Frequency equation using new set of fundamental solutions with application on the free vibration of Timoshenko beams with intermediate rigid or elastic span

T. A. El-Sayed*, S. H. Farghaly

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Stepped beams are crucial power transmission components in many mechanical engineering systems. These beams may be dynamically analyzed using the stepped Timoshenko model or the rigid mass model. In this paper, a new set of fundamental solutions is derived in order to normalize the Timoshenko beam equation at the origin of the coordinates. This set of solutions is used to derive the frequency equation of both stepped and rigid mass models. The validity ranges of these models were investigated by comparing the modal frequency results of both models. In addition, selected cases were compared using mode shape analysis. Three different models with classical end conditions are considered through this work. These are free–free, pinned–pinned and clamped–free beam configurations. The numerical results of the current work show that increasing the intermediate diameter ratio and decreasing the length ratio of the rigid mass results in decreasing the percentage deviation between the rigid mass model results and the elastic model results.

Original languageEnglish
Pages (from-to)4764-4780
Number of pages17
JournalJVC/Journal of Vibration and Control
Volume24
Issue number20
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • elastic support
  • rigid body
  • set of fundamental solutions
  • stepped beam
  • Timoshenko beam

ASJC Scopus subject areas

  • Automotive Engineering
  • Materials Science(all)
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering

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