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Temperature change effect on torsional vibration of nanorods embedded in an elastic medium using Rayleigh–Ritz method

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Abstract

This paper studies torsional vibration of carbon nanotubes/nanorods embedded in an elastic medium under thermal stresses. Nonlocal theory is applied to the nanorod equations. The thermal stresses act in axial and other directions, and their amounts vary as temperature changes. The elastic medium is modeled as a rotational spring around the nanorod. Hamilton’s principle is used to obtain motion equation. Rayleigh–Ritz method is used to solve the differential equation of motion. Effect of nonlocal scale coefficient, low and high temperatures, elastic medium stiffness, and nanorod diameter and length is investigated. Influence of temperature on the frequencies depends on the values of stiffness of elastic medium, and nanotube diameter and length.

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Acknowledgements

The authors are grateful to the Iran University of Science and Technology and University of Salahaddin-Erbil for supporting this work.

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. School of Mechanical Engineering, Iran University of Science and Technology, 11369, Narmak, Tehran, Iran

    Sardar S. Abdullah & Shahrokh Hosseini-Hashemi

  2. Center of Excellence in Railway Transportation, Iran University of Science and Technology, 11369, Narmak, Tehran, Iran

    Shahrokh Hosseini-Hashemi

  3. Mechanical Department, College of Engineering, Salahaddin University-Erbil, Erbil, 44001, Iraq

    Sardar S. Abdullah & Nazhad A. Hussein

  4. School of Engineering, Damghan University, Damghan, Islamic Republic of Iran

    Reza Nazemnezhad

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  1. Sardar S. Abdullah
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  2. Shahrokh Hosseini-Hashemi
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Correspondence to Reza Nazemnezhad.

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Abdullah, S.S., Hosseini-Hashemi, S., Hussein, N.A. et al. Temperature change effect on torsional vibration of nanorods embedded in an elastic medium using Rayleigh–Ritz method. J Braz. Soc. Mech. Sci. Eng. 42, 588 (2020). https://doi.org/10.1007/s40430-020-02664-0

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