IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i10p1456-d1390657.html
   My bibliography  Save this article

On Aspects of Continuous Approximation of Diatomic Lattice

Author

Listed:
  • Igor V. Andrianov

    (Chair and Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstrasse 18, D-52062 Aachen, Germany)

  • Lelya A. Khajiyeva

    (Department of Mathematical and Computer Modeling, Al-Farabi Kazakh National University, 71 Al-Farabi Ave., 050040 Almaty, Kazakhstan)

  • Askar K. Kudaibergenov

    (Department of Mathematical and Computer Modeling, Al-Farabi Kazakh National University, 71 Al-Farabi Ave., 050040 Almaty, Kazakhstan)

  • Galina A. Starushenko

    (Department of Information Technology and Information Systems, Dnipro University of Technology, 19 Dmytra Yavornytskoho Ave., 49005 Dnipro, Ukraine)

Abstract

This paper is devoted to the continualization of a diatomic lattice, taking into account natural intervals of wavenumber changes. Continualization refers to the replacement of the original pseudo-differential equations by a system of PDEs that provides a good approximation of the dispersion relations. In this regard, the Padé approximants based on the conditions for matching the values of the dispersion relations of the discrete and continuous models at several characteristic points are utilized. As a result, a sixth-order unconditionally stable system with modified inertia is obtained. Appropriate boundary conditions are formulated. The obtained continuous approximation accurately describes the amplitude ratios of neighboring masses. It is also shown that the resulting continuous system provides a good approximation for the natural frequencies.

Suggested Citation

  • Igor V. Andrianov & Lelya A. Khajiyeva & Askar K. Kudaibergenov & Galina A. Starushenko, 2024. "On Aspects of Continuous Approximation of Diatomic Lattice," Mathematics, MDPI, vol. 12(10), pages 1-13, May.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1456-:d:1390657
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/10/1456/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/10/1456/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. I. V. Andrianov & J. Awrejcewicz & D. Weichert, 2010. "Improved Continuous Models for Discrete Media," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-35, 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:12:y:2024:i:10:p:1456-:d:1390657. 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.