Vibration control of nonlinear dynamical system via negative cubic velocity feedback | ||
| ERU Research Journal | ||
| Volume 4, Issue 2, April 2025, Pages 2630-2643 PDF (663.92 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/erurj.2025.331356.1197 | ||
| Authors | ||
| Abdullah Reda Shref* 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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