Coupling Vibration Study Of Wind-Train-Track-Bridge System

With the rapid development of long span bridges in high-speed railway, the risks are increased when the high-speed train running on the long span bridges under cross winds. Therefore, the safety and comfort of the running train, the reliability of the track and the bridge under cross winds need more attention. However the existed research is scarce. On the basis of existing research data, a dynamic analysis model of wind-train-track-bridge system is presented to consider the effect of cross winds, train, track and bridge. An analysis program WTTBDAS is developed to study the dynamic responses of the bridge, the track and the running train under cross winds. The wind-train interaction, the wind-bridge interaction, the wheel-rail interaction and the bridge-track interaction are fully considered in this model, it can well reflect the aerodynamic coupling interaction among wind, train and bridge, and the geometric and mechanical coupling relationship between train, track and bridge, and the time variation characteristics of the system due to the train movement.Firstly, a 4-axle railway vehicle model with two suspension systems is presented. The model is regarded as multiple rigid body system, it consists of a car body, two bogies, four wheel-sets and the connections including various kinds of non-linear factors between the three components. The car body, each bogie or each wheel-set is assigned five degrees of freedom:the vertical displacement, the lateral displacement, the roll displacement, the yaw displacement and the pitch displacement with respect to its mass center. As a result, the total degrees of freedom of the model are 35. The dynamic models of ballast track and REHDA track are established. In the model, rails are modeled as Euler beams laid on elasticity supports, sleepers and discrete ballast blocks are modeled as rigid bodies, the dynamic model of bridge is established by FEM.Secondly, methods are introduced to simulate the time domain sample of track irregularities and wind velocity field. The interactions between cross winds, the railway vehicle, the track and the bridge are discussed in detail. A new type wheel-rail relationship is applied to consider the elastic contact and wheel-rail separation. The Hertz non-linear contact theory is used to solve the wheel-rail normal forces. Furthermore, the aerodynamic effect of the vehicle or deck is taken into account in the determination of aerodynamic coefficients of deck or vehicle respectively. Wind loads on bridge are static wind loads, buffeting loads and self-excited loads, on railway vehicles are static wind loads and buffeting loads. An explicit-implicit hybrid dynamic integration method is introduced to solve the dynamic responses of the wind-train-track-bridge coupling system, and a program WTTBDAS based on this method is developed. The reliability of WTTBDAS is verified by variety of numerical examples and measured data.Finally, a high-speed railway cable-stayed bridge with 65+221+560+221 +65m span is analyzed. The effects of vehicle speed, rows of vehicles, vehicle type, track structure type and track irregularities for the dynamic responses of the train-track-bridge system are also analyzed. The effects of different wind loads, wind speed, vehicle speed for the dynamic responses of the wind-train-track-bridge system under cross winds are analyzed in detail. A method to estimate the critical wind speed is introduced.The results show that the dynamic model of wind-train-track-bridge system under cross winds is more reliable, and the range of application for the dynamic model of train-track-bridge system is extended. Major conclusions can be drawn as follows:(1) Vehicle type has different effects on the dynamic responses of subsystems, which related to static axle load, spring, damper, air spring parameters and so on. (2) Ballasted track and non-ballasted track have certain different influences on the dynamic responses of the system, then can meet the requirements when high-speed vehicles running on the extra long span bridge. (3) The effects of track irregularities on the displacement responses of bridge are slight, however the effects on the acceleration responses of bridge are significant to some extent. Track irregularities have significant effects on vehicle responses and track responses. (4) Vehicle speed has significant effects on the responses of bridge, vehicle and track without cross winds. The effects of the vehicle rows on the bridge responses are significant, however slight on the vehicle responses and track responses. (5) Static wind loads on the bridge affects on the displacement responses of bridge prominently, however slight on the acceleration responses of bridge, vehicle responses and track responses. Static wind loads on the vehicle has small influences on the vertical dynamic responses of system, but it has great influences on the lateral dynamic responses of system. The fluctuating wind affects on the system responses is significant. It shows that cross winds can remarkable increase the response of bridge and vehicle. (6) The dynamic responses of bridge, track and vehicle are increased with wind speed, in particular wind speed over 20 m/s. (7) When the wind speed is 25 m/s, vehicle speed has slightly influence on the mid span lateral displacement of bridge, significantly on the other items such as vertical displacement and acceleration of bridge, derailment coefficient and wheel-set decrement ratios.