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Nonlinear vibration of microbeams subjected to a uniform magnetic field and rested on nonlinear elastic foundation

  • Süleyman Murat Bağdatlı ORCID logo , Necla Togun ORCID logo EMAIL logo , Burak Emre Yapanmış and Şevki Akkoca
Published/Copyright: November 14, 2023
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 79 Issue 1

Abstract

This study investigates the nonlinear vibration motions of the Euler–Bernoulli microbeam on a nonlinear elastic foundation in a uniform magnetic field based on Modified Couple Stress Theory (MCST). The effect of size, foundation, and magnetic field on the nonlinear vibration motion of microbeam has been examined. The governing equations related to the nonlinear vibration motions of the microbeam are obtained by using Hamilton’s Principle, and the Multiple Time Scale Method was used to obtain the solutions for the governing equations. The linear natural frequencies of microbeam are presented in the table according to nonlinear parameters and boundary conditions. The linear and nonlinear natural frequency ratio graphs are shown. The present study results are also compared with previous work for validation. It is observed that length scale parameters and magnetic force have a more significant effect on the natural frequency of microbeams. It is seen that when the linear elastic foundation coefficient, the Pasternak foundation and the magnetic force effects increase, the ratio of nonlinear and linear natural frequency decreases.

Keywords: microbeam; modified couple stress theory; magnetic field; perturbation method; nonlinear vibration
Corresponding author: Necla Togun, Department of Mechanical Engineering, Gaziantep University, Üniversite Bulvarı Şehitkamil, Gaziantep, Türkiye, E-mail:

  1. Research ethics: This article does not contain any studies with human participants or animals performed by any of the authors.

  2. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  3. Competing interests: On behalf of all the authors, the corresponding author states that there is no conflict of interest.

  4. Research funding: None declared.

  5. Data availability: Not applicable.

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Received: 2023-08-10
Accepted: 2023-10-23
Published Online: 2023-11-14
Published in Print: 2024-01-29

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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  1. Frontmatter
  2. Atomic, Molecular & Chemical Physics
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  4. Dynamical Systems & Nonlinear Phenomena
  5. Nonlinear vibration of microbeams subjected to a uniform magnetic field and rested on nonlinear elastic foundation
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https://doi.org/10.1515/zna-2023-0225
Keywords for this article
microbeam; modified couple stress theory; magnetic field; perturbation method; nonlinear vibration

Articles in the same Issue

  1. Frontmatter
  2. Atomic, Molecular & Chemical Physics
  3. Green creation of CoFe2O4 nanosorbent for superior toxic Cd ions elimination
  4. Dynamical Systems & Nonlinear Phenomena
  5. Nonlinear vibration of microbeams subjected to a uniform magnetic field and rested on nonlinear elastic foundation
  6. Delta-shock for the Chaplygin gas Euler equations with source terms
  7. Gravitation & Cosmology
  8. Some versions of Chaplygin gas model in modified gravity framework and validity of generalized second law of thermodynamics
  9. Quantum Theory
  10. Bargmann transform and statistical properties for nonlinear coherent states of the isotonic oscillator
  11. Solid State Physics & Materials Science
  12. Low-temperature small-angle electron-electron scattering rate in Fermi metals
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