Experimental Study On Synchronous And Asynchronous Vibration Of Double Cables

Cable structure is widely used in the cable-stayed bridge,transmission line and other kinds of projects,but as a flexible structure,it is easy to produce a sharp vibration under external excitation.for multi cable structure,the adjacent cable can produce synchronous vibration and asynchronous vibration,lead to cable collision and other problems,causing great harm to the original structure,so the cable structure nonlinear vibration problem is still one of the important research subject at present.In order to study the causes of this phenomenon,scholars at home and abroad have carried out a large number of studies on the amplitude-frequency characteristics and phase-frequency characteristics of cable,but they mainly focus on a set of specific parameters and do not deeply study the influence law of parameter difference on phase-frequency characteristics of cable structure.In this paper,model test,parameter analysis,comparison and induction are used to study the influence of parameter differences on phase frequency characteristics of horizontal cable.The main content is as follows:(1)Considering the sag and geometric nonlinearity of the suspended cables,on the basis of the ordinary differential equation for the motion of a suspended cable under Axial end excitation in the plane,the multiple scales method is used to obtain the amplitude-frequency response equation of the main resonance in the plane.And the amplitude frequency characteristics and phase frequency characteristics of cables under different sag-to-span ratios are discussed by numerical examples.The results show that the first-order natural frequency is inversely proportional to the sag-to-span ratios.At the same time,the influence of increasing or decreasing the same parameters on the natural frequency is not the same due to the influence of initial cable force.In addition,the response phase of cables in the main resonance region will change suddenly at a certain excitation frequency.For cables with different parameters,the frequency of phase change is also different because of the difference of their natural frequencies.This conclusion is deduced to the double cable structure,which indicates that for two cables with different parameters,there may be synchronous vibration and asynchronous vibration at the same excitation frequency.(2)The principle of dynamic similarity is used to design a single horizontal cable-mass block model.Then the horizontal cable free vibration experiments and the sweep experiments in the main resonance regions,subharmonic resonance regions and superharmonic resonance regions under four different sag-to-span ratios conditions are carried out.The Fourier transform is used to get the phase difference between in-plane response and excitation with the excitation frequency.The research shows that in the main resonance regions and superharmonic resonance regions,there will be a mutation of phase difference because of their unique "jump" in the frequency sweep process,from in-phase to anti-phase,or from anti-phase to in-phase.Then the fourth-order Runge-Kutta method is used to verify the experiment results.For the subharmonic resonance,the phase difference between the response and the excitation is always maintained at 90 degrees during the frequency sweep process.In addition,the transient cable force changes significantly during the vibration of the cable.When the response amplitude is the largest,the average and maximum of the transient cable force will increase by 2% and 8% compared with the initial cable force.(3)On the basis of single horizontal cable-mass block model experiments,the double horizontal cable-mass block model experiments are carried out.The experiment mainly focuses on the relative relation of the in-plane responses of the double-cable structure in the mid-span under different parameters.The variation of parameters adopts the method of changing the sag-to-span ratios of only one cable.And in the experiment process,there is a certain difference in the axial excitation amplitude of the two cables,but the measured excitation is always in the same phase.Finally,the transient dynamics analysis of ANSYS is used to verify the experiment results on some conditions.The research shows that there are obvious "synchronous" and "asynchronous" vibration phenomena in the main resonance and ultraharmonic resonance regions of the double cables.The main reason for this phenomenon is that the resonance interval between the two cables has a certain deviation due to the different sag-to-span ratios.In the process of frequency sweep experiment,the initial phase of its response changes abruptly when one of the cables jumps.At the same time,the two cables change into "asynchronous" vibration.This phenomenon continues until the other cable also jumps,and then the two cables turn into "synchronous" vibration.Compared with different working conditions,the excitation amplitude has a great influence on the cable response amplitude,while the influence on the resonance interval deviation is small.The difference of sag-to-span ratios has a very obvious influence on the size of the asynchronous vibration region of the double cable.The results of ANSYS transient dynamics analysis are consistent with the experiment results.