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A Solution Procedure Combining Analytical and Numerical Approaches to Investigate a Two-Degree-of-Freedom Vibro-Impact Oscillator

Author

Listed:
  • Nicolae Herisanu

    (Department of Mechanics and Strength of Materials, University Politehnica Timisoara, 300222 Timisoara, Romania
    Center for Fundamental Technical Research, Romanian Academy-Branch of Timisoara, 300223 Timisoara, Romania)

  • Vasile Marinca

    (Department of Mechanics and Strength of Materials, University Politehnica Timisoara, 300222 Timisoara, Romania
    Center for Fundamental Technical Research, Romanian Academy-Branch of Timisoara, 300223 Timisoara, Romania)

Abstract

In this paper, a new approach is proposed to analyze the behavior of a nonlinear two-degree-of-freedom vibro-impact oscillator subject to a harmonic perturbing force, based on a combination of analytical and numerical approaches. The nonlinear governing equations are analytically solved by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM), which provided highly accurate explicit analytical solutions. Benefiting from these results, the application of Schur principle made it possible to analyze the stability conditions for the considered system. Various types of possible motions were emphasized, taking into account possible initial conditions and different parameters, and the explicit analytical solutions were found to be very useful to analyze the kinetic energy loss, the contact force, and the stability of periodic motions.

Suggested Citation

  • Nicolae Herisanu & Vasile Marinca, 2021. "A Solution Procedure Combining Analytical and Numerical Approaches to Investigate a Two-Degree-of-Freedom Vibro-Impact Oscillator," Mathematics, MDPI, vol. 9(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1374-:d:574582
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    References listed on IDEAS

    as
    1. Emans, Joseph & Wiercigroch, Marian & Krivtsov, Anton M., 2005. "Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam system with impacts," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1661-1670.
    2. Srdjan Jović & Vladimir Raičević & Ljubiša Garić, 2012. "Vibro-Impact System Based on Forced Oscillations of Heavy Mass Particle along a Rough Parabolic Line," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-17, June.
    3. Blazejczyk-Okolewska, Barbara & Czolczynski, Krzysztof & Kapitaniak, Tomasz, 2009. "Dynamics of a two-degree-of-freedom cantilever beam with impacts," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1991-2006.
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