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Nonlinear Vibration of Electrostatically Actuated Microbeam

Author

Listed:
  • Gamal M. Ismail

    (Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
    Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt)

  • Md. Alal Hosen

    (Department of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi 6204, Bangladesh)

  • Mostafa Mohammadian

    (Department of Mechanical Engineering, Gorgan Branch, Islamic Azad University, Gorgan 98542022, Iran)

  • Maha M. El-Moshneb

    (Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt)

  • Mahmoud Bayat

    (Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 29208, USA
    Ingram School of Engineering, Texas State University, San Marcos, TX 78666, USA)

Abstract

In this paper, an analytical technique based on the global residue harmonic balance method (GRHBM) is applied in order to obtain higher-order approximate analytical solutions of an electrostatically actuated micro-beam. To illustrate the applicability and accuracy of the method, a high level of accuracy was established for the analytical solutions by comparing the results of the solutions with the numerical solution as well as the already published literature, such as the variational approach (VA), Hamiltonian approach (HA), energy balance method (EBM), and homotopy analysis method (HAM). It is shown that the GRHB method can be easily applied to nonlinear problems and provides solutions with a higher precision than existing methods. The obtained analytical expressions are employed to study the effects of axial force, initial gape, and electrostatic load on nonlinear frequency.

Suggested Citation

  • Gamal M. Ismail & Md. Alal Hosen & Mostafa Mohammadian & Maha M. El-Moshneb & Mahmoud Bayat, 2022. "Nonlinear Vibration of Electrostatically Actuated Microbeam," Mathematics, MDPI, vol. 10(24), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4762-:d:1004029
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