Reducing the Primary Resonance Vibrations of a Cantilever Beam Using a Proportional Fractional-Order Derivative Controller

Many studies aim to suppress vibrations in vibrating dynamic systems, such as bridges, highways, and aircraft. In this study, we scrutinize the primary resonance of a cantilever beam excited by an external force via a proportional fractional-order derivative controller (PFD). The average method is u...

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Main Authors: M.N. Abd El-Salam, Rageh K. Hussein
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/11/1886
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author M.N. Abd El-Salam
Rageh K. Hussein
author_facet M.N. Abd El-Salam
Rageh K. Hussein
author_sort M.N. Abd El-Salam
collection DOAJ
description Many studies aim to suppress vibrations in vibrating dynamic systems, such as bridges, highways, and aircraft. In this study, we scrutinize the primary resonance of a cantilever beam excited by an external force via a proportional fractional-order derivative controller (PFD). The average method is used to obtain the approximate solution of the vibrating system. The stability of the control system is illustrated using the Routh–Hurwitz criterion. We investigate the performance of some chosen parameters of the studied system to generate response curves. The performance of the linear fractional feedback control is studied at different values of the fractional order.
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spelling doaj-art-2c7c95afb61d4367ae3026e8d48161962025-08-20T02:32:57ZengMDPI AGMathematics2227-73902025-06-011311188610.3390/math13111886Reducing the Primary Resonance Vibrations of a Cantilever Beam Using a Proportional Fractional-Order Derivative ControllerM.N. Abd El-Salam0Rageh K. Hussein1Basic Sciences Department, Higher Technological Institute, Tenth of Ramadan City 44634, EgyptPhysics Department, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi ArabiaMany studies aim to suppress vibrations in vibrating dynamic systems, such as bridges, highways, and aircraft. In this study, we scrutinize the primary resonance of a cantilever beam excited by an external force via a proportional fractional-order derivative controller (PFD). The average method is used to obtain the approximate solution of the vibrating system. The stability of the control system is illustrated using the Routh–Hurwitz criterion. We investigate the performance of some chosen parameters of the studied system to generate response curves. The performance of the linear fractional feedback control is studied at different values of the fractional order.https://www.mdpi.com/2227-7390/13/11/1886cantilever beamlinear fractional feedback controlaverage methodstabilityprimary resonance
spellingShingle M.N. Abd El-Salam
Rageh K. Hussein
Reducing the Primary Resonance Vibrations of a Cantilever Beam Using a Proportional Fractional-Order Derivative Controller
Mathematics
cantilever beam
linear fractional feedback control
average method
stability
primary resonance
title Reducing the Primary Resonance Vibrations of a Cantilever Beam Using a Proportional Fractional-Order Derivative Controller
title_full Reducing the Primary Resonance Vibrations of a Cantilever Beam Using a Proportional Fractional-Order Derivative Controller
title_fullStr Reducing the Primary Resonance Vibrations of a Cantilever Beam Using a Proportional Fractional-Order Derivative Controller
title_full_unstemmed Reducing the Primary Resonance Vibrations of a Cantilever Beam Using a Proportional Fractional-Order Derivative Controller
title_short Reducing the Primary Resonance Vibrations of a Cantilever Beam Using a Proportional Fractional-Order Derivative Controller
title_sort reducing the primary resonance vibrations of a cantilever beam using a proportional fractional order derivative controller
topic cantilever beam
linear fractional feedback control
average method
stability
primary resonance
url https://www.mdpi.com/2227-7390/13/11/1886
work_keys_str_mv AT mnabdelsalam reducingtheprimaryresonancevibrationsofacantileverbeamusingaproportionalfractionalorderderivativecontroller
AT ragehkhussein reducingtheprimaryresonancevibrationsofacantileverbeamusingaproportionalfractionalorderderivativecontroller