Suppressing Nonlinear Resonant Vibrations via NINDF Control in Beam Structures
In this paper, a unique method for controlling the effects of nonlinear vibrational responses in a cantilever beam system under harmonic excitation is presented. The Nonlinear Integral Negative Derivative Feedback (NINDF) controller is used for this purpose in this study. With this method, the canti...
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MDPI AG
2025-06-01
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| author | Yasser A. Amer Rageh K. Hussein Sharif Abu Alrub Ahmed S. Elgazzar Tarek M. Salman Fatma Mousa M. N. Abd El-Salam |
| author_facet | Yasser A. Amer Rageh K. Hussein Sharif Abu Alrub Ahmed S. Elgazzar Tarek M. Salman Fatma Mousa M. N. Abd El-Salam |
| author_sort | Yasser A. Amer |
| collection | DOAJ |
| description | In this paper, a unique method for controlling the effects of nonlinear vibrational responses in a cantilever beam system under harmonic excitation is presented. The Nonlinear Integral Negative Derivative Feedback (NINDF) controller is used for this purpose in this study. With this method, the cantilever beam is represented by a three-DOF nonlinear system, and the NINDF controller is represented by a first-order and second-order filter. The authors derive analytical solutions for the autonomous system with the controller by utilising perturbation analysis on the linearised system model. This study aims to reduce vibration amplitudes in a nonlinear dynamic system, specifically when 1:1 internal resonance occurs. The stability of the system is assessed using the Routh–Hurwitz criterion. Moreover, symmetry is present in the frequency–response curves (FRCs) for a variety of parameter values. The results show that, when compared to other controllers, the effectiveness of vibration suppression is directly correlated with the product of the NINDF control signal. The amplitude response of the system is demonstrated, and the analytical solutions are validated through numerical simulations using the fourth-order Runge–Kutta method. The accuracy and reliability of the suggested approach are demonstrated via the significant correlation between the analytical and numerical results. |
| format | Article |
| id | doaj-art-eb573d13ba054af1a4e0ab11945aa8eb |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-eb573d13ba054af1a4e0ab11945aa8eb2025-08-20T03:28:26ZengMDPI AGMathematics2227-73902025-06-011313213710.3390/math13132137Suppressing Nonlinear Resonant Vibrations via NINDF Control in Beam StructuresYasser A. Amer0Rageh K. Hussein1Sharif Abu Alrub2Ahmed S. Elgazzar3Tarek M. Salman4Fatma Mousa5M. N. Abd El-Salam6Mathematics Department, Science Faculty, Zagazig University, Zagazig 44511, EgyptPhysics Department, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi ArabiaPhysics Department, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi ArabiaMathematics Department, Faculty of Science, Arish University, Arish 45516, EgyptMathematics Department, Faculty of Science, Arish University, Arish 45516, EgyptBasic Sciences Department, Higher Technological Institute, 10th of Ramadan City 44634, EgyptBasic Sciences Department, Higher Technological Institute, 10th of Ramadan City 44634, EgyptIn this paper, a unique method for controlling the effects of nonlinear vibrational responses in a cantilever beam system under harmonic excitation is presented. The Nonlinear Integral Negative Derivative Feedback (NINDF) controller is used for this purpose in this study. With this method, the cantilever beam is represented by a three-DOF nonlinear system, and the NINDF controller is represented by a first-order and second-order filter. The authors derive analytical solutions for the autonomous system with the controller by utilising perturbation analysis on the linearised system model. This study aims to reduce vibration amplitudes in a nonlinear dynamic system, specifically when 1:1 internal resonance occurs. The stability of the system is assessed using the Routh–Hurwitz criterion. Moreover, symmetry is present in the frequency–response curves (FRCs) for a variety of parameter values. The results show that, when compared to other controllers, the effectiveness of vibration suppression is directly correlated with the product of the NINDF control signal. The amplitude response of the system is demonstrated, and the analytical solutions are validated through numerical simulations using the fourth-order Runge–Kutta method. The accuracy and reliability of the suggested approach are demonstrated via the significant correlation between the analytical and numerical results.https://www.mdpi.com/2227-7390/13/13/2137beamMTSPMNINDFsimultaneous resonance caseFREsIRC |
| spellingShingle | Yasser A. Amer Rageh K. Hussein Sharif Abu Alrub Ahmed S. Elgazzar Tarek M. Salman Fatma Mousa M. N. Abd El-Salam Suppressing Nonlinear Resonant Vibrations via NINDF Control in Beam Structures Mathematics beam MTSPM NINDF simultaneous resonance case FREs IRC |
| title | Suppressing Nonlinear Resonant Vibrations via NINDF Control in Beam Structures |
| title_full | Suppressing Nonlinear Resonant Vibrations via NINDF Control in Beam Structures |
| title_fullStr | Suppressing Nonlinear Resonant Vibrations via NINDF Control in Beam Structures |
| title_full_unstemmed | Suppressing Nonlinear Resonant Vibrations via NINDF Control in Beam Structures |
| title_short | Suppressing Nonlinear Resonant Vibrations via NINDF Control in Beam Structures |
| title_sort | suppressing nonlinear resonant vibrations via nindf control in beam structures |
| topic | beam MTSPM NINDF simultaneous resonance case FREs IRC |
| url | https://www.mdpi.com/2227-7390/13/13/2137 |
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