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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MDPI AG
2025-06-01
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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. |
| format | Article |
| id | doaj-art-2c7c95afb61d4367ae3026e8d4816196 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| 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 |