The cable-stayed bridge with cable-stayed cable as the main component has the characteristics of large flexibility,small damping and light weight,and is prone to complex nonlinear vibration under complex environmental excitation,of which the coupling vibration of the cable-stayed cable with the main beam and the tower is one of the main forms of vibration.Under different excitations,the vibration between the cable-stayed cable,the main girder and the tower in the cable-stayed bridge shows strong coupling,which can easily cause local failure of the structure and affect the overall stability of the structure in actual engineering,posing a threat to the safety and comfort of the bridge.In this paper,in order to understand the vibration characteristics of the cable-stayed bridge structure,the theoretical method and numerical analysis method are studied,and the following work is mainly completed:(1)Based on the assumption of continuum mechanics,the Lagrange strain description is obtained by the change of the configuration of the continuum,and the Lagrange strain expression of the three basic structural elements(cable-stayed cable,main girder and tower)of the cable-stayed bridge is derived based on the Lagrange strain description.(2)Based on hamilton’s variational principle,a refined dynamic model of the cablestayed bridge is established,the nonlinear motion equation of the cable-stayed bridge is obtained,and the mechanical and geometric conditions of the corresponding structural system are obtained by discussing the continuity of different structural systems at the junction of the tower beam.(3)Using the quasi-static hypothesis,the nonlinear dynamic model of the cable-stayed bridge is down-ordered,and the miniature kinetic model of the cable-stayed bridge is derived.On this basis,by introducing the dimensionless coefficient,the corresponding dimensionless dynamic model is obtained.(4)The in-plane and out-of-plane vibration motion equations and control equations of the cable-stayed bridge are obtained by linearizing the dynamic model of the cable-stayed bridge,and the eigenvalues of the cable-stayed bridge are solved by using the separation variable method.The natural frequency and natural mode of the cable-stayed bridge are obtained by numerical examples,and the localization factors of the cable-stayed bridge modalities are analyzed,and the influence of the stiffness ratio,vertical span ratio,cable inclination angle and structural system on the natural frequency of the cable-stayed bridge are discussed.(5)Finally,the conditions under which internal resonances may occur on cable-stayed bridges are elaborated,and the conditions for global,mixed,and local modal occurrences of cable-stayed bridges are discussed.