New semi-analytical solution for a uniformly moving mass on a beam on a two-parameter visco-elastic foundation

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Abstract

In this paper a new semi-analytical solution for the moving mass problem is presented. Firstly, the problem of a mass traversing a finite beam on an elastic foundation is reviewed and some new aspects are added. Then, the new semi-analytical solution is deduced for an infinite beam. The semi-analytical solution of the displacement under the mass is derived with the help of integral transforms and the full deflection shape is obtained by linking together two semi-infinite beams. An iterative procedure is suggested for the determination of the frequency of the oscillation induced by the moving mass. Results deduced for infinite beams are confirmed by analysis of long finite beams, with the help of derivations given in the first part of this paper. Convergence analysis on finite beams is also presented, and, in addition, the effects of the normal force, of the harmonic component of the vertical force and of the foundation damping are discussed.

Original languageEnglish
Pages (from-to)142-162
Number of pages21
JournalInternational Journal of Mechanical Sciences
Volume127
DOIs
Publication statusPublished - 1 Jul 2017

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Damping
integral transformations
deflection
derivation
damping
harmonics
oscillations

Keywords

  • Finite, infinite and semi-infinite beams
  • Harmonic load component
  • Mass-induced frequency
  • Moving mass
  • Normal force
  • Semi-analytical solution
  • Transverse vibrations

Cite this

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title = "New semi-analytical solution for a uniformly moving mass on a beam on a two-parameter visco-elastic foundation",
abstract = "In this paper a new semi-analytical solution for the moving mass problem is presented. Firstly, the problem of a mass traversing a finite beam on an elastic foundation is reviewed and some new aspects are added. Then, the new semi-analytical solution is deduced for an infinite beam. The semi-analytical solution of the displacement under the mass is derived with the help of integral transforms and the full deflection shape is obtained by linking together two semi-infinite beams. An iterative procedure is suggested for the determination of the frequency of the oscillation induced by the moving mass. Results deduced for infinite beams are confirmed by analysis of long finite beams, with the help of derivations given in the first part of this paper. Convergence analysis on finite beams is also presented, and, in addition, the effects of the normal force, of the harmonic component of the vertical force and of the foundation damping are discussed.",
keywords = "Finite, infinite and semi-infinite beams, Harmonic load component, Mass-induced frequency, Moving mass, Normal force, Semi-analytical solution, Transverse vibrations",
author = "Zuzana Dimitrovov{\'a}",
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T1 - New semi-analytical solution for a uniformly moving mass on a beam on a two-parameter visco-elastic foundation

AU - Dimitrovová, Zuzana

N1 - sem pdf conforme despacho. FCT, through IDMEC, under LAETA, project UID/EMS/50022/2013.

PY - 2017/7/1

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N2 - In this paper a new semi-analytical solution for the moving mass problem is presented. Firstly, the problem of a mass traversing a finite beam on an elastic foundation is reviewed and some new aspects are added. Then, the new semi-analytical solution is deduced for an infinite beam. The semi-analytical solution of the displacement under the mass is derived with the help of integral transforms and the full deflection shape is obtained by linking together two semi-infinite beams. An iterative procedure is suggested for the determination of the frequency of the oscillation induced by the moving mass. Results deduced for infinite beams are confirmed by analysis of long finite beams, with the help of derivations given in the first part of this paper. Convergence analysis on finite beams is also presented, and, in addition, the effects of the normal force, of the harmonic component of the vertical force and of the foundation damping are discussed.

AB - In this paper a new semi-analytical solution for the moving mass problem is presented. Firstly, the problem of a mass traversing a finite beam on an elastic foundation is reviewed and some new aspects are added. Then, the new semi-analytical solution is deduced for an infinite beam. The semi-analytical solution of the displacement under the mass is derived with the help of integral transforms and the full deflection shape is obtained by linking together two semi-infinite beams. An iterative procedure is suggested for the determination of the frequency of the oscillation induced by the moving mass. Results deduced for infinite beams are confirmed by analysis of long finite beams, with the help of derivations given in the first part of this paper. Convergence analysis on finite beams is also presented, and, in addition, the effects of the normal force, of the harmonic component of the vertical force and of the foundation damping are discussed.

KW - Finite, infinite and semi-infinite beams

KW - Harmonic load component

KW - Mass-induced frequency

KW - Moving mass

KW - Normal force

KW - Semi-analytical solution

KW - Transverse vibrations

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