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

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dc.contributor.authorAdair, Desmond
dc.contributor.authorIbrayev, Askar
dc.contributor.authorTazabekova, Alima
dc.contributor.authorKim, Jong R.
dc.date.accessioned2019-12-11T05:45:51Z
dc.date.available2019-12-11T05:45:51Z
dc.date.issued2019-02-26
dc.descriptionhttps://www.hindawi.com/journals/sv/2019/3405075/en_US
dc.description.abstractAnalytical 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.en_US
dc.identifier.citationAdair, D., Ibrayev, A., Tazabekova, A., & Kim, J. R. (2019). Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method. Shock and Vibration, 2019, 1–10. https://doi.org/10.1155/2019/3405075en_US
dc.identifier.other000460921200001
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/4351
dc.language.isoenen_US
dc.publisherHindawien_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectWinkler parameteren_US
dc.subjectAdomian modified decomposition methoden_US
dc.subjectAMDMen_US
dc.subjectaxially loaded Euler–Bernoulli beamsen_US
dc.subjectFree Vibrationsen_US
dc.subjectElastic Foundation Usingen_US
dc.titleFree Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Methoden_US
dc.typeArticleen_US
workflow.import.sourcescience

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