Abstract
A modified moving loads’ model is proposed for the vehicle-bridge coupling vibration simulation. Taking the vehicle-bridge interaction model (VBI) as the reference, the accuracy and applicability of the three calculation models, namely, moving loads’ model, moving mass model, and spring-damper-mass model, are compared using the frequently-used railway simply-supported beam with a span of 32 meters as the research object. Influencing factors such as vehicle speed, mass ratio of vehicle and beam, and primary spring stiffness on the dynamic response of the vehicle-bridge system are discussed in detail. The results show that the moving load model has the best performance on the stability of the deviation rate, but its calculation results are smaller than the other two methods as well as the VBI. The values of the deviation rate for the moving mass model and the spring-damper-mass model are large, and the stability of those are insufficient in the range of 80%∼120% of the first resonance velocity. Except for that, the results of the two models are in good agreement with the VBI model. According to above analysis, a modified moving loads’ model with two amplification coefficients, namely, 1.10 for the range of 90%∼105% of the first resonance velocity and 1.05 for other velocities, are proposed, which has higher calculation efficiency and accuracy.
Highlights
Since 1997, China’s trains have increased their speeds six times [1], from the “Green Railway Carriage” era 20 years ago, to the “Red Railway Carriage” 15 years ago, and to the “China Railway High-Speed (CRH)” in 2007, and even the “China Rejuvenation (CR)” in recent years; the operating speed has increased from the top speed of 140 km/h to the current 350 km/h, and the speed will develop to 400 km/h in the future [2], and it is constantly being refreshed
Four different vehicle-bridge coupling calculation models are calculated. e speed range covers the range of 50 km/ h∼500 km/h, and the change of the vehicle-bridge mass ratio and various primary spring stiffness covers many types of vehicles
Compared with the other three models, the moving load model lacks the inertial force generated by the mass under the dynamic action, which makes the calculation results of the bridge midspan dynamic coefficient smaller and cannot cover all the calculation results of the vehicle-bridge interaction model (VBI) model, which makes the calculation results dangerous. erefore, multiplying the range of 90%∼105% of its resonance speed by a coefficient of 1.1 and multiplying the remaining speeds by a coefficient of 1.05 to obtain a result consistent with the degree of freedom of space
Summary
Since 1997, China’s trains have increased their speeds six times [1], from the “Green Railway Carriage” era 20 years ago, to the “Red Railway Carriage” 15 years ago, and to the “China Railway High-Speed (CRH)” in 2007, and even the “China Rejuvenation (CR)” in recent years; the operating speed has increased from the top speed of 140 km/h to the current 350 km/h, and the speed will develop to 400 km/h in the future [2], and it is constantly being refreshed. Willis ignored the mass of the bridge in a report on bridge vibration and simplified the train load to moving concentration; Timoshenko [6] considered the bridge quality, simplified the train load to moving concentrated force, and established the bridge vibration equation that only considered the vertical direction; Inglis [7] and Kolousek [8] regarded the train load as a single-moving periodic force and considered the mass of the bridge and the vehicle to analyze the problem of single wheel crossing the bridge. In order to consider the influence of the train mass on the vibration of the vehicle bridge, Yang and Yau [19, 20] simplified the vehicle into a suspended mass, distributed the mass to the car body and the bogie, established a bridge. Compared with UIC776-2 [18] specification, “in dynamic calculation, the train is represented by axle load and spacing and passes through the bridge at a constant speed. is model is sufficient for dynamic calculation.” It is recommended that similar regulations be added to the Chinese code
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