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Dynamics of the Vibro-Impact Nonlinear Damped and Forced Oscillator under the Influence of the Electromagnetic Actuation

Author

Listed:
  • Nicolae Herisanu

    (Department of Mechanics and Strength of Materials, University Politehnica Timisoara, 300006 Timisoara, Romania
    Center for Advanced and Fundamental Technical Research, Department of Electromechanics and Vibration, Romanian Academy, 300223 Timisoara, Romania)

  • Bogdan Marinca

    (Department of Applied Electronics, University Politehnica Timisoara, 300006 Timisoara, Romania)

  • Vasile Marinca

    (Department of Mechanics and Strength of Materials, University Politehnica Timisoara, 300006 Timisoara, Romania
    Center for Advanced and Fundamental Technical Research, Department of Electromechanics and Vibration, Romanian Academy, 300223 Timisoara, Romania)

Abstract

The main objective of the present work is to find an approximate analytical solution for the nonlinear differential equation of the vibro-impact oscillator under the influence of the electromagnetic actuation near the primary resonance. The trigger of vibro-impact regime is due to Hertzian contact. The optimal auxiliary functions method (OAFM) is utilized to give an analytical approximate solution of the problem. The influences of static normal load and electromagnetic actuation near the primary resonance are completely studied. The main novelties of the proposed procedure are the presence of some new adequate auxiliary functions, the introduction of the convergence-control parameters, the original construction of the initial and of the first iteration, and the freedom to choose the method for determining the optimal values of the convergence-control parameters. All these led to an explicit and accurate analytical solution, which is another novelty proposed in the paper. This technique is very accurate, simple, effective, and easy to apply using only the first iteration. A second objective was to perform an analysis of stability of the model using the multiple scales method and the eigenvalues of the Jacobian matrix.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3301-:d:912532
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    References listed on IDEAS

    as
    1. Nicolae Herisanu & Vasile Marinca, 2020. "An Efficient Analytical Approach to Investigate the Dynamics of a Misaligned Multirotor System," Mathematics, MDPI, vol. 8(7), pages 1-18, July.
    2. Cveticanin, L., 2006. "Homotopy–perturbation method for pure nonlinear differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1221-1230.
    3. 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.
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