Study On Parametric Vibration And Multiphysics Nonlinear Vibration Of Cable

As a kind of flexible structure,the cable-stayed structure has excellent mechanical properties and spatial extension ability,and has been widely used in the production and life of the people.For example,the cable-stayed bridge and the cable-stayed space structure are widely used at present,as well as the submerged floating tunnel is planned to be built.The cable-stayed structure is generally considered to consist of three main components: the tower(column),the inclined cable and the suspension body.Generally,the column(column)provide vertical support,the suspension body provide spatial extent and the cable connects the suspension and the column to form a cable-stayed structure.This paper reviews the research status of parametric vibrations of cable-stayed structures’ cable at home and abroad.It introduces the research progress of parametric vibrations of cable-stayed bridge,the submerged floating tunnel,the cable-stayed space structure and mast.The literature shows that although the specific forms of the cable-stayed structure are different,the mechanism of parametric vibrations is the same.Based on the static analysis of the horizontal cable,the original configuration of cable ignoring flexural rigidity and the original configuration of cable considering flexural rigidity are established.The applicability of the parabolic configuration is discussed by comparing the two initial configurations(catenary configuration and parabolic configuration)when the flexural rigidity is neglected.It is pointed out that the parabolic configuration can meet the requirement of engineering accuracy under normal working conditions.The curves of the influence coefficient of the flexural rigidity and the change rate of the sag are plotted to analysis the influence of flexural rigidity on sag.Based on the dynamic analysis of the horizontal cable,the free vibration equation of the horizontal cable considering flexural rigidity is established to analysis the influence of flexural rigidity on frequency.It is pointed out that the physical stiffness has little influence on the sag and the natural frequency of the cable under normal working conditions.The excitation of the end of the cable is considered as the ideal excitation to establish the forced vibration equation of horizontal cable under transverse excitation and the parametric vibration equation of horizontal cable under axial excitation.The coupling effects of parametric and forcing is considered to establish the coupling vibration equation of stayed cable.The response of stayed cable under parametric and forcing excitation is analyzed based on numerical computation.It is pointed out that,in cable-stayed structure,long cable is more easily excited resonance and short cable is more easily excited primary parametric resonance;the firing time of primary parametric resonance of short cable will be advanced with the influence of the forced vibration.The firing time of long cable will be delayed.Considering the excitation of the end of the cable as the non-ideal excitation to establish the coupling vibration equation of stayed cable and suspension body.It is pointed out that,the influence of water can effectively weaken the parametric vibration of cables,while the transient parameter vibration can not be ignored;The cable is more sensitive to the initial disturbance of the platform;Increasing the platform damping can weaken the parametric vibration of anchor cable more effectively;The existence of vortex force does not significantly increase the maximum amplitude of the cable,but it will lead to sustained periodic vibration of the cable.Considering the influence of the flow field,a coupled vibration equation of vortex and parametric excitation of cable-suspension is established.The influence of flow,initial disturbances,initial tension,damping ratio and vortex on parametric vibration is analyzed.Considering the influence of the temperature field,a coupled vibration equation of temperature and parametric excitation of cable-suspension is established.The influence of temperature on parametric vibration is analyzed.It is pointed out that The influence of temperature on the vibration of cables is mainly reflected in the natural frequencies of the cables and the resonant excitation frequencies of the cables,the decrease of temperature will increase the excitation frequency of the cable,reduce the resonance region,lead the resonance region to the backward shift;The increase of temperature will decrease the excitation frequency of the cable,increase the resonance region,lead the resonance region to the forward offset.The influence of temperature on the vibration amplitude is very small and can be neglected.