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Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity

  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Naeem, Muhammad Nawaz (Department of Mathematics, Govt. College University Faisalabad) ;
  • Tounsi, Abdelouahed (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria Faculty of Technology, Civil Engineering Department) ;
  • Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir)
  • Received : 2019.06.03
  • Accepted : 2019.08.20
  • Published : 2019.11.25
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Abstract

Vibration analysis of carbon nanotubes (CNTs) is very essential field owing to their many promising applications in tiny instruments. In current study, the Eringen's nonlocal elasticity theory with clamped-clamped and clamped-free end conditions is utilized for the vibration analysis of armchair and zigzag SWCNTs. The Fourier method is utilized to solve the ordinary differential equation. The motion equation for this system is developed using a novel wave propagation method. Complex exponential functions have been used and the axial model depends on BCs that has been described at the edges of CNTs. The behavior of different nonlocal parameters is considered to find the vibrational frequency of SWCNTs. It is exhibited that the effect of frequencies against aspect ratio by varying the bending rigidity. It has been investigated that by increasing the nonlocal parameter decreases the frequencies and on increasing the aspect ratio increases the frequencies for both the tubes. To generate the fundamental natural frequencies of SWCNTs, computer software MATLAB engaged. The numerical results are validated with existing open text. Since the percentage of error is negligible, the model has been concluded as valid.

Keywords

Acknowledgement

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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  4. Eringen's nonlocal model sandwich with Kelvin's theory for vibration of DWCNT vol.25, pp.4, 2019, https://doi.org/10.12989/cac.2020.25.4.343
  5. Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method vol.76, pp.3, 2019, https://doi.org/10.12989/sem.2020.76.3.413
  6. Analysis of nonlocal Kelvin's model for embedded microtubules: Via viscoelastic medium vol.26, pp.6, 2020, https://doi.org/10.12989/sss.2020.26.6.809
  7. Thermal frequency analysis of FG sandwich structure under variable temperature loading vol.77, pp.1, 2019, https://doi.org/10.12989/sem.2021.77.1.057
  8. Frequency and thermal buckling information of laminated composite doubly curved open nanoshell vol.10, pp.1, 2019, https://doi.org/10.12989/anr.2021.10.1.001
  9. Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method vol.10, pp.1, 2019, https://doi.org/10.12989/anr.2021.10.1.025
  10. On thermally induced instability of FG-CNTRC cylindrical panels vol.10, pp.1, 2021, https://doi.org/10.12989/anr.2021.10.1.043
  11. Stoneley wave propagation in nonlocal isotropic magneto-thermoelastic solid with multi-dual-phase lag heat transfer vol.38, pp.2, 2019, https://doi.org/10.12989/scs.2021.38.2.141
  12. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity vol.77, pp.2, 2019, https://doi.org/10.12989/sem.2021.77.2.217
  13. Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates vol.10, pp.2, 2019, https://doi.org/10.12989/anr.2021.10.2.151
  14. Elastic wave phenomenon of nanobeams including thickness stretching effect vol.10, pp.3, 2019, https://doi.org/10.12989/anr.2021.10.3.271
  15. Electromagnetic field and initial stress on a porothermoelastic medium vol.78, pp.1, 2021, https://doi.org/10.12989/sem.2021.78.1.001
  16. Mechanical analysis of bi-functionally graded sandwich nanobeams vol.11, pp.1, 2019, https://doi.org/10.12989/anr.2021.11.1.055
  17. Free vibration analysis of carbon nanotube RC nanobeams with variational approaches vol.11, pp.2, 2021, https://doi.org/10.12989/anr.2021.11.2.157
  18. Computer modeling for frequency performance of viscoelastic magneto-electro-elastic annular micro/nanosystem via adaptive tuned deep learning neural network optimization vol.11, pp.2, 2019, https://doi.org/10.12989/anr.2021.11.2.203