Vibration control of nonlinear dynamical system via negative cubic velocity feedback
Shref, A., Amer, Y., Abd El-Salam, M., khaled, O., Youssef, E. (2025). Vibration control of nonlinear dynamical system via negative cubic velocity feedback. EKB Journal Management System, 4(2), 2630-2643. doi: 10.21608/erurj.2025.331356.1197
Abdullah Reda Shref; Y.A. Amer; M. N. Abd El-Salam; O. M. khaled; E.S.M. Youssef. "Vibration control of nonlinear dynamical system via negative cubic velocity feedback". EKB Journal Management System, 4, 2, 2025, 2630-2643. doi: 10.21608/erurj.2025.331356.1197
Shref, A., Amer, Y., Abd El-Salam, M., khaled, O., Youssef, E. (2025). 'Vibration control of nonlinear dynamical system via negative cubic velocity feedback', EKB Journal Management System, 4(2), pp. 2630-2643. doi: 10.21608/erurj.2025.331356.1197
Shref, A., Amer, Y., Abd El-Salam, M., khaled, O., Youssef, E. Vibration control of nonlinear dynamical system via negative cubic velocity feedback. EKB Journal Management System, 2025; 4(2): 2630-2643. doi: 10.21608/erurj.2025.331356.1197

Vibration control of nonlinear dynamical system via negative cubic velocity feedback

ERU Research Journal
Volume 4, Issue 2, April 2025, Page 2630-2643  XML PDF (663.92 K)
Document Type: Original Article
DOI: 10.21608/erurj.2025.331356.1197
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Authors
Abdullah Reda Shref email 1; Y.A. Amer2; M. N. Abd El-Salam3; O. M. khaled4; E.S.M. Youssef5
1Faculty of Artificial Intelligence, Egyptian Russian University, Badr City, 11829, Cairo, Egypt
2Mathematics Department, Science Faculty, Zagazig University, Zagazig, Egypt
3Basic Sciences Department, Higher Technological Institute, 10th of Ramadan City, Egypt
4Department of Mathematical and Computer Science, Faculty of Sci. Port said University, Port Said, Egypt
5Faculty of Artificial Intelligence, Egyptian Russian University, Cairo 11829, Egypt
Abstract
    The aim of this study is to highlight how specific parameters, especially nonlinear feedback control, can enhance system stability and optimize vibration control. Our findings contribute to the ongoing development of advanced strategies for managing vibrations in nonlinear dynamic systems. In this research paper, we investigate the reduction of vibrations in a hybrid Rayleigh-van der Pol-Duffing oscillator using negative cubic velocity feedback control. This system is modeled as a single-degree-of-freedom oscillator that incorporates both cubic and fifth-order nonlinear terms, along with an externally applied force. To derive a solution from the initial approximation, the multiple scales method was utilized, providing an effective analytical approach for examining the nonlinear behavior of the system. We conducted a comprehensive analysis both graphically and numerically, examining the system’s behavior before and after implementing negative cubic velocity feedback, with a particular focus on the primary resonance condition. MATLAB was used as the main computational tool to explore the effects of different parameters, including the impact of negative cubic velocity feedback on the primary system’s response.
Keywords
Negative Cubic velocity feedback; multiple scales method; Primary resonance; Stability; Fixed point
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