Application of variational iteration method to free vibration analysis of a tapered beam mounted on two-degree of freedom subsystems

T. A. El-Sayed*, H. H. El-Mongy

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper, the modified variational iteration method (VIM) is applied to solve the free vibration problem of a tapered Euler–Bernoulli beam mounted on two-degrees of freedom mass-spring-damper subsystems. Both conical and wedge beams are investigated. The efficiency of the technique is demonstrated via several numerical examples. The natural frequencies and mode shapes of both uniform and tapered beams with attached subsystems are obtained. Several cases are presented as verification examples by comparison with published literature. Moreover, new results of the studied model are introduced, taking into account the effect of taper ratio and subsystem parameters variation. It is shown that by adjusting the number of iterations, highly accurate results are obtained that are identical to the results got from the exact solution method until the eighth figure. The numerical results prove that the variational iteration method demonstrates the efficiency and accuracy in solving the free vibration problem of non-uniform and integrated beam systems.

Original languageEnglish
Pages (from-to)349-364
Number of pages16
JournalApplied Mathematical Modelling
Volume58
Early online date16 Feb 2018
DOIs
Publication statusPublished - Jun 2018

Keywords

  • Free vibrations
  • Mass-spring-damper
  • Subsystem
  • Tapered beam
  • Variational iteration method

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