Mechanics of Composite Materials

, Volume 50, Issue 1, pp 95–104 | Cite as

Buckling Analysis of Chiral Single-Walled Carbon Nanotubes by Using the Nonlocal Timoshenko Beam Theory

  • M. Zidour
  • T. H. Daouadji
  • K. H. Benrahou
  • A. Tounsi
  • El A. Adda Bedia
  • L. Hadji
Article
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On the basis of the nonlocal elasticity theory, the Timoshenko beam model is utilized to investigate the elastic buckling of chiral single-walled carbon nanotubes (SWCNTs) under axial compression. Based on the governing equations of the nonlocal Timoshenko beam model, an analytical solution for nonlocal critical buckling loads is obtained. The influence of a nonlocal small-scale coefficient, the vibration mode number, the chirality of SWWCNTs, and their aspect ratio on the nonlocal critical buckling loads is studied and discussed.

Keywords

single-walled carbon nanotubes buckling nonlocal elasticity chirality small scale 
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Notes

Acknowledgments

This research was supported by the Algerian National Agency for the Development of University Research (ANDRU) and the University of Sidi bel Abbes (UDL SBA) in Algeria.

References

  1. 1.
    S. Iijima, “Helical microtubules of graphitic carbon,” Nature, 354, 56-8 (1991).CrossRefGoogle Scholar
  2. 2.
    S. Iijima and T. Ichihashi, “Single-shell carbon nanotubes of 1 nm diameter,” Nature, 363, 603 (1993).CrossRefGoogle Scholar
  3. 3.
    M. S. Dresselhaus and P. Avouris, “Carbon nanotubes: synthesis, structure, properties and application,” Top Appl. Phys., 80, 1-11 (2001).CrossRefGoogle Scholar
  4. 4.
    A. Bachtold, P. Hadley, T. Nakanishi, and D. Cees, “Logic circuits with carbon nanotube transistors,” Science, 294, No. 5545, 1317-1321 (2001).CrossRefGoogle Scholar
  5. 5.
    H. Dai, J. H. Hafner, A. G. Rinzler, D. T. Colbert, and R. E. Smalley, “Nanotubes as nanoprobes in scanning probe microscopy,” Nature, 384, 147-150 (1996).CrossRefGoogle Scholar
  6. 6.
    E. T. Thostenson, Z. Ren, and T. W. Chou, “Advances in the science and technology of carbon nanotubes and their composites (a review), “Compos. Sci. Technol., 61, 1899-1912 (2001).CrossRefGoogle Scholar
  7. 7.
    E. W. Wong, P. E. Sheehan, and C. M. Lieber, “Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes,” Science, 277, 1971-1975 (1997).CrossRefGoogle Scholar
  8. 8.
    C. Q. Ru, “Elastic buckling of single-walled carbon nanotube ropes under high pressure,” Physical Review B, 62, 10405-10408 (2000).CrossRefGoogle Scholar
  9. 9.
    X. Wang and H. Cai, “Effects of initial stress on the non-coaxial resonance of multi-wall carbon nanotubes,” Acta Materialia, 54, 2067-2074 (2006).CrossRefGoogle Scholar
  10. 10.
    J. N. Reddy and S. D. Pang, “Nonlocal continuum theories of beams for the analysis of carbon nanotubes,” J. Appl. Phys., 103, 023511 (2008).CrossRefGoogle Scholar
  11. 11.
    Q. Wang, V. K. Varadan, and S. T. Quek, “Small-scale effect on the elastic buckling of carbon nanotubes with nonlocal continuum models,” Physics Letters A, 357, 130-135 (2006).CrossRefGoogle Scholar
  12. 12.
    K. Amara, A. Tounsi, I. Mechab, and E. A. Adda Bedia, “Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field,”, Appl. Mathematical Modelling, 34, 3933-3942 (2010).CrossRefGoogle Scholar
  13. 13.
    Y. Zhang, G. Liu, and X. Han, “Transverse vibrations of double-walled carbon nanotubes under compressive axial load,” Phys. Lett. A, 340, 258-266 (2005).CrossRefGoogle Scholar
  14. 14.
    A. Benzair, A. Tounsi, A. Besseghier, H. Heireche, N. Moulay, and L. Boumia, “The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory,” J. Physics D, 41, 225404 (2008).CrossRefGoogle Scholar
  15. 15.
    L. Wang and H. Hu, “Flexural wave propagation in single-walled carbon nanotubes,” Phys. Rev. B, 71, 195412 (2005).CrossRefGoogle Scholar
  16. 16.
    Y. G. Hu, K. M. Liew, and Q. Wang, “Nonlocal elastic beam models for flexural wave propagation in double-walled carbon nanotubes,” J. Appl. Phys, 106, 044301 (2009).CrossRefGoogle Scholar
  17. 17.
    T. Murmu and S. C. Pradhan, “Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory,” Comput. Mater. Sci, 46, 854-859 (2009).CrossRefGoogle Scholar
  18. 18.
    T. Murmu and S. C. Pradhan, “Thermal effects on the stability of embedded carbon nanotubes,” Comput. Mater. Sci, 47, 721-726 (2010).CrossRefGoogle Scholar
  19. 19.
    J. Yoon, C. Q. Ru, and A. Mioduchowski, “Vibration of an embedded multiwall carbon nanotubes,” Compos. Sci. Technol, 63, 1533-1545 (2003).CrossRefGoogle Scholar
  20. 20.
    T. Murmu and S. Adhikari, “Nonlocal effects in the longitudinal vibration of double-nanorod systems,” Physica E, 43, 415-422 (2010).CrossRefGoogle Scholar
  21. 21.
    B. I. Yakobson, C. J. Brabec, and J. Bernholc, “Nanomechanics of carbon tubes: instabilities beyond linear response,” Phys. Rev. Lett, 76, 2511-2514 (1996).CrossRefGoogle Scholar
  22. 22.
    C. Thomsen, S. Reich, H. Jantoljak, I. Loa, K. Syassen, M. Burghard, G. S. Duesberg, and S. Roth, “Raman spectroscopy on single- and multi-walled nanotubes under high pressure,” Appl. Phys. A, 69, 309-312 (1999).CrossRefGoogle Scholar
  23. 23.
    J. A. Elliott, J. K. W. Sandler, A. H. Windle, R. J. Young, and S. P. Shaffer, “Collapse of single-wall carbon nanotubes is diameter dependent,” Phys. Rev. Lett, 92, 095501 (2004).CrossRefGoogle Scholar
  24. 24.
    A. R. Ranjbartoreh, A. Ghorbanpour, and B. Soltani, “Double-walled carbon nanotube with surrounding elastic medium under axial pressure,” Physica E, 39, 230-239 (2007).CrossRefGoogle Scholar
  25. 25.
    A. R. Ranjbartoreh, G. X. Wang, A. A. Ghorbanpour, and A. Loghman, “Comparative consideration of axial stability of single- and double-walled carbon nanotube and its inner and outer tubes,” Physica E, 41, 202-208 (2008).CrossRefGoogle Scholar
  26. 26.
    G. M. Odegard, T. S. Gates, L. M. Nicholson, and K. E. Wise, “Equivalent-continuum modeling of nano-structured materials,” Compos. Sci. Technol, 62, 1869-1880 (2002).CrossRefGoogle Scholar
  27. 27.
    H. W. Zhang, L. Wang, and J. B. Wang, “Computer simulation of buckling behaviour of double-walled carbon nanotubes with abnormal interlayer distances,” Comput. Mater. Sci, 39, 664 (2007).CrossRefGoogle Scholar
  28. 28.
    Y. Jin and F. G. Yuan, “Simulation of elastic properties of single-walled carbon nanotubes,” Compos. Sci. Technol, 63, 1507-1515 (2003).CrossRefGoogle Scholar
  29. 29.
    C. F. Cornwell and L. T. Wille, “Elastic properties of single-walled carbon nanotubes in compression,” Solid. State. Commun, 101, 555-558 (1997).CrossRefGoogle Scholar
  30. 30.
    D. W. Brenner, “Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films,” Phys. Rev. B, 42, 9458-9471 (1990).CrossRefGoogle Scholar
  31. 31.
    W. X. Bao, C. C. Zhu, and W. Z. Cui, “Simulation of Young’s modulus of single-walled carbon nanotubes by molecular dynamics,” Physica B, 352, 156-163 (2004).CrossRefGoogle Scholar
  32. 32.
    J. Z. Liu, Q. S. Zheng, and Q. Jiang, “Effect of a rippling mode on resonances of carbon nanotubes,” Phys. Rev. Lett, 86, 4843-4846 (2001).CrossRefGoogle Scholar
  33. 33.
    T. W. Tombler, C. W. Zhou, L. Alexseyev, et al, “Reversible nanotube electro-mechanical characteristics under local probe manipulation,” Nature, 405, 769 (2000).CrossRefGoogle Scholar
  34. 34.
    M. Michele, and R. Marco, “Prediction of Young’s modulus of single-wall carbon nanotubes by molecular mechanics,” Compos. Sci. and Technol., 66, 1597-1605 (2006).CrossRefGoogle Scholar
  35. 35.
    Y. Tokio, “Recent development of carbon nanotube,” Synth. Met, 70, 1511-1518 (1995).CrossRefGoogle Scholar
  36. 36.
    A. C. Eringen, Nonlocal Polar Field Models, Academic Press, New York, (1976).Google Scholar
  37. 37.
    A. C. Eringen, “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” J. Appl. Phys, 54, 4703-4710 (1983).CrossRefGoogle Scholar
  38. 38.
    J. D. Achenbach, Wave Propagation in Elastic Solids, North-Holland Pub. Company, Amsterdam, (1973).Google Scholar
  39. 39.
    Yi-Ze. Wang, Li. Feng-Ming, and K. Kishimoto, “Scale effects on the thermal buckling properties of carbon nanotubes,” Physics Letters A, 374, 4890-4893 (2010).Google Scholar
  40. 40.
    Y. Q. Zhang, G. R. Liu, H. F. Qiang, and G. Y. Li, “Investigation of buckling of double-walled carbon nanotubes embedded in an elastic medium using the energy method,” Int. J. Mech. Sci., 48, 53-61 (2006).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • M. Zidour
    • 1
    • 2
  • T. H. Daouadji
    • 1
    • 2
  • K. H. Benrahou
    • 1
  • A. Tounsi
    • 1
  • El A. Adda Bedia
    • 1
  • L. Hadji
    • 1
    • 2
  1. 1.Laboratoire des Matériaux et HydrologieUniversité de Sidi Bel AbbésSidi Bel AbbésAlgeria
  2. 2.Université Ibn KhaldounTiaretAlgeria

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