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Application of Chebyshev–Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures

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Abstract

This research develops a nonlocal couple stress theory to investigate static stability and free vibration characteristics of functionally graded (FG) nanobeams. The theory introduces two parameters based on nonlocal elasticity theory and modified couple stress theory to capture the size effects much accurately. Therefore, a nonlocal stress field parameter and a material length scale parameter are used to involve both stiffness-softening and stiffness-hardening effects on responses of FG nanobeams. The FG nanobeam is modeled via a higher order refined beam theory in which shear deformation effect is verified needless of shear correction factor. A power-law distribution is used to describe the graded material properties. The governing equations and the related boundary conditions are derived by Hamilton’s principle and they are solved applying Chebyshev–Ritz method which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the provided data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters such as nonlocal and length scale parameters, power-law exponent, slenderness ratio, shear deformation and various boundary conditions on natural frequencies and buckling loads of FG nanobeams in detail.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran

    Farzad Ebrahimi & Mohammad Reza Barati

  2. Division of Mechanics, Civil Engineering Department, Engineering Faculty, Akdeniz University, 07058, Antalya, Turkey

    Ömer Civalek

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  1. Farzad Ebrahimi
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  2. Mohammad Reza Barati
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  3. Ömer Civalek
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Correspondence to Farzad Ebrahimi.

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Ebrahimi, F., Barati, M.R. & Civalek, Ö. Application of Chebyshev–Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures. Engineering with Computers 36, 953–964 (2020). https://doi.org/10.1007/s00366-019-00742-z

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  • DOI: https://doi.org/10.1007/s00366-019-00742-z

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