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Free Vibration of FG-CNTRCs Nano-Plates/Shells with Temperature-Dependent Properties

Author

Listed:
  • Ammar Melaibari

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia)

  • Ahmed Amine Daikh

    (Department of Technology, University Centre of Naama, Naama 45000, Algeria
    Laboratoire d’Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, Mascara 29000, Algeria)

  • Muhammad Basha

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia)

  • Ahmed W. Abdalla

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

  • Ramzi Othman

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia)

  • Khalid H. Almitani

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia)

  • Mostafa A. Hamed

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia)

  • Alaa Abdelrahman

    (Mechanical Design and Production 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 80204, Saudi Arabia
    Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig 44519, Egypt)

Abstract

This article presents a mathematical continuum model to analyze the free vibration response of cross-ply carbon-nanotube-reinforced composite laminated nanoplates and nanoshells, including microstructure and length scale effects. Different shell geometries, such as plate (infinite radii), spherical, cylindrical, hyperbolic-paraboloid and elliptical-paraboloid are considered in the analysis. By employing Hamilton’s variational principle, the equations of motion are derived based on hyperbolic sine function shear deformation theory. Then, the derived equations are solved analytically using the Galerkin approach. Two types of material distribution are proposed. Higher-order nonlocal strain gradient theory is employed to capture influences of shear deformation, length scale parameter (nonlocal) and material/microstructurescale parameter (gradient). Temperature-dependent material properties are considered. The validation of the proposed mathematical model is presented. Detailed parametric analyses are carried out to highlight the effects of the carbon nanotubes (CNT) distribution pattern, the thickness stretching, the geometry of the plate/shell, the boundary conditions, the total number of layers, the length scale and the material scale parameters, on the vibrational frequencies of CNTRC laminated nanoplates and nanoshells.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:583-:d:748486
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    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. Ahmed E. Abouelregal & Marin Marin, 2020. "The Size-Dependent Thermoelastic Vibrations of Nanobeams Subjected to Harmonic Excitation and Rectified Sine Wave Heating," Mathematics, MDPI, vol. 8(7), pages 1-13, July.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Emad E. Ghandourah & Ahmed Amine Daikh & Samir Khatir & Abdulsalam M. Alhawsawi & Essam M. Banoqitah & Mohamed A. Eltaher, 2023. "A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium," Mathematics, MDPI, vol. 11(10), pages 1-26, May.

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