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Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method
Joint Authors
Kim, Jong
Adair, Desmond
Ibrayev, Askar
Tazabekova, Alima
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-02-26
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Adair, Desmond& Ibrayev, Askar& Tazabekova, Alima& Kim, Jong. 2019. Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method. Shock and Vibration،Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1211157
Modern Language Association (MLA)
Adair, Desmond…[et al.]. Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method. Shock and Vibration No. 2019 (2019), pp.1-10.
https://search.emarefa.net/detail/BIM-1211157
American Medical Association (AMA)
Adair, Desmond& Ibrayev, Askar& Tazabekova, Alima& Kim, Jong. Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method. Shock and Vibration. 2019. Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1211157
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1211157