Title of the article

SIMULATION OF FREE VIBRATIONS OF MULTI-WALLED CARBON NANOTUBE BASED ON NON-LOCAL THEORY OF THIN ELASTIC ORTHOTROPIC SHELLS

Authors

Mikhasev G.I., Doctor of Physical and Mathematical Sciences, Professor, Head of the Bio- and Nanomechanics Department, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.
Sheiko A.N., Master's student, Bio- and Nanomechanics Department, Belarusian State University, Minsk, Republic of Belarus

In the section  
Year 2013 Issue 4 Pages 60-64
Type of article RAR Index UDK 539.3 Index BBK  
Abstract

The mathematical model of multi-walled carbon nanotube embedded in an elastic matrix is proposed. The effect of the surrounding elastic medium are considered using the Winkler-type spring constant. The tube may be prestressed by external forces. The Flugge type equations for orthotropic cylindrical shells, including the initial membrane hoop and axial stresses, are used as the governing ones. The constitutive equations are formulated by considering the small-scale effects. The dependence of natural frequencies upon a number of waves in the longitudinal direction, tube length and the motion directions of walls as well is studied.

Keywords multi-walled carbon nanotube, nonlocal theory of elasticity, van der Waals forces, equations of motion, free vibrations
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Bibliography
  • Xu M. Free transverse vibrations of nano-to-micron scale beams. Proc. R. Soc. Lond. A., 2006, vol. 462, pр. 2977-2995.
  • Peddieson J., Buchanan R., McNitt R.P. Application of nonlocal continuum models to nanotechnology. Int. J. Eng. Sci., 2003, vol. 41, pр. 305-312.
  • Harik V.M. Ranges of Applicability for the Continuum Beam Model in the Mechanics of Carbon Nanotubes and Nanorows. Solid State Commum., 2001, vol. 120, pp. 331-335.
  • Sun C.T., Zhang H. Size-dependent elastic moduli of platelike nanomaterials. J. Appl. Phys, 2003, vol. 93, pp. 1212-1218.
  • Eringen A.C. Nonlocal continuum field theories. New-York, Springer, 2002.
  • Chang T., Geng J., Guo X. Prediction of chirality- and size-dependent elastic properties of single-walled carbon nanotubes via a molecular mechanics model. Proc. R. Soc. A., 2006, vol. 462, pp. 2523-2540.
  • Wang L. [et al.]. Size dependence of the thin-shell model for carbon nanotubes. Physical Review Letters, 2005, vol. 95, pp. 105501-105504.
  • Ru C.Q. Chirality-dependent mechanical behavior of carbon nanotubes based on an anisitropic elastic shell model. Math. Mech. Solids, 2009, vol. 14, pp. 88-101.
  • Fazelzadeh S.A., Ghavanloo E. Nonlocal anisotropic elastic sshell model for vibrations of single-walled carbon nanotubes with arbitrary chirality. Composite Structures, 2012, vol. 94(3), pp. 1016-1022.
  • Peng J. [et al.]. Can a single-wall carbon nanotube be modeled as a thin shell. Journal of the Mechanics and Physics of Solids, 2008, vol. 56, pp. 2213-2224.
  • Mikhasev G.I. Uravnenija dvizhenija mnogostennoj uglerodnoj nanotrubki, osnovannye na nelokal'noj teorii ortotropnyh obolochek [The equations of motion of multi-walled carbon nanotubes based on nonlocal theory of orthotropic shells]. Dokl. NAN Belarusi [NAS of Belarus report], 2011, vol. 55, no. 6, pp. 119-123.
  • Mikhasev G. On localized modes of free vibrations of singlewalled carbon nanotubes embedded in nonhomogeneous elastic medium. Z. Angew. Math. Mech., 2013. DOI 10.1002/zamm.201200140.
  • Hernandez E. [et al.]. Elastic properties of C and BxCyNz composite nanotubes. Phys. Rev. Lett., 1998, vol. 80, pp. 4502-4505.
  • Popov V.N., Van Doren V.E., Balkanski M. Elastic properties of single-walled carbon nanotubes. Phys. Rev. B61, 2000, pp. 3078-3084.
  • Chang T. A molecular based anisotropic shell model for single-walled carbon nanotubes. J. Mech. Phys. Solids, 2010, vol. 58, pp. 1422-1433.
  • Flugge W. Stattik und Dynamik der Schalen. Berlin, Springer. 1934.
  • Usuki T., Yogo K. Beam equations for multi-walled carbon nanotubes derived from Flugge shell theory. Proc. R. Soc. A., 2009, vol. 465, pp. 1199-1226.
  • Ambarcumjan S.A. Obshhaja teorija anizotropnyh obolochek [General theory of anisotropic shells]. Moscow, Nauka. 1974. 448 p.
  • Mikhasev G.I., Tovstik P.E. Lokalizovannye kolebanija i volny v tonkih obolochkah [Local oscillations and waves in thin shells]. Asimptoticheskie metody [Asymptotic methods]. Moscow, FIZMATLIT, 2009. 292 p.