Research On Nonlinear Dynamics Of Cable Structures With Different Initial Configurations

At present,the cable-stayed bridge is the best in other structural systems because of its high efficiency and excellent architectural appearance.In particular,because the cable structure has clear mechanical characteristics and mainly bears tensile stress,it is widely used in the construction of long-span bridges,especially for bridges with spans of more than 1000 meters.With the increase of the number of cable bearing bridges,it is particularly important to design a cable bearing bridge which is safe,economical and reasonable.One of the main problems in the design of cable bearing bridge is the stability of its initial configuration,and the weight of stiffening beam and the Irvine parameter of cable have great influence on the initial configuration of cable.At the same time,as the span of the cable bearing bridge increases,the overall stiffness will decrease,and the nonlinear vibration problem of the cable bearing bridge becomes more and more prominent.So it will be more meaningful to study the nonlinear dynamics of cable structure by establishing mechanical model,and reveal the dynamic performance of cable structure under different initial configurations and the nonlinear dynamic behavior under different excitations.This paper mainly explores the relationship between the two from the theoretical basis(1)From the aspect of statics,this paper deduces the initial configuration of suspension cable in two states of empty cable and considering the weight of stiffening beam.It is found that the dimensionless equations of the two states are different.It is also found that the dimensionless equations of the initial configuration of suspension cable in two simulation modes of simplifying the weight of stiffening beam to uniform load and mass are consistent.At the same time,the construction drawings of 30 suspension bridges are collected,and the weight of stiffening beam is statistically analyzed,which provides practical basis for the later theoretical research.(2)The influence of the initial configuration on the natural characteristics of the suspension cable is explored,and the influence of the bending stiffness on the natural characteristics of the suspension cable under different initial configurations is also studied.Based on different initial configurations,the transcendental equations of natural frequency and vibration of two kinds of linear mechanical models are derived,and the calculation examples are analyzed based on practical engineering.The results show that the influence of bending stiffness on the frequency and mode shape of suspension cable is closely related to the value of Irvine parameter,and the bending stiffness has a great influence on the higher frequency and mode shape of long cable.In addition,the influence of the initial configuration of suspension cable on the internal mode shape is also closely related to the value of Irvine parameter;Under the same Irvine parameter,the natural frequency of the cable is negatively correlated with the initial configuration in the state of empty cable,but it is positively correlated with the initial configuration in the state of considering the weight of stiffening beam,and the influence of the initial configuration on the vibration mode is consistent with that of the initial configuration on the natural frequency.(3)The influence of initial configuration on the nonlinear vibration characteristics of suspension surface is studied.Based on Hamilton’s principle,the nonlinear vibration equation of suspension cable under in-plane distributed external excitation is derived,and the multi-scale method is used to solve the perturbation problem.The results show that the change of the initial configuration of the suspension cable will cause the qualitative and quantitative changes of the amplitude frequency curve of the nonlinear vibration of the suspension cable,and also cause the change of the excitation frequency required for the "jump phenomenon" of the suspension cable.In the same way,the instantaneous phase frequency characteristics in the suspension plane are quite different in different initial configurations.(4)The influence of internal resonance on the in-plane instantaneous phase-frequency characteristics of inclined cable under different initial configurations is investigated.The results show that the change of the initial configuration of the cable will cause a sharp change of the instantaneous phase difference between the response and the excitation,especially when the internal resonance is considered.The main reason is that the internal resonance makes the frequency doubling component and the drift term caused by the out of plane response exist in the in-plane approximate solution,and the latter has a significant influence on the instantaneous phase difference,and the proportion of the drift term caused by the out of plane response in the overall drift term is the key parameter to measure the influence of the internal resonance on the instantaneous phase difference.