Skip to main content
Log in

Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity

  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

In the present study, the torsional vibration behavior of double walled carbon nanotubes (DWCNTs) is investigated using nonlocal elasticity theory. The effects of van der Waals Force interaction, nanotube length and nonlocal parameter are studied in detail. Two frequency set are obtained for DWCNTs for a given half wave number. It is also shown that some mode shapes are anti-phase and some of them are in-phase. The present results can be useful in design of nano electromechanical systems like nanobearings and rotary servomotors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Ansari, R., Gholami, R., Ajori, S.: Torsional vibration analysis of carbon nanotubes based on the strain gradient theory and molecular dynamic simulations. J. Vib. Acoust. 135, 51016 (2013)

    Article  Google Scholar 

  • Arda, M., Aydogdu, M.: Torsional statics and dynamics of nanotubes embedded in an elastic medium. Compos. Struct. 114, 80–91 (2014)

    Article  Google Scholar 

  • Aydogdu, M.: A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration. Phys. E Low-Dimens. Syst. Nanostructures 41, 1651–1655 (2009a)

    Article  Google Scholar 

  • Aydogdu, M.: Axial vibration of the nanorods with the nonlocal continuum rod model. Phys. E Low-Dimens. Syst. Nanostructures 41, 861–864 (2009b)

    Article  Google Scholar 

  • Aydogdu, M.: Longitudinal wave propagation in nanorods using a general nonlocal unimodal rod theory and calibration of nonlocal parameter with lattice dynamics. Int. J. Eng. Sci. 56, 17–28 (2012)

    Article  Google Scholar 

  • Aydogdu, M.: A nonlocal rod model for axial vibration of double-walled carbon nanotubes including axial van der Waals force effects. J. Vib. Control. (2014a). doi:10.1177/1077546313518954

  • Aydogdu, M.: Longitudinal wave propagation in multiwalled carbon nanotubes. Compos. Struct. 107, 578–584 (2014b)

    Article  Google Scholar 

  • Demir, Ç., Civalek, Ö.: Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models. Appl. Math. Model. 37, 9355–9367 (2013)

    Article  Google Scholar 

  • Dong, K., Zhu, S.Q., Wang, X.: Wave propagation in multiwall carbon nanotubes embedded in a matrix material. Compos. Struct. 82, 1–9 (2008)

    Article  Google Scholar 

  • Dong, L., Nelson, B.J., Fukuda, T., Arai, F., Nakajima, M.: Towards linear nano servomotors with integrated position sensing. In: Proceedings of the IEEE international conference on robotics and automation, pp. 855–860 (2005)

  • Eringen, A.C.: Nonlocal polar elastic continua. Int. J. Eng. Sci. 10, 1–16 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  • Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)

    Article  Google Scholar 

  • Fazelzadeh, S.A., Ghavanloo, E.: Nonlocal anisotropic elastic shell model for vibrations of single-walled carbon nanotubes with arbitrary chirality. Compos. Struct. 94, 1016–1022 (2012)

    Article  Google Scholar 

  • Ghannadpour, S.A.M., Mohammadi, B., Fazilati, J.: Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method. Compos. Struct. 96, 584–589 (2013)

    Article  Google Scholar 

  • Gheshlaghi, B., Hasheminejad, S.M., Abbasion, S.: Size dependent torsional vibration of nanotubes. Phys. E Low-Dimens. Syst. Nanostructures. 43, 45–48 (2010)

    Article  Google Scholar 

  • Hall, A.R., Paulson, S., Cui, T., Lu, J.P., Qin, L.-C., Washburn, S.: Torsional electromechanical systems based on carbon nanotubes. Rep. Prog. Phys. 75, 116501 (2012)

    Article  Google Scholar 

  • He, X.Q., Kitipornchai, S., Liew, K.M.: Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction. J. Mech. Phys. Solids 53, 303–326 (2005)

    Article  MATH  Google Scholar 

  • Hu, Y.G., Liew, K.M., Wang, Q.: Modeling of vibrations of carbon nanotubes. Procedia Eng. 31, 343–347 (2012)

    Article  Google Scholar 

  • Hu, Y.-G., Liew, K.M., Wang, Q., He, X.Q., Yakobson, B.I.: Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes. J. Mech. Phys. Solids 56, 3475–3485 (2008)

    Article  MATH  Google Scholar 

  • Iijima, S.: Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)

    Article  Google Scholar 

  • Khademolhosseini, F., Phani, A.S., Nojeh, A., Rajapakse, N.: Nonlocal continuum modeling and molecular dynamics simulation of torsional vibration of carbon nanotubes. IEEE Trans. Nanotechnol. 11, 34–43 (2012)

    Article  Google Scholar 

  • Kimoto, Y., Mori, H., Mikami, T., Akita, S., Nakayama, Y., Higashi, K., Hirai, Y.: Molecular dynamics study of double-walled carbon nanotubes for nano-mechanical manipulation. Jpn. J. Appl. Phys. 44, 1641 (2005)

    Article  Google Scholar 

  • Li, C., Chou, T.-W.: A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487–2499 (2003)

    Article  MATH  Google Scholar 

  • Li, C., Lim, C.W., Yu, J.: Twisting statics and dynamics for circular elastic nanosolids by nonlocal elasticity theory. Acta Mech. Solida Sin. 24, 484–494 (2011)

    Article  Google Scholar 

  • Lim, C.W., Li, C., Yu, J.L.: Free torsional vibration of nanotubes based on nonlocal stress theory. J. Sound Vib. 331, 2798–2808 (2012)

    Article  Google Scholar 

  • Murmu, T., Adhikari, S., Wang, C.Y.: Torsional vibration of carbon nanotube-buckyball systems based on nonlocal elasticity theory. Phys. E Low-Dimens. Syst. Nanostructures. 43, 1276–1280 (2011)

    Article  Google Scholar 

  • Peddieson, J., Buchanan, G.R., McNitt, R.P.: Application of nonlocal continuum models to nanotechnology. Int. J. Eng. Sci 41, 305–312 (2003)

    Article  Google Scholar 

  • Ru, C.Q.: Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium. J. Mech. Phys. Solids 49, 1265–1279 (2001)

    Article  MATH  Google Scholar 

  • Selim, M.M.: Torsional vibration of carbon nanotubes under initial compression stress. Braz J. Phys. 40, 283–287 (2010)

    Article  Google Scholar 

  • Shen, H.S., Zhang, C.L.: Torsional buckling and postbuckling of double-walled carbon nanotubes by nonlocal shear deformable shell model. Compos. Struct. 92, 1073–1084 (2010)

    Article  Google Scholar 

  • Wang, C.Y., Zhang, L.C.: A critical assessment of the elastic properties and effective wall thickness of single-walled carbon nanotubes. Nanotechnology 19, 075705 (2008)

    Article  Google Scholar 

  • Wang, C.Y., Zhao, Y., Adhikari, S., Feng, Y.T.: Vibration of axially strained triple-wall carbon nanotubes. J. Comput. Theor. Nanosci. 7, 2176–2185 (2010)

    Article  Google Scholar 

  • Wang, Q., Liew, K.M.: Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures. Phys. Lett. A 363, 236–242 (2007)

    Article  Google Scholar 

  • Wang, Q., Zhou, G.Y., Lin, K.C.: Scale effect on wave propagation of double-walled carbon nanotubes. Int. J. Solids Struct. 43, 6071–6084 (2006)

    Article  MATH  Google Scholar 

  • Yoon, J., Ru, C.Q., Mioduchowski, A.: Sound wave propagation in multiwall carbon nanotubes. J. Appl. Phys. 93, 4801–4806 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Metin Aydogdu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aydogdu, M., Arda, M. Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity. Int J Mech Mater Des 12, 71–84 (2016). https://doi.org/10.1007/s10999-014-9292-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10999-014-9292-8

Keywords

Navigation