Non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonance

Non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonance

In this paper, active control with time delay was implemented for eliminating the vibration of the non-linear system excited by external and parametric forcing amplitude in the presence of 1:4 internal resonances. Multiple time scale method is applied to determine first-order approximations of the c...

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Main Authors: M. Sayed, A. A. Mousa, D. Y. Alzaharani
Format: Article
Language:English
Published: JVE International 2016-06-01
Series:Journal of Vibroengineering
Subjects:
time delay
saturation control
active control
stability
jump phenomenon
Online Access:https://www.jvejournals.com/article/16413
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spelling doaj-1b9ff8344c1748aeb2be546c2d093c572020-11-24T21:56:46ZengJVE InternationalJournal of Vibroengineering1392-87162538-84602016-06-011842515253610.21595/jve.2016.1641316413Non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonanceM. Sayed0A. A. Mousa1D. Y. Alzaharani2Department of Engineering Mathematics, Faculty of Electronic Engineering, Menofia University, Menouf 32952, EgyptDepartment of Mathematics and Statistics, Faculty of Science, Taif University, El-Taif, El-Haweiah, P.O. Box 888, Zip Code 21974, Kingdom of Saudi ArabiaDepartment of Mathematics, Faculty of Arts and Science in Baljurashi, Al-Baha University, Al Baha, Kingdom of Saudi ArabiaIn this paper, active control with time delay was implemented for eliminating the vibration of the non-linear system excited by external and parametric forcing amplitude in the presence of 1:4 internal resonances. Multiple time scale method is applied to determine first-order approximations of the controlled system. The stability of the system is investigated analytically using Lyapunov first method and numerically using frequency, force-response curves and phase-plane method for the considered resonance case. Effects of different parameters on the steady state response of the controlled system are investigated. Variation of some parameters leads to the bending of the frequency, force-response curves and hence to the jump phenomenon occurrence.https://www.jvejournals.com/article/16413time delaysaturation controlactive controlstabilityjump phenomenon
collection DOAJ
language English
format Article
sources DOAJ
author M. Sayed
A. A. Mousa
D. Y. Alzaharani
spellingShingle M. Sayed
A. A. Mousa
D. Y. Alzaharani
Non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonance
Journal of Vibroengineering
time delay
saturation control
active control
stability
jump phenomenon
author_facet M. Sayed
A. A. Mousa
D. Y. Alzaharani
author_sort M. Sayed
title Non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonance
title_short Non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonance
title_full Non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonance
title_fullStr Non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonance
title_full_unstemmed Non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonance
title_sort non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonance
publisher JVE International
series Journal of Vibroengineering
issn 1392-8716
2538-8460
publishDate 2016-06-01
description In this paper, active control with time delay was implemented for eliminating the vibration of the non-linear system excited by external and parametric forcing amplitude in the presence of 1:4 internal resonances. Multiple time scale method is applied to determine first-order approximations of the controlled system. The stability of the system is investigated analytically using Lyapunov first method and numerically using frequency, force-response curves and phase-plane method for the considered resonance case. Effects of different parameters on the steady state response of the controlled system are investigated. Variation of some parameters leads to the bending of the frequency, force-response curves and hence to the jump phenomenon occurrence.
topic time delay
saturation control
active control
stability
jump phenomenon
url https://www.jvejournals.com/article/16413
work_keys_str_mv AT msayed nonlineartimedelaysaturationcontrollerforreductionofanonlinearvibratingsystemvia14internalresonance
AT aamousa nonlineartimedelaysaturationcontrollerforreductionofanonlinearvibratingsystemvia14internalresonance
AT dyalzaharani nonlineartimedelaysaturationcontrollerforreductionofanonlinearvibratingsystemvia14internalresonance
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