The Nonlinear Vibration Research On The Cable-simple Beam Model Of The Cable-stayed Bridge

With the development of society, growing national economy, transportation plays an increasingly important role.In the construction and the improvement of the transportation facilities,the effection of bridges is even more and more notable.The cable-stayed bridge has not only become a new favorite in the eyes of the bridge designers with the advantages of its span, cost, mechanical characteristics and others,but also has been widely recognized. The stayed cable is one of the main stress components.It has the characteristics of soft quality, small damping and is fatigue and fragile;the vibration problem has drawn wide attention and become a research hotspot. Meanwhile, the establishment of a simple and reasonable mechanical model has very great significance to the structural designs and calculations of cable-stayed bridges.One of the representative cable-stayed bridge models is the cable-beam model,which has obvious advantages.Combinating these facts,this paper is carried out as follows:(1)Derivation to the three-dimensional geometric nonlinear vibration equation with the consideration of the sag and the flexibility of cables is carried out by using the Hamilton variational principle.The potential resonance mode of the plane motion of the cable is considered.The nonlinear vibration equation of a cable under the movement of the support is established and solved;the parametric vibration response is obtained and the related parametric analysis is conducted.(2)Combinating the cable-beam structure model put forward in recent years,a cable-simple beam model is established,which is much suitable for cable-stayed bridges in run. The interaction between one cable and the beam under the condition of nonlinear vibration is analyzed.Meanwhile, the ralated vibration problems under the force vibration are considered.(3)On the basis of the cable-simpe beam model,consideration is given to the interaction between cables.The plane motion equations of the double cable-simple beam coupling system is established and the nonlinear vibration property that may exist in the multi-cable-simple beam system is explored.