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On the stability analysis of a restrained functionally graded nanobeam in an elastic matrix with neutral axis effects

  • Ömer Civalek , Büşra Uzun EMAIL logo and Mustafa Özgür Yaylı
Published/Copyright: April 18, 2024

Abstract

In this work, a general eigenvalue solution of an arbitrarily constrained nonlocal strain gradient nanobeam made of functionally graded material is presented for the first time for the stability response by the effect of the Winkler foundation. Elastic springs at the ends of the nanobeam are considered in the formulation, which have not been considered in most studies. In order to analyze deformable boundary conditions, linear equation systems are derived in terms of infinite power series by using the Fourier sine series together with the Stokes’ transform. The higher-order force boundary conditions are used to obtain a coefficient matrix including different end conditions, power-law index, elastic medium, and small-scale parameters. A general eigenvalue problem of technical interest, associated with nonlocal strain gradient theory, is mathematically evaluated and presented in detail. Parametric results are obtained to investigate the effects of material length scale parameter, Winkler stiffness, power-law index, nonlocal parameter, and elastic springs at the ends. In addition, the effects of the other higher-order elasticity theories simplified from nonlocal strain gradient theory are also investigated and some benchmark results are presented.


Corresponding author: Büşra Uzun, Engineering Faculty, Department of Civil Engineering, Bursa Uludag University, Gorukle Campus, 16059, Bursa, Türkiye, E-mail:

  1. Research ethics: Not applicable.

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

  3. Competing interests: The authors state no competing interests.

  4. Research funding: None declared.

  5. Data availability: Not applicable.

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Received: 2023-12-28
Accepted: 2024-03-11
Published Online: 2024-04-18
Published in Print: 2024-07-26

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