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Analytical investigation on free torsional vibrations of noncircular nanorods

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Abstract

This paper is devoted to the free torsional behavior of the nanorods containing noncircular cross sections. The rectangular cross section is chosen to be the case of the study. Three various boundary conditions, namely the clamped–clamped (C–C), clamped–free (C–F), and clamped–torsional spring (C–T) boundary conditions, are used to model the nanorod. Hamilton’s principle is utilized to derive the equation of motion along with associated boundary conditions. The derived equation is reformulated by Eringen’s nonlocal elasticity approach to exhibit the small-scale effect. An analytical method is established to discretize and analyze the equation of motion. The novelty of this work is the analysis of the torsional vibration in rectangular nanorods, which are not observed in previous works. For the results, the influences of the horizontal and vertical aspect ratios (\(a/b\) and \(b/a\)) (for C–C and C–F boundary conditions) and the influences of the nonlocal parameter and stiffness of the boundary spring (for C–T boundary condition) are illustrated schematically and tabularly.

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Authors and Affiliations

  1. Department of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran

    Farshad Khosravi

  2. Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran

    Seyed Amirhosein Hosseini

  3. Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran

    Babak Alizadeh Hamidi

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  1. Farshad Khosravi
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  2. Seyed Amirhosein Hosseini
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  3. Babak Alizadeh Hamidi
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Correspondence to Seyed Amirhosein Hosseini.

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Khosravi, F., Hosseini, S.A. & Hamidi, B.A. Analytical investigation on free torsional vibrations of noncircular nanorods. J Braz. Soc. Mech. Sci. Eng. 42, 514 (2020). https://doi.org/10.1007/s40430-020-02587-w

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  • DOI: https://doi.org/10.1007/s40430-020-02587-w

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