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Free transverse vibration of double-walled carbon nanotubes embedded in viscoelastic medium

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Abstract

This paper aims to study the vibration characteristics of viscoelastic double-walled carbon nanotubes embedded in a viscoelastic medium. In doing this, the governing equations of the system are derived by combining the Euler–Bernoulli beam theory, nonlocal viscoelastic model and Kelvin viscoelastic foundation model. Subsequently, the transfer function method is employed to solve the governing equations, which enables one to obtain the natural frequencies and the corresponding mode shapes in closed form for the DWCNTs with arbitrary boundary conditions. Here, the developed mechanics model is first compared with the existing techniques available in the literature, where excellent agreement is achieved. Also, a detailed parametric study is conducted to examine the effect of boundary conditions, nonlocal parameter, relaxation time, slenderness ratio, stiffness coefficient and damping coefficient on the vibration response of the DWCNTs.

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Authors and Affiliations

  1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, China

    D. P. Zhang, Y. Lei & Z. B. Shen

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  1. D. P. Zhang
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  2. Y. Lei
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  3. Z. B. Shen
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Correspondence to Y. Lei.

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Zhang, D.P., Lei, Y. & Shen, Z.B. Free transverse vibration of double-walled carbon nanotubes embedded in viscoelastic medium. Acta Mech 227, 3657–3670 (2016). https://doi.org/10.1007/s00707-016-1686-2

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  • DOI: https://doi.org/10.1007/s00707-016-1686-2

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