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About Oscillations in Nonlinear Systems with Elastic Bonds

Author

Listed:
  • Valery Ochkov

    (Department of Theoretical Bases of Heat Engineering, National Research University Moscow Power Engineering Institute, 111250 Moscow, Russia)

  • Inna Vasileva

    (Department of Mathematics, Military Educational and Scientific Center of the Air Force “N.E. Zhukovsky and Y.A. Gagarin Air Force Academy”, 394064 Voronezh, Russia)

  • Yulia Chudova

    (Department of Theoretical Bases of Heat Engineering, National Research University Moscow Power Engineering Institute, 111250 Moscow, Russia)

  • Anton Tikhonov

    (Department of Physics and Technology of Electrical Materials and Components, National Research University Moscow Power Engineering Institute, 111250 Moscow, Russia)

Abstract

This article deals with oscillations that occur with a certain combination of parameters in a nonlinear system with elastic bonds, formed by three cylinders pulled together by an elastic thread. The aim of this work was to develop a methodology for studying nonlinear oscillatory systems based on the analysis of the potential energy of a system and the balance of the forces acting on it. The novelty of the work lies in the proposed methods for determining the conditions for the occurrence of vibrations and in those for calculating the threshold value of the elasticity coefficient of an elastic thread, at which an oscillatory process is guaranteed to occur. The differential equations of oscillations were compiled and numerically solved both with and without allowance for friction forces. The critical value of the elasticity coefficient of the thread at which periodic oscillations occurred was determined. A study of the motion of the system was carried out.

Suggested Citation

  • Valery Ochkov & Inna Vasileva & Yulia Chudova & Anton Tikhonov, 2023. "About Oscillations in Nonlinear Systems with Elastic Bonds," Mathematics, MDPI, vol. 11(8), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1765-:d:1118133
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    References listed on IDEAS

    as
    1. Roman Parovik, 2020. "Mathematical Modeling of Linear Fractional Oscillators," Mathematics, MDPI, vol. 8(11), pages 1-26, October.
    2. Ahmed A. Abd El-Latif & Janarthanan Ramadoss & Bassem Abd-El-Atty & Hany S. Khalifa & Fahimeh Nazarimehr, 2022. "A Novel Chaos-Based Cryptography Algorithm and Its Performance Analysis," Mathematics, MDPI, vol. 10(14), pages 1-22, July.
    3. Valery Ochkov & Inna Vasileva & Konstantin Orlov & Julia Chudova & Anton Tikhonov, 2022. "Visualization in Mathematical Packages When Teaching with Information Technologies," Mathematics, MDPI, vol. 10(19), pages 1-21, September.
    4. (Benn)Wu, Xu-Hong & He, Ji-Huan, 2008. "EXP-function method and its application to nonlinear equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 903-910.
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    Cited by:

    1. Igor Maciejewski & Sebastian Pecolt & Andrzej Błażejewski & Bartosz Jereczek & Tomasz Krzyzynski, 2024. "Experimental Study of the Energy Regenerated by a Horizontal Seat Suspension System under Random Vibration," Energies, MDPI, vol. 17(17), pages 1-18, August.

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