IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v413y2022ics0096300321006901.html
   My bibliography  Save this article

Free vibration and snap-through instability of FG-CNTRC shallow arches supported on nonlinear elastic foundation

Author

Listed:
  • Babaei, Hadi

Abstract

This paper analytically investigates the nonlinear free vibration and snap-through instability of nanocomposite shallow arches reinforced with carbon nanotubes (CNTs). The functionally graded (FG) carbon nanotube reinforced composite (CNTRC) arch with shallow curvature is analysed under uniformly distributed transverse loading. The arch is assumed to rest on a three-parameter nonlinear elastic foundation in a uniform temperature field. Thermo-mechanical properties of the arch are graded through the thickness and are considered to be temperature-dependent. The equations of motion are established based on a general high-order shear deformation theory. These nonlinear equations are derived by Hamilton’s principle within the framework of the von Kármán assumption. The static equilibrium equations and dynamic equations of motion are solved analytically for the arch with immovable simply supported edges. The two-step perturbation technique and Galerkin method are implemented to obtain the closed-form solutions. The novel results illustrate the influences of CNT distribution pattern, foundation stiffness and geometrical parameters on the linear/nonlinear frequency and snap-through instability of the arch. It is shown that the minimum value of limit loads/frequencies belongs to the FG-O type of nanocomposite arches and the maximum ones are obtained in FG-X pattern.

Suggested Citation

  • Babaei, Hadi, 2022. "Free vibration and snap-through instability of FG-CNTRC shallow arches supported on nonlinear elastic foundation," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    • Handle: RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321006901
    DOI: 10.1016/j.amc.2021.126606
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321006901
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126606?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.

    References listed on IDEAS

    as
    1. Abdelrahman, Alaa A. & Esen, Ismail & Eltaher, Mohamed A, 2021. "Vibration response of Timoshenko perforated microbeams under accelerating load and thermal environment," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    2. Şeref D. Akbaş & Hakan Ersoy & Bekir Akgöz & Ömer Civalek, 2021. "Dynamic Analysis of a Fiber-Reinforced Composite Beam under a Moving Load by the Ritz Method," Mathematics, MDPI, vol. 9(9), pages 1-11, May.
    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.
    1. Jahangiri, M. & Asghari, M., 2023. "The strain gradient-based torsional vibration analysis of micro-rotors with nonlinear flexural-torsional coupling," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    2. Nelson Andrés López Machado & Juan Carlos Vielma Pérez & Leonardo Jose López Machado & Vanessa Viviana Montesinos Machado, 2022. "An 8-Nodes 3D Hexahedral Finite Element and an 1D 2-Nodes Structural Element for Timoshenko Beams, Both Based on Hermitian Intepolation, in Linear Range," Mathematics, MDPI, vol. 10(5), pages 1-23, 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:eee:apmaco:v:413:y:2022:i:c:s0096300321006901. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.