Models for Calculating the Dynamic Performance of the Railway (MCD)

Consult the full list
Consult the schedule


Zuzana Dimitrovová

Invited speakers for specific lectures

Konrad Malicki

Leoš Horníček

Michaël Steenbergen

Piotr Koziol


• Provide trainees with knowledge about possible models of the railway.
• Provide trainees with the ability to choose the appropriate model for the objective in question.

Requirements on previous knowledge

• Basic notions of continuum mechanics, structural dynamics, finite element method, general programming concepts.


• Simplified models (reduced): types of simplifications, the most widely used models, their advantages and limitations, their usefulness and feasibility, determination of their parameters.
• Methods of solution to obtain dynamic response of the simplified model subject to moving forces: analytical and semi-analytical methods.
• Moving forces: Steady-state response, critical velocity, receptance.
• The effect of cancellation and resonance.
• Inertia effects on moving object, support structure and foundation, moving object instability.
• Complete 3D finite element models, viscoelastic boundaries, creation of models in commercial software ANSYS and LS DYNA, APDL programming language.
• Uncertainties in input data, statistical analysis, numerical calibration, metaheuristic optimization.

Recommended literature

• Parts of syllabus of MMC e RM/LEG (Z. Dimitrovová, 2019)
• K.L. Knothe and S.L. Grassie, “Modelling of railway track and vehicle-track interaction at high frequencies,” Vehicle System Dynamics, vol. 22, pp. 209-262, 1993.
• Z. Dimitrovová, “Semi-analytical approaches to vibrations induced by moving loads with the focus on the critical velocity and instability of the moving system”, Chapter 4, pp. 97-152, em Ground Vibration from High Speed Railways, V.V. Krylov (Ed), ICE Publishing, Thomas Telford Ltd. ISBN: 9780727763792,
• Syllabus of MCD (Z. Dimitrovová, 2020)
• A.F.S Rodrigues, Viability and applicability of simplified models for dynamic analysis of railway tracks, Ph.D. thesis. NOVA School of Science and Technology, NOVA University of Lisbon, Portugal, (2017).


Practical test (30%), Report (individual) or program in APDL (groups of 2) and its presentation (70%).

Study language