IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i15p2700-d876211.html
   My bibliography  Save this article

Analytic Matrix Method for Frequency Response Techniques Applied to Nonlinear Dynamical Systems II: Large Amplitude Oscillations

Author

Listed:
  • Elena Hernandez

    (Departamento de Ingeniería Química, Universidad de Guadalajara, Guadalajara 44430, Mexico)

  • Octavio Manero

    (Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de Mexico, CDMX, Mexico City 04510, Mexico)

  • Fernando Bautista

    (Departamento de Física, Universidad de Guadalajara, Guadalajara 44430, Mexico)

  • Juan Paulo Garcia-Sandoval

    (Departamento de Ingeniería Química, Universidad de Guadalajara, Guadalajara 44430, Mexico)

Abstract

This work is the second in a series of articles that deal with analytical solutions of nonlinear dynamical systems under oscillatory input that may exhibit harmonic frequencies. Frequency response techniques of nonlinear dynamical systems are usually analyzed with numerical methods, because in most cases analytical solutions such as the harmonic balance series solution turn out to be difficult, if not impossible, as they are based on an infinite series of trigonometric functions with harmonic frequencies. The key contribution of the analytic matrix methods reported in the present series of articles is to work with the invariant submanifold of the problem and to propose the solution as infinite power series of the oscillatory input; this procedure is a direct one that speeds up the computations compared to traditional series solution methods. The method reported in the first contribution of this series allows for the computation of the analytical solution only for small and medium amplitudes of the oscillatory input, because these series may diverge when large amplitudes are applied. Therefore, the analytic matrix method reported here, which is a reconfiguration of the method proposed in the first contribution in this series, allows the solving of problems in the regime of large-amplitude oscillations where the contributions of the high order harmonics affect the amplitudes of the low order harmonics, leading to amplitude- and frequency-dependent coefficients for the infinite series of trigonometric function expansion.

Suggested Citation

  • Elena Hernandez & Octavio Manero & Fernando Bautista & Juan Paulo Garcia-Sandoval, 2022. "Analytic Matrix Method for Frequency Response Techniques Applied to Nonlinear Dynamical Systems II: Large Amplitude Oscillations," Mathematics, MDPI, vol. 10(15), pages 1-21, July.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2700-:d:876211
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/15/2700/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/15/2700/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Elena Hernandez & Octavio Manero & Fernando Bautista & Juan Paulo Garcia-Sandoval, 2021. "Analytic Matrix Method for Frequency Response Techniques Applied to Nonlinear Dynamical Systems I: Small and Medium Amplitude Oscillations," Mathematics, MDPI, vol. 9(24), pages 1-21, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2700-:d:876211. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.