Free vibrations with large amplitude of axially loaded beams on an elastic foundation using the Adomian modified decomposition method

Desmond Adair, Askar Ibrayev, Alima Tazabekova, Jong Kim

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Analytical solutions describing free transverse vibrations with large amplitude of axially loaded Euler–Bernoulli beams for various end restrains resting on a Winkler one-parameter foundation are obtained using the Adomian modified decomposition method (AMDM). The AMDM allows the governing equation to become a recursive algebraic equation, and, after some additional simple mathematical operations, the equations can be cast as an eigenvector problem whose solution results in the calculation of natural frequencies and corresponding closed-form series solution of the mode shapes. Important to the use of the Adomian modified decomposition method is the treatment of the nonlinear Fredholm integral coefficient, which forms part of the governing equation. In addition to the calculation of natural frequencies and mode shapes, investigations are made of the effects on the free vibrations of the Winkler parameter and of increasing the axial loading.

Original languageEnglish
Article number3405075
JournalShock and Vibration
Volume2019
DOIs
Publication statusPublished - Jan 1 2019

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free vibration
vibration
decomposition
Decomposition
Natural frequencies
modal response
resonant frequencies
Eigenvalues and eigenfunctions
transverse oscillation
casts
eigenvectors
method
coefficients
parameter
calculation

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Condensed Matter Physics
  • Geotechnical Engineering and Engineering Geology
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Free vibrations with large amplitude of axially loaded beams on an elastic foundation using the Adomian modified decomposition method. / Adair, Desmond; Ibrayev, Askar; Tazabekova, Alima; Kim, Jong.

In: Shock and Vibration, Vol. 2019, 3405075, 01.01.2019.

Research output: Contribution to journalArticle

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