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Investigation of Size-Dependent Vibration Behavior of Piezoelectric Composite Nanobeams Embedded in an Elastic Foundation Considering Flexoelectricity Effects

Author

Listed:
  • Alaa A. Abdelrahman

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

  • Mohamed S. Abdelwahed

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia)

  • Hani M. Ahmed

    (Department of Civil and Environmental Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia)

  • Amin Hamdi

    (Department of Civil and Environmental Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia)

  • Mohamed A. Eltaher

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia)

Abstract

This article investigates the size dependent on piezoelectrically layered perforated nanobeams embedded in an elastic foundation considering the material Poisson’s ratio and the flexoelectricity effects. The composite beam is composed of a regularly squared cut-out elastic core with two piezoelectric face sheet layers. An analytical geometrical model is adopted to obtain the equivalent geometrical variables of the perforated core. To capture the Poisson’s ratio effect, the three-dimensional continuum mechanics adopted to express the kinematics are kinetics relations in the framework of the Euler–Bernoulli beam theory (EBBT). The nonlocal strain gradient theory is utilized to incorporate the size-dependent electromechanical effects. The Hamilton principle is applied to derive the nonclassical electromechanical dynamic equation of motion with flexoelectricity impact. A closed form solution for resonant frequencies is obtained. Numerical results explored the impacts of geometrical and material characteristics on the nonclassical electromechanical behavior of nanobeams. Obtained results revealed the significant effects of the mechanical, electrical, and elastic foundation parameters on the dynamic behavior of piezoelectric composite nanobeams. The developed procedure and the obtained results are helpful for many industrial purposes and engineering applications, such as micro/nano-electromechanical systems (MEMS) and NEMS.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1180-:d:1082720
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    References listed on IDEAS

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    1. Giovanni Tocci Monaco & Nicholas Fantuzzi & Francesco Fabbrocino & Raimondo Luciano, 2021. "Trigonometric Solution for the Bending Analysis of Magneto-Electro-Elastic Strain Gradient Nonlocal Nanoplates in Hygro-Thermal Environment," Mathematics, MDPI, vol. 9(5), pages 1-22, March.
    2. 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.
    3. khabaz, Mohamad Khaje & Eftekhari, S. Ali & Toghraie, Davood, 2022. "Vibration and dynamic analysis of a cantilever sandwich microbeam integrated with piezoelectric layers based on strain gradient theory and surface effects," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    4. Boyina, Kalyan & Piska, Raghu, 2023. "Wave propagation analysis in viscoelastic Timoshenko nanobeams under surface and magnetic field effects based on nonlocal strain gradient theory," Applied Mathematics and Computation, Elsevier, vol. 439(C).
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