WIT Press

Validation of a new longitudinal train dynamics code for time domain simulations and modal analyses


Free (open access)


Volume 5 (2021), Issue 1



Page Range

41 - 56

Paper DOI



WIT Press


Nicola Bosso, Matteo Magelli, Nicolò Zampieri


Large speeds and axle-loads are required for modern freight trains, which can cause a big rise in in-train forces on wagon coupling elements for both tensile and compressive states, thus possibly leading to breaking of the coupling systems and to train derailments, respectively. Therefore, longitudinal train dynamics (LTD) simulations are a key tool for the prediction of the in-train forces and for the design of coupling and braking systems as well as for the optimization of the train composition. LTD simulations are typically carried out in time domain, to account for all the system non-linearities, mainly the hysteretic behaviour of the coupling system mechanical impedance characteristic. Although time domain simulations are a powerful tool to predict in-train forces considering all the system non-linearities, also frequency domain analyses can be useful to quickly compute the system dynamic behaviour. More in detail, modal analysis can provide important information on the system natural frequencies, so that the frequency content of the input forces can be checked to avoid the excitation of the system natural vibration modes.

The paper shows the development of a new efficient time domain simulation LTD code implemented in MATLAB, provided with a modal analysis post-processing routine. The code was validated on the four time domain simulation scenarios suggested by the international benchmark of LTD simulators, and a simplified modal analysis was also carried out on the same train configurations. The validation process highlighted that the new code provides stable numerical outputs with a good computational efficiency, while the modal analysis routine showed that the train eigenfrequencies can vary significantly according to the deflection, relative speed and loading state on each coupler.


draft gear, dynamics modelling, long train simulation, LTD benchmark, modal analysis, train dynamics