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Multi-Control Strategies on a Cubic–Quintic Nonlinear Hybrid Oscillator with External Excitation Under Resonance Conditions

Author

Listed:
  • Asma Alanazy

    (Mathematics Department, Faculty of Science, Northern Border University, Arar 1321, Saudi Arabia)

  • Yasser A. Amer

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44759, Egypt)

  • Ashraf Taha EL-Sayed

    (Department of Basic Science, Modern Academy for Engineering and Technology, Cairo 11439, Egypt)

  • Fatma Sh. Mohammed

    (Department of Basic Science, Higher Institute of Engineering and Technology, Fifth Settlement, Cairo 11835, Egypt)

  • Taher A. Bahnasy

    (Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta 31734, Egypt)

Abstract

The goal of this article is to reduce the vibration of a hybrid oscillator with a cubic–quintic nonlinear term under internal and external forces in the worst resonance case. To eliminate the harmful vibration in the system, the following strategies are suggested: nonlinear derivative feedback control (NDF), linear negative velocity feedback control (LNVC), nonlinear integral positive position feedback (NIPPF), integral resonant control (IRC), negative velocity with time delay (TD), and positive position feedback (PPF). It is discovered that the PPF control suppresses vibration more effectively than typical controllers, which reduces the vibration to 0.0001 with an effectiveness of 99.92%. Moreover, the main advantages of the PPF controller are its low cost and the fast response. The multiple time scale perturbation technique (MSPT) is used to apply the theoretical methodology and obtain a perturbed response. In order to close the concurrent primary and internal resonance case, frequency response (FR) equations are also used to study and analyze the system’s stability. The MATLAB software is used to complete and clarify all numerical topics. The FR curves are examined to determine the amplitude’s subsequent impact from variations in the parameters’ values. Lastly, a comparison of the numerical and analytical solutions is performed utilizing time history. Along with comparing the impact of our PPF damper on the hybrid oscillator, earlier research is also provided.

Suggested Citation

  • Asma Alanazy & Yasser A. Amer & Ashraf Taha EL-Sayed & Fatma Sh. Mohammed & Taher A. Bahnasy, 2025. "Multi-Control Strategies on a Cubic–Quintic Nonlinear Hybrid Oscillator with External Excitation Under Resonance Conditions," Mathematics, MDPI, vol. 13(6), pages 1-24, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:957-:d:1611831
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    References listed on IDEAS

    as
    1. Bauomy, H.S. & EL-Sayed, A.T. & El-Bahrawy, F.T., 2024. "Integral resonant negative derivative feedback suppression control strategy for nonlinear dynamic vibration behavior model," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    2. Chun-Hui He & Chao Liu & Ji-Huan He & Khaled A. Gepreel, 2021. "Low Frequency Property Of A Fractal Vibration Model For A Concrete Beam," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-7, August.
    3. Huang, Chengdai & Li, Huan & Cao, Jinde, 2019. "A novel strategy of bifurcation control for a delayed fractional predator–prey model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 808-838.
    4. Ji-Huan He & Shuai-Jia Kou & Chun-Hui He & Zuo-Wei Zhang & Khaled A. Gepreel, 2021. "Fractal Oscillation And Its Frequency-Amplitude Property," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-9, June.
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