Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method

Autor: Desmond Adair, Askar Ibrayev, Alima Tazabekova, Jong R. Kim
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Shock and Vibration, Vol 2019 (2019)
Druh dokumentu: article
ISSN: 1070-9622
1875-9203
DOI: 10.1155/2019/3405075
Popis: 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.
Databáze: Directory of Open Access Journals
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