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

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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.

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References

  1. S. Iijima, “Helical microtubules of graphitic carbon,” Nature, 354, 56-8 (1991).

    Article  Google Scholar 

  2. S. Iijima and T. Ichihashi, “Single-shell carbon nanotubes of 1 nm diameter,” Nature, 363, 603 (1993).

    Article  Google Scholar 

  3. M. S. Dresselhaus and P. Avouris, “Carbon nanotubes: synthesis, structure, properties and application,” Top Appl. Phys., 80, 1-11 (2001).

    Article  Google Scholar 

  4. A. Bachtold, P. Hadley, T. Nakanishi, and D. Cees, “Logic circuits with carbon nanotube transistors,” Science, 294, No. 5545, 1317-1321 (2001).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  8. C. Q. Ru, “Elastic buckling of single-walled carbon nanotube ropes under high pressure,” Physical Review B, 62, 10405-10408 (2000).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  15. L. Wang and H. Hu, “Flexural wave propagation in single-walled carbon nanotubes,” Phys. Rev. B, 71, 195412 (2005).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  18. T. Murmu and S. C. Pradhan, “Thermal effects on the stability of embedded carbon nanotubes,” Comput. Mater. Sci, 47, 721-726 (2010).

    Article  Google Scholar 

  19. J. Yoon, C. Q. Ru, and A. Mioduchowski, “Vibration of an embedded multiwall carbon nanotubes,” Compos. Sci. Technol, 63, 1533-1545 (2003).

    Article  Google Scholar 

  20. T. Murmu and S. Adhikari, “Nonlocal effects in the longitudinal vibration of double-nanorod systems,” Physica E, 43, 415-422 (2010).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  28. Y. Jin and F. G. Yuan, “Simulation of elastic properties of single-walled carbon nanotubes,” Compos. Sci. Technol, 63, 1507-1515 (2003).

    Article  Google Scholar 

  29. C. F. Cornwell and L. T. Wille, “Elastic properties of single-walled carbon nanotubes in compression,” Solid. State. Commun, 101, 555-558 (1997).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  33. T. W. Tombler, C. W. Zhou, L. Alexseyev, et al, “Reversible nanotube electro-mechanical characteristics under local probe manipulation,” Nature, 405, 769 (2000).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  35. Y. Tokio, “Recent development of carbon nanotube,” Synth. Met, 70, 1511-1518 (1995).

    Article  Google Scholar 

  36. A. C. Eringen, Nonlocal Polar Field Models, Academic Press, New York, (1976).

    Google Scholar 

  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).

    Article  Google Scholar 

  38. J. D. Achenbach, Wave Propagation in Elastic Solids, North-Holland Pub. Company, Amsterdam, (1973).

    Google Scholar 

  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).

  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).

    Article  Google Scholar 

Download references

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.

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Authors and Affiliations

  1. Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbés, BP 89 Cité Ben M’hidi, 22000, Sidi Bel Abbés, Algeria

    M. Zidour, T. H. Daouadji, K. H. Benrahou, A. Tounsi, El A. Adda Bedia & L. Hadji

  2. Université Ibn Khaldoun, BP 78 Zaaroura, 14000, Tiaret, Algeria

    M. Zidour, T. H. Daouadji & L. Hadji

Authors
  1. M. Zidour
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  2. T. H. Daouadji
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  3. K. H. Benrahou
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  4. A. Tounsi
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  5. El A. Adda Bedia
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  6. L. Hadji
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Correspondence to M. Zidour.

Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 50, No. 1, pp. 133-146, January-February, 2014.

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Zidour, M., Daouadji, T.H., Benrahou, K.H. et al. Buckling Analysis of Chiral Single-Walled Carbon Nanotubes by Using the Nonlocal Timoshenko Beam Theory. Mech Compos Mater 50, 95–104 (2014). https://doi.org/10.1007/s11029-014-9396-0

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  • DOI: https://doi.org/10.1007/s11029-014-9396-0

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