IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i9p1036-d548314.html
   My bibliography  Save this article

Convergence Analysis of the Straightforward Expansion Perturbation Method for Weakly Nonlinear Vibrations

Author

Listed:
  • Soledad Moreno-Pulido

    (Department of Mathematics, College of Engineering, University of Cadiz, 11519 Puerto Real, CA, Spain
    These authors contributed equally to this work.)

  • Francisco Javier García-Pacheco

    (Department of Mathematics, College of Engineering, University of Cadiz, 11519 Puerto Real, CA, Spain
    These authors contributed equally to this work.)

  • Alberto Sánchez-Alzola

    (Department of Statistics and Operation Research, College of Engineering, University of Cadiz, 11519 Puerto Real, CA, Spain
    These authors contributed equally to this work.)

  • Alejandro Rincón-Casado

    (Department of Mechanics, College of Engineering, University of Cadiz, 11519 Puerto Real, CA, Spain
    These authors contributed equally to this work.)

Abstract

There are typically several perturbation methods for approaching the solution of weakly nonlinear vibrations (where the nonlinear terms are “small” compared to the linear ones): the Method of Strained Parameters , the Naive Singular Perturbation Method , the Method of Multiple Scales , the Method of Harmonic Balance and the Method of Averaging . The Straightforward Expansion Perturbation Method (SEPM) applied to weakly nonlinear vibrations does not usually yield to correct solutions. In this manuscript, we provide mathematical proof of the inaccuracy of the SEPM in general cases. Nevertheless, we also provide a sufficient condition for the SEPM to be successfully applied to weakly nonlinear vibrations. This mathematical formalism is written in the syntax of the first-order formal language of Set Theory under the methodology framework provided by the Category Theory.

Suggested Citation

  • Soledad Moreno-Pulido & Francisco Javier García-Pacheco & Alberto Sánchez-Alzola & Alejandro Rincón-Casado, 2021. "Convergence Analysis of the Straightforward Expansion Perturbation Method for Weakly Nonlinear Vibrations," Mathematics, MDPI, vol. 9(9), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1036-:d:548314
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/9/1036/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/9/1036/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yiu-Yin Lee, 2022. "Modified Elliptic Integral Approach for the Forced Vibration and Sound Transmission Analysis of a Nonlinear Panel Backed by a Partitioned Cavity," Mathematics, MDPI, vol. 10(6), pages 1-14, March.

    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:9:y:2021:i:9:p:1036-:d:548314. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.