Discrete Analysis And Damage Identification Of Vertical Vibration Of Suspension Bridge

Suspension bridges generally have a long span,long construction period,high investment,and have a huge impact on local economic and social image.Due to the existence of prestress,the damage symptoms of suspension bridges are generally not significant,but the damage consequences are extremely serious.The cables and hangers,as the main mechanical components of suspension bridge,are prone to damage,and there will be a need for damage determination over time.Various accidents in recent years also demonstrated the need to focus on the structural safety of suspension bridges.As a nonlinear structural system with large flexibility,the theoretical research of suspension bridge is not perfect at present,the classical continuity equations for vertical vibrations cannot be solved numerically,the effect of changes in member properties on mechanical behaviour is not clear,and the sensitivity of local damage identification methods needs to be improved.It is necessary to clarify the influence mechanism and mechanical performance of local damage,and find a more effective local damage identification method.Based on the theoretical analysis,a new calculation and analysis method is found in this paper.The change of structural vibration characteristics after local damage is obtained by discretization analysis method,and a suitable damage identification method is found.The main research contents and results of this paper are as follows :(1)Through collecting and sorting out the existing theories related to suspension bridges,the situation of each parameter affecting the vibration frequency and vibration pattern of suspension bridge structures is analysed.Various methods and formulas for calculating the structural force deformation after damage to the cables are innovatively provided,and the changes in the mechanical behaviour of the cables under different loads are analysed;the characteristics of structural deformation under concentrated loads are found.A finite element modelling analysis was carried out with reference to a real suspension bridge,and the structural deformation analysis under load was carried out on the model after applying pre-strain and iterative calculations.The results were basically consistent with the innovative method proposed,and the deficiencies of the static method in determining the location of damage were clarified.(2)To address the problem that the classical continuity vibration equation for suspension bridges cannot be solved numerically,a new and improved continuity equation is proposed,which can be calculated numerically and reveals the influence of each parameter on vertical vibration.The improved continuity equation shows that the contribution of the cables and stiffening girder to the lower order symmetric vibration varies in the opposite direction as the order increases;the coefficients associated with the cables tend to be constant after a certain order,while the effect of the stiffening girder becomes more obvious.It is clear that the continuity analysis method cannot determine the damage location of the cables.(3)In order to clarify the influence of each structural parameter on the vertical vibration of the suspension bridge,a discrete analysis method is innovatively proposed with reference to the classical continuity analysis method to realise the matrix solution for the natural frequency and vibration mode of the suspension bridge.The experimental model suspension bridge is subjected to the finite element method for finding the shape and the vibration analysis by using the block Lansos,and the experimental vibration measurement and analysis of the experimental suspension bridge are also carried out,and the results of both frequencies and vibration shapes are basically consistent with the calculation results of the discretization method.The discretisation method is consistent with the classical theoretical results in terms of the influence coefficients of the cables at the inversion of the symmetric and antisymmetric frequencies,and the variation of the vibration modes of the first order vibration.The discretization analysis reveals that the cables elastic stiffness matrix is asymmetrical and the vibration modes are not orthogonal at all orders;compound vibration of the structure may occur when the elastic stiffness of the cables are not properly proportioned to the axial tension,and when it is not properly proportioned to the bending stiffness of the stiffening girder.The discretization method can be used to calculate the effect of local property changes on the vibration behaviour of the structure.(4)The local damage of the cables and stiffening girder will reduce the local stiffness of the structure,but it does not necessarily reduce the natural frequency of all orders,and may even increase,the high-order frequency after damage is generally lower than the undamaged frequency.The local damage of the hangers does not affect the structural stiffness matrix,but causes the mass redistribution between the particles.When the bending stiffness of the stiffening girder is small,the change of the mass redistribution is small.The difference of mass distribution may cause the frequency change of each order to be higher or lower than that without damage,and there is no regularity.The damage will cause a sudden change in the local vibration mode,but the mode shape of the damage may increase or decrease,it has nothing to do with the symmetric vibration form.Affected by the accompanying longitudinal vibration,the curvature of the symmetrical position will also undergo a corresponding sudden change,and the value will be smaller.(5)Frequency and vibration mode do not help to determine the location of damage,but the curvature abruptness reflects the discontinuity of the vibration pattern and thus detects damage.The value of the curvature abruptness is related to many factors and cannot fully represent the degree of damage.In order to reduce the influence of the curvature of the vibration mode,an innovative approach to damage identification by curvature mode ratio is proposed,which is more sensitive to damage,but with attention to the interference of vibration nodes and symmetry positions.The local damage of the cables affects the stiffness of the four particles,the local damage of the hangers affects the three particles,and the damage of the stiffening girder affects the stiffness of the two particles.The change of the performance parameters of each particle may cause the curvature and curvature mode ratio to change,attention should be paid to these problems in damage identification.The local damage of the cables can be identified conveniently by curvature mode ratio method,but it is difficult to find the damage of the hangers and the stiffening girder.By systematically combing and using the discretization method,the mechanical properties of the vertical vibration of the suspension bridge are comprehensively analyzed,and many new phenomena caused by the local damage of the components are found.By analyzing the available mechanical behavior after damage,it is found that the curvature mode ratio method can locate the local damage of the suspension bridge more efficiently.This study can promote an in-depth understanding of the structural performance of suspension bridges,and has certain theoretical research significance and practical application value.