Running and Standing Waves of Timoshenko Beam

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2 Scopus citations


Standing waves of a Timoshenko beamof finite length and their connectionwith running waves for an infinite beam are considered. It is shown that the principle of a “closed cycle” of a running wave is completely identical to the usual procedure of direct satisfaction from the side of the general solution for an infinite Timoshenko beam, to the boundary conditions of a beam of finite length. The question of the existence of a second frequency spectrum under arbitrary boundary conditions of a beam is discussed. A “relaxed approach” to the concept of the second frequency spectrum is proposed. The results of the theoretical analysis are confirmed by numerical calculations for the Timoshenko beam with elastic supports and elastic sealing of its end sections.

Original languageEnglish
Pages (from-to)203-210
Number of pages8
JournalMechanics of Solids
Issue number2
StatePublished - 1 Mar 2018

Scopus subject areas

  • Mechanics of Materials
  • Physics and Astronomy(all)


  • finite element method
  • running and standing waves
  • second frequency spectrum
  • Timoshenko beam
  • “closed loop” principle


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