A Coupled Model For A Deformable Moving Vehicle And A Pile-Supported Periodic Viaduct

It is well known that in high-speed railways,the bridge structure accounts for a large proportion,and the viaduct model with bridge instead of road is more common,in particular the periodic viaduct is a simplified model of high-speed railways.The movement of the train on bridge is a complex kinetic process,with the constant improvement of the train running speed,load increasing,the vibration of bridge is increased by the interaction between vehicle and bridge,thus increase the unsafe factors of elevated railway,therefore,it is necessary to start from vehicle bridge coupling vibration,the vehicle and the interaction of periodic viaduct.In this thesis,the rigid body model and the deformable body model of the vehicle are investigated,and the dynamic response of the periodic viaduct supported by rigid support and pile foundation under the action of moving vehicle is studied by using the interaction between vehicle and bridge.The main research contents of this thesis include:(1)Dynamic response of rigidly-supported periodic viaduct(RSPV)under the action of a rigid moving vehicle.The Fourier series are used to expand the vehicle bridge force between the rigid moving vehicle and the periodic viaduct.In order to get the action of RSPV expression under the rigid dynamic responses of the vehicle,this study introduces the basic solution of RSPV。Using Newton’s second law,the dynamic equation of rigid a moving vehicle is obtained.By using the periodicity of the basic solution of RSPV,the Fourier coefficients of each force can be obtained by solving the governing equation,so as to determine the dynamic response of RSPV and vehicle.Numerical results show that for large quality train speed,vehicle-viaduct interaction force will be negative,in the process of making trains do not increase security,at the same time,with the increase of vehicle speed on the dynamic response of a RSPV whole showed a trend of increase.Also,the RSPV displacement response at low frequency of peak value is greater than the corresponding peak value of high frequency band,the movement speed of the vehicle,the greater the low frequency response is more significant.In addition,when the vehicle resonates with the bridge,RSPV dynamic response is more significant.(2)Dynamic response of rigidly-supported periodic viaduct under the action of a moving deformable vehicle.Euler Bernoulli beam theory is used to describe the vehicle body vibration,and the discrete dynamic equation of the vehicle beam is established by the finite element method.Combined with the coupled equation of vehicle and viaduct,the Fourier coefficients of the displacement of deformable vehicle body and each force can be obtained.Then the dynamic response of RSPV under the action of a moving deformable vehicle can be obtained.Numerical results show that the response of RSPV generally increases with the increase of the vehicle speed,and presents shockwave response characteristics.In addition,In the vicinity of the vehicle’s natural vibration frequency,the shear response of the RSPV significantly increases.Under the vehicle’s base frequency vibration,the vibration energy of the bridge is relatively concentrated,which is not conducive to the safety of the bridge structure.The deformation of the deformable vehicle body has great influence on the vibration of the vehicle body.The comparison of the vertical displacement of the center of mass of rigid and deformable vehicle bodies shows that,from the perspective of the response value,the results obtained by the two models are quite different,but from the perspective of the variation trend,the vertical displacement obtained by the two models is basically the same.(3)Calculation model of dynamic response of pile-supported periodic viaduct(PSPV)under the action of a moving deformable vehicle.In order to consider the influence of pile-soil-structure coupling on the dynamic response of viaduct,the boundary element method is firstly applied to consider the pile-soil interaction,so as to determine the compliance of the top of pile foundation.Based on the bridge pier and pile foundation connection conditions and the finite element model of rigidly-supported periodic viaduct,the basic solution of dynamic response of PSPV is obtained.The Fourier coefficients of the above forces are obtained by using the vehicle and viaduct coupled conditions,as well as the basic solutions of the dynamic response of the periodic viaduct supported by pile foundation,so the dynamic response of a moving deformable vehicle to the pile-soil coupled periodic viaduct can be obtained.Numerical results show that the dynamic response of the periodic viaduct considering the pile-soil coupled is less than that of the viaduct considering only the vehicle-viaduct coupled.In the calculation model of the coupled of a moving deformable vehicle and periodic viaduct and pile-soil,due to pile-soil coupled,the energy of vehicle-viaduct coupled vibration can radiate to the foundation,which is conducive to the safety of the structure.Therefore,it is more reasonable to consider pile-soil coupled in the dynamic design of viaduct.