IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i24p4797-d1006011.html
   My bibliography  Save this article

Dynamic Analysis of Sigmoid Bidirectional FG Microbeams under Moving Load and Thermal Load: Analytical Laplace Solution

Author

Listed:
  • Mohamed A. Attia

    (Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig 44519, Egypt)

  • Ammar Melaibari

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O. Box 80204, Saudi Arabia)

  • Rabab A. Shanab

    (Engineering Mathematics Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig 44519, Egypt)

  • Mohamed A. Eltaher

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O. Box 80204, Saudi Arabia)

Abstract

This paper presents for the first time a closed-form solution of the dynamic response of sigmoid bidirectional functionally graded (SBDFG) microbeams under moving harmonic load and thermal environmental conditions. The formulation is established in the context of the modified couple stress theory to integrate the effects of microstructure. On the basis of the elasticity theory, nonclassical governing equations are derived by using Hamilton’s principle in combination with the parabolic higher-order shear deformation theory considering the physical neutral plane concept. Sigmoid distribution functions are used to describe the temperature-dependent thermomechanical material of bulk continuums of the beam in both the axial and thickness directions, and the gradation of the material length scale parameter is also considered. Linear and nonlinear temperature profiles are considered to present the environmental thermal loads. The Laplace transform is exploited for the first time to evaluate the closed-form solution of the proposed model for a simply supported (SS) boundary condition. The solution is verified by comparing the predicted fundamental frequency and dynamic response with the previously published results. A parametric study is conducted to explore the impacts of gradient indices in both directions, graded material length scale parameters, thermal loads, and moving speed of the acted load on the dynamic response of microbeams. The results can serve as a principle for evaluating the multi-functional and optimal design of microbeams acted upon by a moving load.

Suggested Citation

  • Mohamed A. Attia & Ammar Melaibari & Rabab A. Shanab & Mohamed A. Eltaher, 2022. "Dynamic Analysis of Sigmoid Bidirectional FG Microbeams under Moving Load and Thermal Load: Analytical Laplace Solution," Mathematics, MDPI, vol. 10(24), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4797-:d:1006011
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/24/4797/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/24/4797/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Eltaher, Mohamed A. & Mohamed, Nazira, 2020. "Nonlinear stability and vibration of imperfect CNTs by Doublet mechanics," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Xiao-Ting He & Meng-Qiao Zhang & Bo Pang & Jun-Yi Sun, 2022. "Solution of the Thermoelastic Problem for a Two-Dimensional Curved Beam with Bimodular Effects," Mathematics, MDPI, vol. 10(16), pages 1-22, August.
    3. Ammar Melaibari & Alaa A. Abdelrahman & Mostafa A. Hamed & Ahmed W. Abdalla & Mohamed A. Eltaher, 2022. "Dynamic Analysis of a Piezoelectrically Layered Perforated Nonlocal Strain Gradient Nanobeam with Flexoelectricity," Mathematics, MDPI, vol. 10(15), pages 1-22, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Yi-Lun Liao & Shao-Chen Tseng & Ching-Kong Chao, 2023. "Interfacial Stresses for a Coated Irregularly Shaped Hole Embedded in an Infinite Solid under Point Heat Singularity," Mathematics, MDPI, vol. 11(4), pages 1-20, February.

    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. Alaa A. Abdelrahman & Mohamed S. Abdelwahed & Hani M. Ahmed & Amin Hamdi & Mohamed A. Eltaher, 2023. "Investigation of Size-Dependent Vibration Behavior of Piezoelectric Composite Nanobeams Embedded in an Elastic Foundation Considering Flexoelectricity Effects," Mathematics, MDPI, vol. 11(5), pages 1-31, February.
    2. Nazira Mohamed & Salwa A. Mohamed & Mohamed A. Eltaher, 2022. "Nonlinear Static Stability of Imperfect Bio-Inspired Helicoidal Composite Beams," Mathematics, MDPI, vol. 10(7), pages 1-20, March.
    3. Ammar Melaibari & Ahmed Amine Daikh & Muhammad Basha & Ahmed W. Abdalla & Ramzi Othman & Khalid H. Almitani & Mostafa A. Hamed & Alaa Abdelrahman & Mohamed A. Eltaher, 2022. "Free Vibration of FG-CNTRCs Nano-Plates/Shells with Temperature-Dependent Properties," Mathematics, MDPI, vol. 10(4), pages 1-24, February.
    4. Yi-Lun Liao & Shao-Chen Tseng & Ching-Kong Chao, 2023. "Interfacial Stresses for a Coated Irregularly Shaped Hole Embedded in an Infinite Solid under Point Heat Singularity," Mathematics, MDPI, vol. 11(4), pages 1-20, February.
    5. Emad E. Ghandourah & Ahmed A. Daikh & Abdulsalam M. Alhawsawi & Othman A. Fallatah & Mohamed A. Eltaher, 2022. "Bending and Buckling of FG-GRNC Laminated Plates via Quasi-3D Nonlocal Strain Gradient Theory," Mathematics, MDPI, vol. 10(8), pages 1-37, April.

    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:10:y:2022:i:24:p:4797-:d:1006011. 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.