Free vibration of nonlinear autonomous systems modeled by 4-th order ordinary differential equations including internal resonance

Free vibration of nonlinear autonomous systems modeled by 4-th order ordinary differential equations including internal resonance

In this article, the dynamic behavior of nonlinear autonomous system modeled by 4-th order ordinary differential equations is considered. Based on the pioneer work of Krylov-Bogoliubov-Mitropolskii (KBM), a modified KBM method is applied to achieve analytical solutions. Two different cases such as n...

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Main Author: Md. Zahurul Islam
Format: Article
Language:English
Published: Elsevier 2018-12-01
Series:Ain Shams Engineering Journal
Online Access:http://www.sciencedirect.com/science/article/pii/S2090447916301332
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spelling doaj-0094c6f77f214d3a892254bc33f5b30a2021-06-02T05:19:59ZengElsevierAin Shams Engineering Journal2090-44792018-12-019413751379Free vibration of nonlinear autonomous systems modeled by 4-th order ordinary differential equations including internal resonanceMd. Zahurul Islam0Department of Applied Mathematics, Rajshahi University, Rajshahi 6205, BangladeshIn this article, the dynamic behavior of nonlinear autonomous system modeled by 4-th order ordinary differential equations is considered. Based on the pioneer work of Krylov-Bogoliubov-Mitropolskii (KBM), a modified KBM method is applied to achieve analytical solutions. Two different cases such as non-resonant and resonant conditions are studied in the presence of quadratic nonlinearities. The utility of the proposed method is justified by numerical result which is generated by Runge-Kutta fourth-order procedure. The analytical solution in each case shows an excellence agreement with numerical results. Keywords: KBM method, Autonomous system, Nonlinearity, Internal resonancehttp://www.sciencedirect.com/science/article/pii/S2090447916301332
collection DOAJ
language English
format Article
sources DOAJ
author Md. Zahurul Islam
spellingShingle Md. Zahurul Islam
Free vibration of nonlinear autonomous systems modeled by 4-th order ordinary differential equations including internal resonance
Ain Shams Engineering Journal
author_facet Md. Zahurul Islam
author_sort Md. Zahurul Islam
title Free vibration of nonlinear autonomous systems modeled by 4-th order ordinary differential equations including internal resonance
title_short Free vibration of nonlinear autonomous systems modeled by 4-th order ordinary differential equations including internal resonance
title_full Free vibration of nonlinear autonomous systems modeled by 4-th order ordinary differential equations including internal resonance
title_fullStr Free vibration of nonlinear autonomous systems modeled by 4-th order ordinary differential equations including internal resonance
title_full_unstemmed Free vibration of nonlinear autonomous systems modeled by 4-th order ordinary differential equations including internal resonance
title_sort free vibration of nonlinear autonomous systems modeled by 4-th order ordinary differential equations including internal resonance
publisher Elsevier
series Ain Shams Engineering Journal
issn 2090-4479
publishDate 2018-12-01
description In this article, the dynamic behavior of nonlinear autonomous system modeled by 4-th order ordinary differential equations is considered. Based on the pioneer work of Krylov-Bogoliubov-Mitropolskii (KBM), a modified KBM method is applied to achieve analytical solutions. Two different cases such as non-resonant and resonant conditions are studied in the presence of quadratic nonlinearities. The utility of the proposed method is justified by numerical result which is generated by Runge-Kutta fourth-order procedure. The analytical solution in each case shows an excellence agreement with numerical results. Keywords: KBM method, Autonomous system, Nonlinearity, Internal resonance
url http://www.sciencedirect.com/science/article/pii/S2090447916301332
work_keys_str_mv AT mdzahurulislam freevibrationofnonlinearautonomoussystemsmodeledby4thorderordinarydifferentialequationsincludinginternalresonance
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