This paper presents a matrix coupled model for the vehicle–track interaction analysis with the crossing panel taken into account. In this model, the wheel–rail contact is assumed to be elastic and solved by the mathematical matrix formulations. Specifically, the determination of the two-point contact during the transition of the wheel load in the crossing panel is demonstrated. To improve the efficiency while ensuring the accuracy in the simulation, a time step size varying solution is applied in the model. The performance of the crossing is validated using field measurement results and simulation results from other numerical methods. The comparable results proved that the model is capable to catch the main features of the wheel–rail interaction in the crossing panel. Moreover, the effect of track irregularities on the vehicle–track interaction is analysed. The simulation results indicate that track irregularities mainly affect wheel–rail interaction in the regular track. In the crossing panel, the variation of the rail geometry plays a dominant role in the wheel–crossing interaction rather than the track irregularity. This study contributes to the perfection of the current model for the vehicle–track interaction analysis and will help to provide more comprehensive guidance for the design, construction and maintenance of the railway track.

In the framework of vehicle-track interaction, this work puts an emphasis on clarifying the influence of sleeper finite element types on system dynamic responses. Three sleeper element types, namely the rigid-body, extensible Euler-Bernoulli beam and solid element are used respectively in the track system modelling with detail mathematical formulations presented. The rails are modelled as Timoshenko beams. The ballasted track system is subject to a moving vehicle with coupled wheel-rail interactions. From aspects of both frequency- and time- domain analysis in the numerical study, the effectiveness of this model has been validated. The influences of the sleeper finite element type, the sleeper support stiffness and damping coefficient on the system responses have been investigated.