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Published in: International Journal of Mechanics and Materials in Design 1/2016

14-12-2014

Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity

Authors: Metin Aydogdu, Mustafa Arda

Published in: International Journal of Mechanics and Materials in Design | Issue 1/2016

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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.

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Literature
go back to reference 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)CrossRef 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)CrossRef
go back to reference Arda, M., Aydogdu, M.: Torsional statics and dynamics of nanotubes embedded in an elastic medium. Compos. Struct. 114, 80–91 (2014)CrossRef Arda, M., Aydogdu, M.: Torsional statics and dynamics of nanotubes embedded in an elastic medium. Compos. Struct. 114, 80–91 (2014)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference Aydogdu, M.: Axial vibration of the nanorods with the nonlocal continuum rod model. Phys. E Low-Dimens. Syst. Nanostructures 41, 861–864 (2009b)CrossRef Aydogdu, M.: Axial vibration of the nanorods with the nonlocal continuum rod model. Phys. E Low-Dimens. Syst. Nanostructures 41, 861–864 (2009b)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference 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.: 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​
go back to reference Aydogdu, M.: Longitudinal wave propagation in multiwalled carbon nanotubes. Compos. Struct. 107, 578–584 (2014b)CrossRef Aydogdu, M.: Longitudinal wave propagation in multiwalled carbon nanotubes. Compos. Struct. 107, 578–584 (2014b)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference Dong, K., Zhu, S.Q., Wang, X.: Wave propagation in multiwall carbon nanotubes embedded in a matrix material. Compos. Struct. 82, 1–9 (2008)CrossRef Dong, K., Zhu, S.Q., Wang, X.: Wave propagation in multiwall carbon nanotubes embedded in a matrix material. Compos. Struct. 82, 1–9 (2008)CrossRef
go back to reference 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) 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)
go back to reference Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)CrossRef Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference Gheshlaghi, B., Hasheminejad, S.M., Abbasion, S.: Size dependent torsional vibration of nanotubes. Phys. E Low-Dimens. Syst. Nanostructures. 43, 45–48 (2010)CrossRef Gheshlaghi, B., Hasheminejad, S.M., Abbasion, S.: Size dependent torsional vibration of nanotubes. Phys. E Low-Dimens. Syst. Nanostructures. 43, 45–48 (2010)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference 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)CrossRefMATH 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)CrossRefMATH
go back to reference Hu, Y.G., Liew, K.M., Wang, Q.: Modeling of vibrations of carbon nanotubes. Procedia Eng. 31, 343–347 (2012)CrossRef Hu, Y.G., Liew, K.M., Wang, Q.: Modeling of vibrations of carbon nanotubes. Procedia Eng. 31, 343–347 (2012)CrossRef
go back to reference 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)CrossRefMATH 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)CrossRefMATH
go back to reference Iijima, S.: Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)CrossRef Iijima, S.: Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference Li, C., Chou, T.-W.: A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487–2499 (2003)CrossRefMATH Li, C., Chou, T.-W.: A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487–2499 (2003)CrossRefMATH
go back to reference 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)CrossRef 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)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference Peddieson, J., Buchanan, G.R., McNitt, R.P.: Application of nonlocal continuum models to nanotechnology. Int. J. Eng. Sci 41, 305–312 (2003)CrossRef Peddieson, J., Buchanan, G.R., McNitt, R.P.: Application of nonlocal continuum models to nanotechnology. Int. J. Eng. Sci 41, 305–312 (2003)CrossRef
go back to reference Ru, C.Q.: Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium. J. Mech. Phys. Solids 49, 1265–1279 (2001)CrossRefMATH Ru, C.Q.: Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium. J. Mech. Phys. Solids 49, 1265–1279 (2001)CrossRefMATH
go back to reference Selim, M.M.: Torsional vibration of carbon nanotubes under initial compression stress. Braz J. Phys. 40, 283–287 (2010)CrossRef Selim, M.M.: Torsional vibration of carbon nanotubes under initial compression stress. Braz J. Phys. 40, 283–287 (2010)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference 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)CrossRef 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)CrossRef
go back to reference 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)CrossRefMATH 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)CrossRefMATH
go back to reference Yoon, J., Ru, C.Q., Mioduchowski, A.: Sound wave propagation in multiwall carbon nanotubes. J. Appl. Phys. 93, 4801–4806 (2003)CrossRef Yoon, J., Ru, C.Q., Mioduchowski, A.: Sound wave propagation in multiwall carbon nanotubes. J. Appl. Phys. 93, 4801–4806 (2003)CrossRef
Metadata
Title
Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity
Authors
Metin Aydogdu
Mustafa Arda
Publication date
14-12-2014
Publisher
Springer Netherlands
Published in
International Journal of Mechanics and Materials in Design / Issue 1/2016
Print ISSN: 1569-1713
Electronic ISSN: 1573-8841
DOI
https://doi.org/10.1007/s10999-014-9292-8

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