Research On The Coupled Vibration Of The Vehicle-periodic Viaduct Under Seismic Waves

Viaduct has become a common form of high-speed railway because of its obvious advantages such as straightness and smoothness and strong anti-settling ability.China is located between the two largest earthquake belts of the world,which means earthquakes occur in China frequently.Earthquakes may damage the bridges and the vehicles running on it,causing serious casualties and economic losses.Therefore,it is necessary to study the response of vehicles and viaducts under the seismic waves.In this thesis,the coupled vibration model of the vehicle and the periodic viaduct under the action of seismic waves is established,in which the seismic waves are modeled as Rayleigh waves and the viaduct is simplified as a periodic structure,and the moving vehicle is simplified into a moving mass and a moving mass-spring system.Based on the model above,the factors affecting the dynamic response of the vehicle and viaduct are numerically analyzed.The main contents of this thesis are as follows:(1)Coupled vibration of a moving mass and a periodic viaduct(PV)under seismic waves The coupled vibration model of the moving mass and PV under the action of seismic waves is established.In order to solve the dynamic response of PV to the moving mass,first expand the mass-PV interaction force into Fourier series to obtain a series of moving load components of different vibration frequencies.Then establish a finite element model to determine the basic solution of PV under unit load in frequency-wavenumber domain.Using the Fourier transform and the above-mentioned basic solution of PV in frequency-wavenumber domain,the dynamic responses of the PV to the moving load components can be obtained.Establish a finite element model for solving the dynamic response of PV under the action of seismic waves,the coupled equation of moving mass and PV can be obtained by using the obtained dynamic response of PV to seismic waves and the dynamic response of PV to the unit series of moving load components.Solving the coupled equation can obtain the Fourier coefficients of the mass-PV interaction force.Finally,using the obtained Fourier coefficients and the dynamic response of PV to the unit series of moving load components and the dynamic response of PV to seismic waves,the overall dynamic response of PV can be obtained.(2)Coupled vibration of moving mass spring system(MSS)and periodic viaduct(PV)under seismic wavesThe coupled vibration model of MSS-PV under seismic waves is established.In order to solve the dynamic response of PV and MSS,the dynamic response of PV under the action of unit series moving load component is obtained by the same method as(1);then the motion equation of upper mass of MSS and coupled equation of PV and the lower part of MSS are established according to Newton’s second law by using the dynamic response of PV under unit series moving load component and seismic waves.Solving the above equations can obtain the Fourier coefficients of the MSS-PV interaction force and the Fourier coefficients of the restoring force of the MSS spring.By using the above Fourier coefficients and the dynamic responses of PV under the action of unit series moving load component and seismic waves,the overall dynamic response of PV under seismic waves and moving MSS and the dynamic response of MSS itself can be obtained finally.This thesis studies the influence of moving speed and vehicle mass on PV dynamic response on the basis of the above two models.The numerical analysis results show that:(1)In the presence of seismic waves,the dynamic response of the PV is significantly related to the moving speed of the vehicle.When the moving speed of the vehicle is low,the out-of-plane shear force of the left section of the PV beam,the interaction force between the vehicle and the PV,and the total displacement of the vehicle are large,and the duration of the PV dynamic response is significantly longer.The frequency components in the PV dynamic response become more complicated.(2)When the mass of the vehicle is changed,the changes in physical quantities such as the left section shear force of the PV beam,the vehicle-bridge interaction force and the PV lateral displacement are more complicated,and do not show any trends,indicating that the vehicle mass has a more complicated influence on the PV dynamic response,and there is no significant linear relationship between the two.(3)The out-of-plane dynamic response of PV is generally greater than the in-plane dynamic response;the dynamic response of PV is usually larger at the mid-span position and smaller at the top of the pier,showing a “V”-shaped trend in the observation cell;the interaction force is larger at the position between the mid-span and the top of the pier,but smaller at the top and the mid-span of the pier,showing an "M"-shaped trend in the observation cell.(4)When considering the vehicle-bridge coupled model under the action of seismic waves,the MSS model is more accurate than the moving mass model.Using the moving mass model will make the bridge dynamic response significantly higher.Therefore,it is advisable to take the vehicle’s own vibration into account and use the MSS model to reduce such errors.Although the research of this subject is limited to simple harmonic seismic waves,for any seismic waves,it can be first decomposed into the superposition of Fourier components,and then the simple harmonic model established in this subject can be used for analysis.For specific engineering problems,a more refined periodic viaduct model can be established.For example,consider the track,track slabs,fasteners and supports,as well as more refined vehicle models,and then conduct research in accordance with the technical route of this topic.