Critical velocity of a uniformly moving load

Z. Dimitrovová, A. F. S. Rodrigues

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)


An analysis of the critical velocity of a load moving uniformly along a beam on a visco-elastic foundation composed of one or two sub-domains is presented. The case study addressed is related to high-speed railway lines. A new formulation of the governing equations in the first order state-space form is proposed for the Timoshenko-Rayleigh beam. Differences in results obtained by Euler-Bernoulli and Timoshenko-Rayleigh beam theories are analysed. It is concluded that, in the case study considered, these differences are negligible. Critical velocities are obtained for load travelling on finite and infinite beams, with and without damping. A new relationship between the viscous damping coefficient and the modal damping ratio is derived and justified. Predictions about critical velocities established in [1] are confirmed numerically for cases not considered in [1], i.e. in cases when the load passes on infinite beams and when damping is considered.

Original languageEnglish
Pages (from-to)44-56
Number of pages13
JournalAdvances in Engineering Software
Issue number1
Publication statusPublished - 2012


  • Euler-Bernoulli beam theory
  • Maximum displacement
  • Modal expansion
  • Non-homogeneous foundation
  • Timoshenko-Rayleigh beam theory
  • Transverse vibration


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