Study On Model Reduction Of Truss Bridge And Its Application In Train-Bridge Coupling Vibration

As the main girder structure of the bridge becomes more and more complex,the number of refined model units established in the finite element software is increasing,resulting in a significant reduction in the efficiency of modeling and solving,especially when multiple working conditions need to be calculated.In order to improve the calculation efficiency,the main girder part is usually simplified to a certain extent in the existing train-bridge coupling system.However,some existing model simplification methods have a certain contradiction between the accuracy of the model and the size of the unit.In order to explore a model reduction method that can not only ensure the calculation accuracy,but also improve the calculation efficiency of the train-bridge coupling analysis,and is suitable for a variety of main grider forms,aiming at the truss bridge,this paper studies the method of reducing the order of the bridge model from two perspectives,namely,the simplification of the modeling method and the reduction of the matrix freedom.These methods are applied to the train-bridge coupling analysis,compared with the response of the full-order model,and the several reduction methods studied are comprehensively analyzed in terms of calculation accuracy,calculation efficiency and applicability.The specific research content is as follows:(1)From the perspective of simplified modeling,through the equivalence of stiffness,mass and mass moment of inertia,the refined finite element model of a complex bridge can be simplified into a single main girder model,and the model can be reduced in order by reducing the number of elements.First,it summarized and reviewed the stiffness equivalent method based on the assumption of the plane section and pointed out the limitations of this method in use.For the shortcomings,the surrogate model method and the simplified model are combined on the basis of this method.The equivalent bending stiffness is optimized by the adaptive Kriging surrogate model,and the reduced-order model is dynamically modified.Through the analysis of calculation examples,it is found that the accuracy of the dynamic characteristics of the modified single main girder model has been improved,and it is not affected by the cross-sectional form of the main girder during use.(2)From the perspective of matrix reduction,the bridge model is reduced in order based on the principle of modal superposition method.Different from the reduction method of truncating the modes directly according to the frequency,the research is carried out on the mode selection criteria for the response concerned in the vehicle-bridge coupling,and the contribution of each mode is measured according to the mode criteria,and the large contribution is selected The modal vectors form a reduced base matrix,and the mass,damping and stiffness matrices of the full-order model are reduced to achieve the order reduction.The Newmark-β method is used to calculate and compare the displacement response of the bridge before and after step reduction under moving load.The results show that selecting important modes according to the response definition criteria of actual concern can significantly reduce the degree of freedom of the model and greatly improve the calculation efficiency.And compared with the method of directly truncating according to the frequency,the reduced-order model can be closer to the response of the full-order model with less degrees of freedom.(3)Based on the proper orthogonal decomposition,the bridge model is reduced in order.First calculate the dynamic response of the full-order model to construct a snapshot matrix,perform eigen-orthogonal decomposition of the snapshot matrix to obtain the POD basis,truncate the low-energy mode based on the energy ratio truncation criterion,and select the POD basis corresponding to the high-energy eigenmode Form a reduced base matrix to reduce the full-order model.A moving load is applied to a long-span suspension bridge,and the POD base pair model is extracted from the linear response and the nonlinear response,and the calculation accuracy of the two reduced-order models is compared.The results show that: The model is reduced in order based on the proper orthogonal decomposition method,and the reduced-order model has less degree of freedom and high calculation accuracy;For long-span suspension bridges with strong geometric nonlinearity,the proper orthogonal decomposition method can effectively extract the nonlinear characteristics of the original nonlinear response,and the calculated results are closer to the original response after the order reduction.This method has certain advantages in order reduction of nonlinear systems.(4)Taking a large-span truss suspension bridge as an example,the above-mentioned order reduction methods are used to reduce the order of the bridge model.The train-bridge coupled vibration method was used to analyze the response of trains and bridges under different train speeds and train formations.The analysis results show that from the comprehensive comparison of bridge mid-span displacement,beam end turning angle,train response and other indicators,the bridge reduced-order model based on proper orthogonal decomposition is generally consistent with the full-order model results,and the calculation efficiency is higher.