Skip to main content
SpringerLink
Log in

Analytical and numerical investigation into the longitudinal vibration of uniform nanotubes

  • Research Article
  • Published:
Frontiers of Mechanical Engineering Aims and scope Submit manuscript

Abstract

In recent years, prediction of the behaviors of micro and nanostructures is going to be a matter of increasing concern considering their developments and uses in various engineering fields. Since carbon nanotubes show the specific properties such as strength and special electrical behaviors, they have become the main subject in nanotechnology researches. On the grounds that the classical continuum theory cannot accurately predict the mechanical behavior of nanostructures, nonlocal elasticity theory is used to model the nanoscaled systems. In this paper, a nonlocal model for nanorods is developed, and it is used to model the carbon nanotubes with the aim of the investigating into their longitudinal vibration. Following the derivation of governing equation of nanorods and estimation of nondimensional frequencies, the effect of nonlocal parameter and the length of the nanotube on the obtained frequencies are studied. Furthermore, differential quadrature method, as a numerical solution technique, is used to study the effect of these parameters on estimated frequencies for both classical and nonlocal theories.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Iijima S. Helical microtubules of graphitic carbon. Nature, 1991, 354(6348): 56–58

    Article  Google Scholar 

  2. Falvo M R, Clary G J, Taylor R M 2nd, Chi V, Brooks F P Jr, Washburn S, Superfine R. Bending and buckling of carbon nanotubes under large strain. Nature, 1997, 389(6651): 582–584

    Article  Google Scholar 

  3. Darkrim F L, Malbrunot P, Tartaglia G P. Review of hydrogen storage by adsorption in carbon nanotubes. International Journal of Hydrogen Energy, 2002, 27(2): 193–202

    Article  Google Scholar 

  4. Belin T, Epron F. Characterization methods of carbon nanotubes: a review. Materials Science and Engineering B, 2005, 119(2): 105–118

    Article  Google Scholar 

  5. Li C, Thostenson E T, Chou T W. Sensors and actuators based on carbon nanotubes and their composites: a review. Composites Science and Technology, 2008, 68(6): 1227–1249

    Article  Google Scholar 

  6. Han Z, Fina A. Thermal Conductivity of Carbon Nanotubes and their Polymer Nanocomposites: A Review. Progress in Polymer Science, 2011, 36(7): 914–944

    Article  Google Scholar 

  7. Herrera-Herrera A V, González-Curbelo M Á, Hernández-Borges J, Rodríguez-Delgado M A. Carbon nanotubes applications in separation science: a review. Analytica Chimica Acta, 2012, 734: 1–30

    Article  Google Scholar 

  8. Sun C T, Zhang H. Size-dependent elastic moduli of platelike nanomaterials. Journal of Applied Physics, 2003, 93(2): 1212–1218

    Article  Google Scholar 

  9. Eringen A C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 1983, 54(9): 4703–4710

    Article  Google Scholar 

  10. Peddieson J, Buchanan G R, McNitt R P. Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science, 2003, 41(3–5): 305–312

    Article  Google Scholar 

  11. Wang Q, Liew K M. Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures. Physics Letters A, 2007, 363(3): 236–242

    Article  Google Scholar 

  12. Murmu T, Pradhan S C. Thermo-mechanical vibration of a singlewalled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory. Computational Materials Science, 2009, 46(4): 854–859

    Article  Google Scholar 

  13. Pradhan S C, Phadikar J K. Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory. Structural Engineering & mechanics. International Journal (Toronto, Ont.), 2009, 33(2): 193–213

    Google Scholar 

  14. Eringen A C. Nonlocal Continuum Field Theories. New York: Springer-Verlag, 2002

    MATH  Google Scholar 

  15. Reddy J N, Pang S D. Nonlocal continuum theories of beams for the analysis of carbon nanotubes. Journal of Applied Physics, 2008, 103(2): 023511

    Article  Google Scholar 

  16. Bellman R, Kashef B G, Casti J. Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of Computational Physics, 1972, 10(1): 40–52

    Article  MATH  MathSciNet  Google Scholar 

  17. Wang X, Bert C W. A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates. Journal of Sound and Vibration, 1993, 162(3): 566–572

    Article  MATH  Google Scholar 

  18. Shu C, Du H. Implementaion of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates. International Journal of Solids and Structures, 1997, 34(7): 819–835

    Article  MATH  Google Scholar 

  19. Kumar B M, Sujith R I. Exact solutions for the longitudinal vibration of non-uniform rods. Journal of Sound and Vibration, 1997, 207(5): 721–729

    Article  MATH  MathSciNet  Google Scholar 

  20. Sundararaghavan V, Waas A. Non-local continuum modeling of carbon nanotubes: physical interpretation of non-local kernels using atomistic simulations. Journal of the Mechanics and Physics of Solids, 2011, 59(6): 1191–1203

    Article  MATH  MathSciNet  Google Scholar 

  21. Gupta S S, Batra R C. Continuum structures equivalent in normal mode vibrations to single-walled carbon nanotubes. Computational Materials Science, 2008, 43(4): 715–723

    Article  Google Scholar 

  22. Wang Q, Wang C M. The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes. Nanotechnology, 2007, 18(7): 1–4

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, SUNY, Stony Brook, NY, 11794, USA

    Masoud Masoumi

  2. Department of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran

    Mehdi Masoumi

Authors
  1. Masoud Masoumi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mehdi Masoumi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mehdi Masoumi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Masoumi, M., Masoumi, M. Analytical and numerical investigation into the longitudinal vibration of uniform nanotubes. Front. Mech. Eng. 9, 142–149 (2014). https://doi.org/10.1007/s11465-014-0292-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11465-014-0292-z

Keywords

Search

Navigation