Dynamic Analysis Method Of Rail Based On Equivalent Beam On Elastic Foundation

With the continuous development of all aspects of railway technology in China,affected by high frequency train load and irregularity,the dynamic impact of rail and bridge structure is increasing in the traintrack-bridge vertical coupling system.At present,the finite element method is widely used to solve the vertical vibration response of rail and bridge structures in the vertical coupled system,and the structure needs to be spatially discretized.Based on the characteristics of the dynamic equilibrium equation of the structure after the transformation,this paper refers to the solution method of the differential equation of the deflection curve of the elastic foundation beam,and constructs the equivalent elastic foundation beam model to avoid the discretization of the structure and solve the dynamic stress response of the rail structure and the bridge structure.The main research contents and conclusions are as follows :(1)Referring to the solution of differential equation of deflection curve of elastic foundation beam,the equivalent elastic foundation beam model for dynamic analysis of simply supported beam is constructed by changing the dynamic balance equation of simply supported beam structure.The equivalent load action term is processed by numerical integration method,and the dynamic response at each load acquisition point on the structure is calculated.By comparing with the mode superposition method,the finite element derivation method and the finite element section method,it is proved that the equivalent elastic foundation beam model is feasible and accurate in solving the dynamic response of simply supported beam structure.(2)In order to consider the discrete support action under the beam,the Green ’s function of each response of the discrete support beam structure under unit load is established,and the dynamic response of the discrete support beam structure is solved in the form of matrix,which increases the application scope of the equivalent elastic foundation beam model.(3)In the train-track-bridge vertical coupling system,the coupling relationship between train system and track-bridge system is considered by two-level iterative calculation.The track-bridge system is divided into track subsystem and bridge subsystem.Considering the influence of bridge displacement on the track subsystem,the bridge displacement influence item is added to the rail displacement matrix equation to solve the dynamic response of the rail structure.The results show that the dynamic response of the equivalent elastic foundation beam model is consistent with the results of the finite element section method,and the calculation results are significantly improved compared with the finite element derivation method.