Models for Calculating the Dynamic Performance of the Railroad


• 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.

General characterization





Responsible teacher

Zuzana Dimitrovova


Weekly - 2

Total - 26

Teaching language



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


• 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).

Teaching method

All subjects of the discipline are covered in theoretical-practical classes.

The exposition and explanation of the various concepts, principles and methods is exemplified by solving some illustrative problems and using simple programs that trainees will be able to run in Octave and ANSYS software.

Trainees are encouraged to prepare an individual report, using the programs provided and choosing one of the topics proposed by the teacher.

Evaluation method

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

Subject matter

• 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, receptivity.
• 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.


Programs where the course is taught: