Research On Statics And Dynamics Characteristics Of Stay Cables Of Super Long Span Bridges Based On Super-long Elastic Rod Model

With the development of China’s communication industry,cable-stayed bridges are currently developing towards lighter and larger spans.The application of super-long cable-stayed cables with low damping and large flexibility is becoming more and more widespread,with a wider range of vibration mode frequencies and a higher probability of substantial resonance of cable-stays under external excitation,which threatens the safe operation of cable-stayed bridges.It is necessary to analyze the dynamic behavior of the cables.Previous studies are based on the traditional elastic beam model,which is not suitable for describing the large deformation problem of cable-stayed wire.In this paper,based on the Kirchhoff dynamic comparison method,a super-long elastic rod model is introduced to study the large deformation behavior of cable-stayed wire.Taking a cable-stayed bridge in China as the research background,the static configuration of the cable-stayed and its parametric vibration under the bridge excitation are studied from both analytical analysis and numerical calculation,and finite element software is used to verify.The main contents of this article include the following:(1)The static shape of a stay cable under self-weight and stretchable conditions was investigated based on a super-long elastic rod model.The equilibrium equations of the stay cable in the general sense were established based on the super-long elastic rod model considering the self-weight,bending rigidity,and elastic tension of the stay cable,and the deflection line,cable force,and cable length corresponding to the equilibrium position shape were discussed in three cases: only elastic tension,only bending rigidity and both elastic tension and bending rigidity were considered.The static parameters of stay cable under the above three different conditions were calculated separately,and the effects of bending rigidity and elastic tension on the geometry of the cable were also analyzed for different cable lengths and forces.(2)Based on the Kirchhoff elastic thin rod model,the internal parametric vibration of the inclined cable under axial excitation was studied.Considering the bending rigidity,sag,and geometric nonlinearity of the stay cable,the parametric vibration equation of the stay cable under axial excitation was established based on the Kirchhoff elastic thin rod dynamics model.The resonance conditions and stability of the stay cable were discussed by analytic analysis of the vibration equation using the multi-scale method.The resonance phenomenon was verified when the ratio of excitation frequency to cable frequency was 1:2,1:1,and 2:1 by numerical solution using the Runge-Kutta method.The effects of excitation frequency,excitation amplitude,cable force,and cable damping on the nonlinear parametric vibration response characteristics of the cable were analyzed.(3)Based on the Kirchhoff elastic thin rod model,the in-plane vibration problem of the tower-cable-deck coupled system of the cable-stayed bridge was studied.Considering the coupling action of the cable-tower-bridge deck,based on the Kirchhoff elastic thin rod dynamics model,the vibration differential equation system of the tower-cable-beam composite structure under the excitation of the bridge deck and the bridge tower was derived.The conditions of resonance of the coupled system were discussed by using the multi-scale method for regenerative expansion.Through numerical methods,the vibration characteristics of free vibration and forced vibration of the coupled system were analyzed,and the influences law of parameters such as frequency ratio,excitation amplitude,cable force,and system damping were discussed.(4)ANSYS finite element software was used to analyze the parametric vibration problem of cable-stayed cables.The finite element models of the bridge and cables were established in the ANSYS finite element software,and the dynamic characteristics of the entire bridge and cables were analyzed and compared with theoretical calculation values.According to the previous analytical analysis,the cable-stayed cables that were more prone to parametric vibration were selected as the research object,namely the cable-stayed cables with a frequency ratio of 1:1 or 1:2 to the entire bridge frequency.The response amplitude of the cable-stayed cable under the end harmonic displacement excitation was analyzed.