IDEAS home Printed from https://ideas.repec.org/a/hin/jnljam/414903.html
   My bibliography  Save this article

Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance

Author

Listed:
  • Dongmei Zhang
  • Fangqi Chen

Abstract

Stability and bifurcation behaviors for a model of simply supported functionally graded materials rectangular plate subjected to the transversal and in-plane excitations are studied by means of combination of analytical and numerical methods. The resonant case considered here is 1 : 1 internal resonances and primary parametric resonance. Two types of degenerated equilibrium points are studied in detail, which are characterized by a double zero and two negative eigenvalues, and a double zero and a pair of pure imaginary eigenvalues. For each case, the stability regions of the initial equilibrium solution and the critical bifurcation curves are obtained in terms of the system parameters which may lead to Hopf bifurcation and 2D torus. With both analytical and numerical methods, bifurcation behaviors on damping parameters and detuning parameters are studied, respectively. A time integration scheme is used to find the numerical solutions for these bifurcation cases, and numerical results agree with the analytic predictions.

Suggested Citation

  • Dongmei Zhang & Fangqi Chen, 2014. "Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, May.
    • Handle: RePEc:hin:jnljam:414903
    DOI: 10.1155/2014/414903
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JAM/2014/414903.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JAM/2014/414903.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/414903?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnljam:414903. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.