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

M.N. Abd El-Salam () and Rageh K. Hussein
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M.N. Abd El-Salam: Basic Sciences Department, Higher Technological Institute, Tenth of Ramadan City 44634, Egypt
Rageh K. Hussein: Physics Department, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia

Mathematics, 2025, vol. 13, issue 11, 1-13

Abstract: 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.

Keywords: cantilever beam; linear fractional feedback control; average method; stability; primary resonance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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