Semi-analytical solution of a moving mass problem

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In this paper a new analytical solution for a moving mass problem is given. The new analytical formula is presented for the deflection shape of an infinite beam that is traversed by a moving mass and supported by a visco-elastic foundation. In such a case the deflection shape resembles the one associated with the moving force with an additional oscillation around it. The frequency of this mass induced oscillation depends on the foundation characteristics and the amplitude can be derived analytically. It is also shown that if the force associated with the mass has a harmonic component, then its frequency is superposed to the one induced by the foundation. The new formula presented accounts also for the effect of the normal force and Pasternak's modulus.

Original languageEnglish
JournalCivil-Comp Proceedings
Publication statusPublished - 2016


  • Eigenvalue expansion
  • Fourier transform
  • Laplace transform
  • Moving mass
  • Semi-analytical solution
  • Transverse vibration


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