Study On Train-track-bridge Coupled Vibration Characteristics Of Long-Span Cable-Stayed Bridge With Unequal-height Towers In Metro Lines

China’s urban rail transit is in a vigorous development stage,and various long-span bridges with novel structures and complex forms came into being.The asymmetric statically indeterminate structures such as cable-stayed bridges with unequal-height towers are favored by many engineers because of its better adaptability to environmental and topographic conditions.However,the asymmetrical arrangement of towers leads to obvious non-uniformity of the structural stiffness along the longitudinal direction.At the same time,with the growth of operation time of the bridge in metro lines,under the comprehensive influence of repeated wheel load and various bridge system excitation(such as shrinkage and creep,temperature effect,etc.),the alignment of main beam will evolve gradually,and the track structure laid on the bridge deck will also produce vertical displacement,so the rail alignment will deteriorate accordingly.Track geometric random irregularity,additional stiffness irregularity and additional geometric irregularity can worsen the wheel rail nonlinear contact state,and then aggravate the wheel rail coupled vibration behavior,which intensify the wheel-rail coupled vibration behaviour,and affects the ride comfort and the running safety of operating trains.The problem of train-track-bridge coupled vibration of long-span cable-stayed bridges with unequal-height towers is becoming more and more prominent,which also puts forward higher requirements for design and operation.Therefore,in order to ensure the safe and stable operation of metro trains on the long-span cable-stayed bridge with unequal-height towers in metro lines,based on the Nanjimen bridge in metro lines,this paper considers the influence factors such as shrinkage,creep and temperature for the train-track-cable-stayed bridge with unequal-height towers coupled system laying three types of ballastless tracks in urban rail transit,the train-track-bridge coupled vibration characteristics of long-span cable-stayed bridge with unequal-height towers in metro lines are studied,and the track structure types suitable for long-span cable-stayed bridge with unequal-height towers are proposed.The main research contents and conclusions are as follows:(1)Based on the train-track-bridge dynamic interaction theory,combined with finite element method,a fine dynamic model of metro train-ballastless track-cable-stayed bridge is established.The model includes three sub-models of metro train,ballastless track and cable-stayed bridge.The wheel-rail spatial dynamic coupled model is used to describe the wheel-rail relationship,and the coupling of node degrees of freedom between ballastless track and cable-stayed bridge is considered as the bridge-rail relationship.For the above dynamic interaction model of metro train-ballastless track-cable-stayed bridge,the explicit-implicit integration method is used to solve it.The commercial software SIMPACK is used to verify the effectiveness of the model.(2)The dynamic response of train-track-bridge system of long-span cable-stayed bridge with unequal-height towers under different driving modes is studied,and the influence law of train speed,train formation and train running direction on the dynamic response of train-track-bridge system is analyzed.The results show that with the gradual increase of train running speed,the dynamic responses of the train also increase gradually,but they are far less than the standard.With the increase of train running speed,the mid span displacement of the bridge increases gradually,while the vertical vibration acceleration increases obviously.The form of train formation has little effect on the dynamic response of vehicles,while the dynamic response results of bridges have obvious changes.The vertical dynamic displacement in the middle of the span is more sensitive to the number of train formation,and the vertical vibration acceleration in the middle of the span is more sensitive to the train speed.Crossing the bridge in different driving directions has little effect on the vehicle dynamic response.When the train passes the bridge in different directions,the dynamic response results of the bridge change obviously.(3)Aiming at the difference of bridge stiffness on both sides of high and low towers of cable-stayed bridge,this paper first analyzes its influence on the dynamic response of tracin-track-bridge system,and then studies the internal relationship between the asymmetric stiffness characteristics of cable-stayed bridge with unequal-height towers and the dynamic performance of train.The results show that when the train runs through both sides of the high and low towers,the difference between the vertical force of wheelset and the derailment coefficient has no clear change law and the value is small,but the difference between the wheel unloading rate and the vertical acceleration of the car body is large and intensifies with the increase of the speed,which will have a significant impact on the safety and comfort of the train.The vertical dynamic displacement amplitude of the observation point on the low tower side is 50% higher than that of the corresponding observation point on the high tower side,and the vertical acceleration amplitude of the observation point on the low tower side is 140% higher than that of the corresponding observation point on the high tower side.In general,the vibration at each position of the main beam on the low tower side is higher and greater.At different speed levels of the train,the second derivative of the additional stiffness irregularity curve caused by the non-uniform stiffness of the main beam to the mileage is directly proportional to the vehicle dynamic parameters such as wheel unloading rate,vertical force of wheelset and vertical acceleration of car body.(4)By deriving the analytical expression,for the monolithic track bed trackcable-stayed bridge and steel spring floating plate track-cable-stayed bridge systems,the mapping relationship between the main beam deformation of cable-stayed bridge and the rail deformation under the excitation of bridge system in different systems is deduced,and the force transmission mechanism of bridge-rail under each excitation in different systems is analyzed.(5)Using the train-track-bridge coupled dynamic model,the impact of bridge system excitation on the dynamic response of train-steel spring floating plate track-cable-stayed bridge is studied,and the dynamic stress difference law of different track structures on the main span side of high and low towers is analyzed.The results show that when the bridge system excitation acts alone or comprehensively,the variation law of each dynamic response of train-track-bridge system is consistent.When considering the bridge system excitation,the dynamic responses of the vehicle increase,and the maximum increase of derailment coefficient is 7.0%;the increase of axle lateral force is 2.8%;the wheel unloading rate increased by 5.3%;the increase of vertical vibration acceleration of car body is 6.7%;the maximum increase of lateral vibration acceleration of car body is 2.8%.The bridge system excitation has little effect on the displacement,acceleration of the track structure and dynamic response of the bridge.(6)The dynamic response of train-track-bridge system under different track types to bridge system excitation is compared and analyzed.Based on the train-track-bridge coupled dynamics,the track structure type suitable for long-span cable-stayed bridge with unequal-height towers is proposed.The results show that In terms of dynamic responses of the vehicle and the displacement and acceleration of the track structure,under the bridge system excitation,steel spring floating plate track type is the largest and the monolithic track bed track is the smallest.In terms of bridge dynamic response,the law is opposite.Considering the comprehensive action,the dynamic stress of the track plate of the monolithic track bed track structure is the largest,and the dynamic stress of the track plate of the steel spring floating plate track structure is the smallest.The maximum dynamic stress of the track slab of the monolithic track bed track structure is close to 2.9MPa,exceeding its concrete axial tensile strength value of2.7MPa,indicating that this track type has poor compatibility with long-span cable-stayed bridge in metro lines.The trapezoidal sleeper ballastless track can be the best choice for long-span cable-stayed bridge in metro lines when the geological environment permits and in addition to special vibration reduction requirements.