Analysis Of Dynamic Responses Of Bridge Under Moving Vehicles

The dynamic response of the bridge under moving vehicles is an important issue in bridge design.However,the bridge is always simplified directly into a beam under moving loads in most existing researches,in which the relatively large errors can be caused due to the ignorance of the vehicle's mass especially when the mass of the bridge and vehicle are almost equally.In this paper,the dynamics of a beam subjected to both moving loads and masses are studied.Based on the previous theoretical studies,the dynamic problems of the bridges with/without the consideration of the mass effect are studied.The main work of the paper is summarized as followed:(1)Researches on dynamics of the bridge under moving loads are reviewed and the main theoretical methods are summarized.Then the schemes to solve dynamics of the bridge with several moving vehicles are stressed in detail,by which the ideas and methods of this paper are put forward.(2)The approach which the FEM and Duhamel integral method are united to solve the dynamic response of the bridge only acted by the moving loads,is extended to the conditions with moving masses.Given the coupling equations caused by the mass effect,the mass effect is reflected by the time-varying mass matrix.Firstly,the beam model is discretized into some finite elements and the continuous modal of the elements can be obtained.Then,the dynamic responses of the modal coordinates are calculated using the Duhamel method in the time domain.Lastly,the dynamic responses of the whole bridge or beam can be obtained by the modal superposition method.(3)The responses of simply supported bridge and complex steel truss bridge are numerical analyzed with single and multiple moving loads,by which the correctness of the proposed method is verified by comparing to the results of FEM.Analytical comparisons between the results with the mass effect and the ones without the mass effect are conducted to show the importance of the factor.(4)The other factors which affect the response of the middle point on the bridge are analyzed,such as the load velocity,mass ratio of vehicle and bridge,the distance between two loads and so on.The analytical results show that the new method on the basis of the finite element method adopted in this thesis can completely meet the requirements of precision and has higher computational efficiency than the Newmark-? method.At the same time,the proposed method can be applied for either conditions neglecting the mass effect or not.When a single load is considered,the maximum displacement becomes greater when the moving speed of the load increases and what's more,the effect of the moving speed acting on the acceleration of the beam is greater.In addition,the results also show that the mass effect can be neglected when the mass ratio of load and bridge is less than 0.3.When several loads are considered,the distance between loads has little influence on the maximum displacement but has evident influence on the acceleration of the middle point on the beam.