IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i3p755-d1055221.html
   My bibliography  Save this article

A Mode-Matching Tailored-Galerkin Approach for Higher Order Interface Conditions and Geometric Variations

Author

Listed:
  • Muhammad Afzal

    (Department of Mathematics, Capital University of Science and Technology, Islamabad 46000, Pakistan)

  • Naveed Akhtar

    (Department of Mathematics, Capital University of Science and Technology, Islamabad 46000, Pakistan)

  • Mohammed Omar Alkinidri

    (Department of Mathematics, College of Science and Arts, King Abdulaziz University, Rabigh 21911, Saudi Arabia)

  • Meshal Shutaywi

    (Department of Mathematics, College of Science and Arts, King Abdulaziz University, Rabigh 21911, Saudi Arabia)

Abstract

The current study focuses on the modeling and analysis of acoustic scattering from an elastic membrane disc located in a cylindrical waveguide that may involve structural discontinuities. The physical problem is governed by Helmholtz’s equation and involves higher order boundary conditions at the interfaces. The Mode-Matching (MM) method in conjunction with Galerkin formulation is developed to solve the governing boundary value problems. The solution procedure is first applied on two prototype problems to formulate the theoretical frame work, which is then used to analyze the structural response of the elastic membranes attached at the mouth of the cylindrical expansion chamber. The aforementioned solution method yields the linear algebraic systems containing infinite equations. These systems are truncated first and then are numerically solved. From the numerical experiments, it is found that geometrical and material properties of the structure significantly affect the transmission loss as well as the scattering energies.

Suggested Citation

  • Muhammad Afzal & Naveed Akhtar & Mohammed Omar Alkinidri & Meshal Shutaywi, 2023. "A Mode-Matching Tailored-Galerkin Approach for Higher Order Interface Conditions and Geometric Variations," Mathematics, MDPI, vol. 11(3), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:755-:d:1055221
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/3/755/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/3/755/
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Afzal, Muhammad & Alkinidri, Mohammed Omar & Safdar, Muhammad & Bilal, Hazrat, 2023. "On the scattering of cylindrical elastic shell having trifurcation and structural variations at interfaces," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

    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:11:y:2023:i:3:p:755-:d:1055221. 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.