Dynamic analysis of three-dimensional bridge–high-speed train interactions using a wheel–rail contact model

A formulation of three-dimensional dynamic interactions between a bridge and a high-speed train using wheel–rail interfaces has been developed. In the interface, contact loss is allowed, the vertical contact is represented by finite tensionless stiffness and the lateral contact is idealized by finite contact stiffness and creepage damping. Such stiffness and damping are nonlinearly dependent on normal contact force. The relative rotations of a wheelset to the rails about its vertical and longitudinal axes are included. Bridge eccentricities and deck displacement due to torsion are accounted for in bridge deck modeling. A numerical algorithm using separate integrations for bridges and trains, and iterations for interface compatibilities is established. A case study of a ten-car train passing over a two-span continuous bridge at various speeds and rail irregularity wavelength ranges is analyzed. The responses of the bridge, car-bodies and wheelsets are investigated for their behavior, acceptability and relations with the wavelengths. Analytical and numerical evaluations of resonant speeds are in good agreement, and the exit span vibration is more amplified than the entrance one at those speeds. The computed relative displacements of all wheelsets to the rail facilitate an explicit assessment for derailment risk.