Singular Perturbation-based Force Identification Of Vibrated Stayed Cables

Due to the complexity of the cable structure boundary condition and the supporting condition as well as the uncertainty of the mechanical parameters of the cable,the classical cable-vibration theory and the hinged-beam theory cannot meet the requirement of the test precision in many cases.Therefore,it is necessary to study the cable force test of some typical cable structures with complex boundary conditions and supporting conditions and obtain a more accurate calculation formula of cable force considering the influence of complex boundary.In this paper,the cable with both ends consolidation and intermediate bracing is taken as the object of study,the mechanical equation of the cable vibration considering the influence of the bending stiffness of the cable is obtained by establishing the mechanical model.Aiming at the difficulty of solving high order differential equation,the singular perturbation method is used to successfully establish the relationship between the cable tension and the vibration frequency of each order,and obtain the gradual expression of the vibration frequency and the mode function.According to the formula of cable frequency and cable force acalculated by singular perturbation method,applicability anlysis of the parameters is carried out by the form of dimensionless analysis,combined with experimental data and practical engineering data as well ANSYS finite element analysis.The influence of the bending stiffness,the intermediate support position and the stiffness of the support spring on the calculation formula is pointed out.At present,the cable force calculation method adopted in the current project does not match the actual situation of the cable,and the calculated cable force and the actual cable force of the cable are quite different.The formula deduced in this paper can be applied in actual engineering as a feasible cable force calculation method.By selecting the corresponding cable force calculation formula according to the actual project in the cable boundary conditions and support,the actual cable at all stages of cable power can be calculated accurately.Aiming at the discrete steel strand cable stayed cable which is widely used in actual engineering,the precision problem of the discrete steel strand cable stayed cable in the actual engineering is studied by frequency method.A large number of frequency test data were collected in the experiment.The influence of several influencing factors on the overall cable force test results was obtained quantitatively by comparative analysis and these factors included uneven distribution of cable force,uneven degree of cable force,cable clamping near both ends,the position of cable clamps,the weight of the casing.At the same time,two cable force calculation methods which are the hinged beam method and the singular perturbation method are compared.The finite element simulation of the whole beam has been carried out.The frequency and mode characteristics of the whole vibration of the cable are analyzed and the selection of the measuring point at the time of frequency acquisition and the recognition of the main frequency in the spectrum are briefly analyzed.