Research On The Coupled Vibrations Of Metro Vehicle-Track-Bridge With High-Pier Subjected To Crosswind In Mountain City

Chongqing is a municipality directly under the central government of China,whose rail transit is increasingly developing.Nevertheless,due to the sinister terrain,the metro lines across numerous wide rivers and deep valleys,causing a large proportion of highpier bridges,and the height of pier is even higher than 100 meters.Compared with the underground line in plain city,the elevated line in mountain city is severely attacked by environmental gusts,which induces the drastic vibration of the dynamic system,especially at the turn of summer and autumn.Furthermore,compared with the short-pier bridge,the high-pier bridge has worse stability under crosswind.Fluctuating crosswind induces the vibration of the high-pier,that leads to the strong vibration of the beam,which causes the intensified vibration of the track structure by the track-bridge interaction.Then the vibration transmits to the car body by wheel-rail interaction,that in turn triggers running instability of metro train to be derailed or overturn in serious cases,which results in loss of running safety or traffic disruption.On this basis,the running safety limits and improvement measures to ensure the normal operation in metro lines in mountain city according to the perspective of dynamics are given,the running safety of the metro train over the high-pier bridge under crosswind is analyzed to provide some theoretical basis for the preliminary design and later maintenance.Primarily,on the basis of the theory of vehicle-track-bridge dynamic interaction,the metro train-track-bridge system model with high-pier subjected to crosswind(WTTB)in mountain city is established.In the dynamic model,metro vehicle,ballastless track and high-pier bridge are considered as three subsystems,which are coupled through wheelrail interaction and track-bridge interaction,and the validity and reliability of the model are verified.Type-B metro train with 4 motor cars and 2 trailers cars is adopted in this model,35 degree of freedom(DOF)of each car model are considered,which are based on multibody dynamics.The rail is simplified as Euler beam,while the elevated structures of the lines are simplified as a three-span simply-supported double-line girder bridge with four piers,which is established based on the finite element method(FEM).Meanwhile,the harmonic superposition method(HSM)is used to numerically simulate the Davenport pulsating wind spectrum,and the dynamic wind speed process of double exponential function description of Chinese Hat Gust was synthesized with stochastic process characteristics of the Chinese Hat Fluctuating Gust(CHFG),in which,the speed-up effect of wind mountain area and wind speed along the elevation gradient change rule are considered,Chinese Hat Fluctuating Gust considered the speed-up effect is given finally.The wind loads of high pier and box girder are considered as static load,buffeting load and self-excited load respectively,which are loaded on the finite element model as distributed load.The wind loads of metro train are simulated as concentrate force and moment,while the loads of head car,middle car and tail car are considered respectively.Next,the dynamic equations are calculated by Newmark-β numerical integration method to ensure the stability of the calculation.The motion equations of Bridges,tracks and trains are solved and the iteration is realized,the safety calculation procedure of high pier viaduct metro train subjected to cross wind disturbance is completed,in addition,the evaluation system of this paper is determined from three parts: the running safety,the running stability of vehicle subsystem and the dynamic response of bridge subsystem.Then,the characteristics of the vehicle-track-bridge dynamic system with high-pier under fluctuating crosswind are studied,and the crosswind conditions,vehicle conditions and bridge structure conditions are analyzed respectively to select the most suitable working conditions.The results show that the wind effect of the head car or middle car is much greater than the tail car,and crosswind maxima in α = 90°.The VBI system is affected by the pulse beam wind load significantly greater than the mean wind effect.Dynamic interaction exists in the vehicle-track-bridge system,which makes the vibration more obvious.Then,the crosswind will greatly aggravate the system vibration.As the formation increases,the bridge deformation increases and the crosswind excitation becomes more obvious.In addition,the influence of high pier bridge on traffic safety is much greater than that of low pier bridge under crosswind,.Based on the above work and the selected dynamic evaluation indexes,the safe running limit management of metro trains in the wind-vehicle-bridge system is studied.The results show that the dynamic index of vehicle-bridge system generally increases with the increase of vehicle speed,but resonance is generated at 20 km/h,60 km/h and 100 km/h.The vehicle-bridge system response increases with the increase of wind speed.The safety cannot be ensured when the standard altitude wind speed reaches 10.8 m/s,the vehicle speed of 60 km/h.The threshold safety region of critical speed and standard altitude mean wind speed is given to control the running speed under various wind speeds.The vehiclebridge system response increases with the height of the bridge pier.When the height of the pier is 63 m,the transverse deformation in the middle span has exceeded its safety limit value,indicating that the safety of the train running on the bridge at 60 km/h in the cross wind of 10 m/s at the standard height can no longer be guaranteed.Finally,the wind barrier measures to improve the safety of metro trains are studied.The results show that the wind barrier on the bridge has two functions: on the one hand,it can effectively improve the safety of metro trains;on the other hand,it can reduce the wind resistance of the bridge.When the height of the wind barrier is 4 m,the antioverturning ability of the vehicle is the best,and the aerodynamic coefficient of the bridge deck is also good.Vehicle aerodynamic coefficient is more sensitive to porosity and increases with the increase of porosity.In this paper,a bilateral barrier was selected,with a height of 5.0 m and a porosity of 3.0 m in the solid upper 2.0 m and a porosity of 30 %.When the standard altitude and wind speed reach 21.3 m/s,the train speed can’t be guaranteed until 60 km/h,which is 97.2 % higher than the critical wind speed of 10.8 m/s when there is no wind barrier under the same conditions.