IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v27y2006i3p606-617.html
   My bibliography  Save this article

Wave propagation properties in oscillatory chains with cubic nonlinearities via nonlinear map approach

Author

Listed:
  • Romeo, Francesco
  • Rega, Giuseppe

Abstract

Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n,n+1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.

Suggested Citation

  • Romeo, Francesco & Rega, Giuseppe, 2006. "Wave propagation properties in oscillatory chains with cubic nonlinearities via nonlinear map approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 606-617.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:3:p:606-617
    DOI: 10.1016/j.chaos.2005.04.087
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905004145
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.04.087?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Sun, Yeong-Jeu, 2008. "Composite tracking control for a class of uncertain nonlinear control systems with uncertain deadzone nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 383-389.
    2. Togueu Motcheyo, A.B. & Macías-Díaz, J.E., 2023. "Nonlinear bandgap transmission with zero frequency in a cross-stitch lattice," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Reis, Eduardo V.M. & Savi, Marcelo A., 2022. "Spatiotemporal chaos in a conservative Duffing-type system," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    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:eee:chsofr:v:27:y:2006:i:3:p:606-617. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.