Development of Simplified Methods for Levitation Force Distribution in Maglev Vehicles Using Frequency Ratio Tests

Maglev vehicles apply the entire vehicle load uniformly onto bridges through levitation forces. In assessing the dynamic characteristics of the maglev train-bridge coupling system, it is reasonable to simplify the distributed levitation force as a concentrated force. This article theoretically derives the analytical response of bridge dynamics under the action of a single constant force and conducts numerical simulations for a moving single constant force and a series of equally spaced constant forces passing over simply supported beams and two-span continuous beams, respectively. The topic of discussion is the response of bridge dynamics when different degrees of force concentration are involved. High-precision displacement and acceleration sensors were utilized to conduct tests on the Shanghai maglev line to verify the accuracy of the simulation results. The results indicate that when simplifying the distributed levitation force into a concentrated force model, a frequency ratio can be used to analyze the conditions for resonance between the train and the bridge and to calculate the critical speed of the train; the levitation distribution force of a high-speed maglev vehicle can be simplified into four groups of concentrated forces based on the number of levitation frames to achieve sufficient accuracy, with the dynamic response of the bridge being close to that under distributed loads.