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Optimal Auxiliary Functions Method for a Pendulum Wrapping on Two Cylinders

Author

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  • Vasile Marinca

    (Center for Fundamental Technical Research, Romanian Academy, 300222 Timisoara, Romania)

  • Nicolae Herisanu

    (Center for Fundamental Technical Research, Romanian Academy, 300222 Timisoara, Romania
    Faculty of Mechanics, University Politehnica Timisoara, 300222 Timisoara, Romania)

Abstract

In the present work, the nonlinear oscillations of a pendulum wrapping on two cylinders is studied by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM). The equation of motion is derived from the Lagrange’s equation. Analytical solutions and natural frequency of the system are calculated. Our results obtained through this new procedure are compared with numerical ones and a very good agreement was found, which proves the accuracy of the method. The presented numerical examples show that the proposed approach is simple, easy to implement and very accurate.

Suggested Citation

  • Vasile Marinca & Nicolae Herisanu, 2020. "Optimal Auxiliary Functions Method for a Pendulum Wrapping on Two Cylinders," Mathematics, MDPI, vol. 8(8), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1364-:d:399053
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    References listed on IDEAS

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    1. Krzysztof Kecik & Jerzy Warminski, 2011. "Dynamics of an Autoparametric Pendulum-Like System with a Nonlinear Semiactive Suspension," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-15, February.
    2. S. Bendersky & B. Sandler, 2006. "Investigation of a spatial double pendulum: an engineering approach," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-22, March.
    3. Chao Fu & Dong Zhen & Yongfeng Yang & Fengshou Gu & Andrew Ball, 2019. "Effects of Bounded Uncertainties on the Dynamic Characteristics of an Overhung Rotor System with Rubbing Fault," Energies, MDPI, vol. 12(22), pages 1-15, November.
    4. J. Warminski & K. Kecik, 2006. "Autoparametric vibrations of a nonlinear system with pendulum," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-19, May.
    5. Nicolae Herisanu & Vasile Marinca & Gheorghe Madescu & Florin Dragan, 2019. "Dynamic Response of a Permanent Magnet Synchronous Generator to a Wind Gust," Energies, MDPI, vol. 12(5), pages 1-11, March.
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    Cited by:

    1. Nicolae Herisanu & Bogdan Marinca & Livija Cveticanin & Vasile Marinca, 2023. "Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation," Mathematics, MDPI, vol. 11(9), pages 1-24, May.
    2. Nicolae Herisanu & Bogdan Marinca & Vasile Marinca, 2022. "Dynamics of the Vibro-Impact Nonlinear Damped and Forced Oscillator under the Influence of the Electromagnetic Actuation," Mathematics, MDPI, vol. 10(18), pages 1-16, September.

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