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Size-dependent nonlinear stability response of perforated nano/microbeams via Fourier series

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Abstract

In this work, perforated and restrained nanobeams with deformable boundary conditions are modeled based on the non-local strain gradient elasticity theory with the elastic medium effect. In this approach in which the Fourier infinite series and Stokes’ transformation are used together, the nanobeam is detached into parts from the two boundary points with the main part. Then using elastic force boundary conditions, a system of linear equations in terms of nonlinearity, elastic medium parameter, spring coefficients and small size effects are derived and the eigenvalue solution of these equations is also presented. The nonlinear stability of restrained nanobeam is examined and the effects of size parameters, perforation and elastic spring coefficients are studied. To reveal the accuracy and effectiveness of the offered model, several numerical applications are solved for the nonlinear stability response of restrained nanobeams with elastic medium effects. The outcomes of this method validated that the presented approach is appropriate for the stability behavior of rigid and restrained nanobeams with perforated cross section.

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Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Engineering, Akdeniz University, Antalya, Turkey

    Ömer Civalek

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Ömer Civalek

  3. Department of Civil Engineering, Faculty of Engineering, Bursa Uludag University, Görükle Campus, 16059, Bursa, Turkey

    Büşra Uzun & Mustafa Özgür Yaylı

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  1. Ömer Civalek
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  2. Büşra Uzun
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Civalek, Ö., Uzun, B. & Yaylı, M.Ö. Size-dependent nonlinear stability response of perforated nano/microbeams via Fourier series. Arch Appl Mech 93, 4425–4443 (2023). https://doi.org/10.1007/s00419-023-02501-5

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