Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method
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Date
2019-02-26
Authors
Adair, Desmond
Ibrayev, Askar
Tazabekova, Alima
Kim, Jong R.
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi
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.
Description
https://www.hindawi.com/journals/sv/2019/3405075/
Keywords
Winkler parameter, Adomian modified decomposition method, AMDM, axially loaded Euler–Bernoulli beams, Free Vibrations, Elastic Foundation Using
Citation
Adair, 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/10.1155/2019/3405075