Stability approach for periodic delay Mathieu equation by the He- multiple-scales method

Stability approach for periodic delay Mathieu equation by the He- multiple-scales method

In the present work, the version of homotopy perturbation included time-scales is applied to the governing equation of time-periodic delay Mathieu equation. Periodical structure for the amplitude of the zero-order perturbation is constructed. The stability analysis is accompanied by considering thre...

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Main Author: Yusry O. El-Dib
Format: Article
Language:English
Published: Elsevier 2018-12-01
Series:Alexandria Engineering Journal
Online Access:http://www.sciencedirect.com/science/article/pii/S1110016818301960
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spelling doaj-dec8c57b50204806b625a7bb3eea29132021-06-02T04:27:30ZengElsevierAlexandria Engineering Journal1110-01682018-12-0157440094020Stability approach for periodic delay Mathieu equation by the He- multiple-scales methodYusry O. El-Dib0Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, EgyptIn the present work, the version of homotopy perturbation included time-scales is applied to the governing equation of time-periodic delay Mathieu equation. Periodical structure for the amplitude of the zero-order perturbation is constructed. The stability analysis is accompanied by considering three-time-scales. Approximate periodic solutions are derived to the second accuracy of perturbations at the harmonic resonance case as well as at the non-harmonic resonance case. Stability conditions are derived in both cases. Numerical calculations have been done to illustrate the stability behavior at both resonance and non-resonance case. It is shown that the time-delay has a destabilizing influence. We note that the delayed of the parametric excitation has a great interested and application to the design of nuclear accelerators. Keywords: Homotopy perturbation method, Multiple-scales perturbation, Periodic delay Mathieu equation, Parametric resonance, Stability analysishttp://www.sciencedirect.com/science/article/pii/S1110016818301960
collection DOAJ
language English
format Article
sources DOAJ
author Yusry O. El-Dib
spellingShingle Yusry O. El-Dib
Stability approach for periodic delay Mathieu equation by the He- multiple-scales method
Alexandria Engineering Journal
author_facet Yusry O. El-Dib
author_sort Yusry O. El-Dib
title Stability approach for periodic delay Mathieu equation by the He- multiple-scales method
title_short Stability approach for periodic delay Mathieu equation by the He- multiple-scales method
title_full Stability approach for periodic delay Mathieu equation by the He- multiple-scales method
title_fullStr Stability approach for periodic delay Mathieu equation by the He- multiple-scales method
title_full_unstemmed Stability approach for periodic delay Mathieu equation by the He- multiple-scales method
title_sort stability approach for periodic delay mathieu equation by the he- multiple-scales method
publisher Elsevier
series Alexandria Engineering Journal
issn 1110-0168
publishDate 2018-12-01
description In the present work, the version of homotopy perturbation included time-scales is applied to the governing equation of time-periodic delay Mathieu equation. Periodical structure for the amplitude of the zero-order perturbation is constructed. The stability analysis is accompanied by considering three-time-scales. Approximate periodic solutions are derived to the second accuracy of perturbations at the harmonic resonance case as well as at the non-harmonic resonance case. Stability conditions are derived in both cases. Numerical calculations have been done to illustrate the stability behavior at both resonance and non-resonance case. It is shown that the time-delay has a destabilizing influence. We note that the delayed of the parametric excitation has a great interested and application to the design of nuclear accelerators. Keywords: Homotopy perturbation method, Multiple-scales perturbation, Periodic delay Mathieu equation, Parametric resonance, Stability analysis
url http://www.sciencedirect.com/science/article/pii/S1110016818301960
work_keys_str_mv AT yusryoeldib stabilityapproachforperiodicdelaymathieuequationbythehemultiplescalesmethod
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