205
Views
28
CrossRef citations to date
0
Altmetric
Original Articles

Thermal Effect on Vibration Characteristics of Armchair and Zigzag Single-Walled Carbon Nanotubes Using Nonlocal Parabolic Beam Theory

, , &
Pages 266-272 | Received 11 Feb 2013, Accepted 13 Mar 2013, Published online: 04 Sep 2014

References

  • Iijima, S. (1991) Helical microtubules of graphitic carbon. Nature, 354: 56–58.
  • Dai, H., Hafner, J. H., Rinzler, A. G., Colbert, D. T., and Smalley, R. E. (1996) Nanotubes as nanoprobes in scanning probe microscopy. Nature, 384: 147–150.
  • Falvo, M. R., Clary, G. J., Taylor, R. M., Chi, V., Brooks, F. P., Washburn, S., and Superfine, R. (1997) Bending and buckling of carbon nanotubes under large strain. Nature, 389: 582–584.
  • Kim, P., and Lieber, C. M. (1999) Nanotube nanotweezers. Science, 286: 2148–2150.
  • Kong, J., Zhou, C., Chapline, M. G., Peng, S., Cho, K., and Dai, H. (2000) Nanotube molecular wires as chemical sensors. Science 287: 622–625.
  • Bachtold, A., Hadley, P., Nakanishi, T., and Dekker, C. (2001) Logic circuits with carbon nanotube transistors. Science 294: 1317–1320.
  • Dharap, P. (2004) Nanotube film based on single-wall carbon nanotubes for strain sensing. Nanotechnology 15: 379–382.
  • Avouris, P., Appenzeller, J., Martel, R., and Wind, S. J. (2003) Carbon nanotube electronics. Proc. IEEE 91(11): 1772–1784.
  • Tsukagoshi, K., Yoneya, N., Uryu, S., Aoyagi, Y., Kanda, A., and Ootuka, Y. (2002) Carbon nanotube devices for nanoelectronics. Physica B 323(1–4): 107–114.
  • Baughman, R. H., Zakhidov, A. A., and de Heer, W. A. (2002) Carbon nanotubes–the route toward applications. Science 297: 787–792.
  • Choi, W. B., Bae, E., Kang, D., Chae, S., Cheong, B., and Ko, J. (2004) Aligned carbon nanotubes for nanoelectronics. Nanotechnology 15: S512.
  • Baughman, R. H. (1999) Carbon nanotube actuators. Science 284: 1340–1344.
  • Iijima, S., Brabec, C., Maiti, A., and Bernholc, J. (1996) Structural flexibility of carbon nanotubes. J. Chem. Phys. 104: 2089–2092.
  • Yakobson, B. I., Campbell, M. P., Brabec, C. J., and Bernholc, J. (1997) High strain rate fracture and C-chain unraveling in carbon nanotubes. Comput. Mater. Sci. 8: 341–348.
  • Wang, L., Ni, Q., Li, M., and Qian, Q. (2008) The thermal effect on vibration and instability of carbon nanotubes conveying fluid. Physica E 40: 3179–3182.
  • Ansari, R., Hemmatnezhad, M., and Rezapour, J. (2011) The thermal effect on nonlinear oscillations of carbon nanotubes with arbitrary boundary conditions, Curr. Appl. Phys. 11: 692–697.
  • Ru, C. Q. (2000) Column buckling of multiwalled carbon nanotubes with interlayer radial displacements. J. Phys. Rev. B 62: 16962.
  • Fu, Y. M., Hong, J. W., and Wang, X. Q. (2006) Analysis of nonlinear vibration for embedded carbon nanotubes. J. Sound Vib. 296: 746–756.
  • Venkateswara Rao, G., Meera Saheb, K., and Ranga Janardhan, G. (2006) Fundamental frequency for large amplitude vibrations of uniform Timoshenko beams with central point concentrated mass using coupled displacement field method. J. Sound Vib 298: 221–232.
  • Iijima, S., Brabec, C., Maiti, A., and Bernholc, J. (1996) Structural flexibility of carbon nanotubes. J. Chem. Phys. 104: 2089–2092.
  • Yoon, J., Ru, C. Q., and Mioduchowski, A. (2004) Timoshenko-beam effects on transverse wave propagation in carbon nanotubes. Compos. Part B 35: 87–93.
  • Wang, C. M., Tan, V. B. C., and Zhang, Y. Y. (2006) Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes. J. Sound Vib. 294: 1060–1072.
  • Hsu, J. C., Chang, R. P., and Chang, W. J. (2008) Resonance frequency of chiral single-walled carbon nanotubes using Timoshenko beam theory. Phys. Lett. A 372: 2757–2759.
  • Zhang, Y. Q., Liu, X., and Zhao, J. H. (2008) Influence of temperature change on column buckling of multiwalled carbon nanotubes. Phys. Lett. A 372 (10): 1676–1681.
  • Zhang, Y. Y., Wang, C. M., and Tan, V. B. C. (2009) Assessment of Timoshenko beam models for vibrational behavior of single-walled carbon nanotubes using molecular dynamics. Adv. Appl. Math. Mech. 1(3): 89–106.
  • Yakobson, B. I., Brabec, C. J., and Bernholc, J. (1996) Nanomechanics of carbon tubes: Instabilities beyond linear response. Phys. Rev. Lett. 76: 2511–2514.
  • Ru, C. Q. (2000) Effective bending stiffness of carbon nanotubes. Phys. Rev. B 62: 9973.
  • Ru, C. Q. (2000) Elastic buckling of single-walled carbon nanotube ropes under high pressure. Phys. Rev. B 62: 10405.
  • Li, C., and Chou, T. W. (2003) A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40: 2487–2499.
  • Tserpes, K. I., and Papanikos, P. (2005) Finite element modeling of single-walled carbon nanotubes. Composites Part B 36: 468–477.
  • Eringen, A. C. (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54: 4703–4710.
  • Eringen, A. C. (2002) Nonlocal Continuum Field Theories, Springer: New York.
  • He, X. Q., Kitipornchaia, S., and Liewb, K. M. (2005) Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction. J. Mech. Phys. Solids 53: 303–326.
  • Wang, Q., Varadan, V. K., and Quek, S. T. (2006) Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models. Phys. Lett. A 357: 130–135.
  • Yang, H. K., and Wang, X. (2007) Torsional buckling of multi-wall carbon nanotubes embedded in an elastic medium. Compos. Struct. 77: 182–192.
  • Murmu, T., and Pradhan, S. C. (2009) Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E 41: 1232–1239.
  • Artan, R., and Tepe, S. (2008) The initial values method for buckling of nonlocal bars with application in nanotechnology. Eur. J. Mech. A/Solids 27: 469–477.
  • Pradhan, S. C. (2009) Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory. Phys. Lett. A 373: 4182–4188.
  • Pradhan, S. C., and Murmu, T. (2009) Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics. Comput. Mater. Sci. 47: 268–274.
  • Reddy, J. N. (2007) Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45: 288–307.
  • Wang, Q., Zhou, G. Y., and Lin, K. C. (2006) Scale effect on wave propagation of double-walled carbon nanotubes. Int. J. Solids Struct. 43: 6071–6084.
  • Wang, Q., and Varadan, V. K. (2006) Vibration of carbon nanotubes studied using nonlocal continuum mechanics. Smart Mater. Struct. 15: 659.
  • Lu, P., Lee, H. P., Lu, C., and Zhang, P. Q. (2007) Application of nonlocal beam models for carbon nanotubes. Int. J. Solids Struct. 44: 5289–5300.
  • Wang, Q., and Wang, C. M. (2007) The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes. Nanotechnology 18: 075702.
  • Wang, C. M., Zhang, Y. Y., and He, X. Q. (2007) Vibration of nonlocal Timoshenko beams. Nanotechnology 18: 105.
  • Khosravian, N., and Rafii-Tabar, H. (2008) Computational modelling of a non-viscous fluid flow in a multi-walled carbon nanotube modelled as a Timoshenko beam. Nanotechnology 19: 275.
  • Heireche, H., Tounsi, A., and Benzair, A. (2008) Scale effect on wave propagation of double–walled carbon nanotubes with initial axial loading. Nanotechnology 19: 185703.
  • Heireche, H., Tounsi, A., Benzair, A., Maachou, M., and Adda Bedia, E. A. (2008) Sound Wave Propagation in Single- Walled Carbon Nanotubes using Nonlocal Elasticity. Physica E 40: 2791.
  • Şimşek, M. (2010) Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory. Physica E 43: 182–191.
  • Şimşek, M. (2011) Forced vibration of an embedded single-walled carbon nanotube traversed by a moving load using nonlocal Timoshenko beam theory. Steel Compos. Struct. 11: 59–76.
  • Şimşek, M. (2011) Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle. Comput. Mater. Sci. 50: 2112–2123.
  • Murmu, T., and Pradhan, S. C. (2009) Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model. Physica E 41: 1628–1633.
  • Arash, B., and Ansari, R. (2010) Evaluation of nonlocal parameter in the vibrations of single-walled carbon nanotubes with initial strain. Physica E 42: 2058–2064.
  • Wang, L., and Hu, H. (2005) Flexural wave propagation in single-walled carbon nanotubes. Phys. Rev. B 71: 195412.
  • Mustapha, K. B., and Zhong, Z. W. (2010) The thermo-mechanical vibration of a single-walled carbon nanotube studied using the Bubnov–Galerkin method. Physica E 43: 375–81.
  • Tounsi, A., Benguediab, S., Adda Bedia, E. A., Semmah, A., and Zidour, M. (2013) Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes. Advances in Nano Research 1(3): 1–11.
  • Semmah, A., Tounsi, A., Zidour, M., Heireche, H., and Naceri, M. (2014) Effect of chirality on critical buckling temperature of a zigzag single-walled carbon nanotubes using nonlocal continuum theory. Fullerenes, Nanotubes and Carbon Nanostructures Inpress.
  • Tounsi, A., Semmah, A., and Bousahla, A. A. (2013) Thermal buckling behavior of nanobeam using an efficient higher-order nonlocal beam theory. Journal of Nanomechanics and Micromechanics (ASCE) 3: 37–42.
  • Reddy, J. N. (1984) A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51: 745–752.
  • Wu, Y., Zhang, X., Leung, A. Y. T., and Zhong, W. (2006) An energy-equivalent model on studying the mechanical properties of single-walled carbon nanotubes. Thin-Walled Structures 44: 667–676.
  • Tokio, Y. (1995) Recent development of carbon nanotube. Synth Met 70: 1511–8.
  • Arash, B., and Wang, Q. (2012) A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Comp. Mater. Sci. 51: 303–313.
  • Arash, B., and Ansari, R. (2010) Evaluation of nonlocal parameter in the vibrations of single-walled carbon nanotubes with initial strain. Physica E, 42: 2058–2064.
  • Zhang, Y. Q., Liu, G. R., and Xie, X. Y. (2005) Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity. Phys. Rev. B 71: 195404.
  • Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N., and Boumia, L. (2008) The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. J. Phys. D. 41: 225404.
  • Cornell, W. D., Cieplak, P., and Bayly, C. I. (1995) A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules. J Am Chem Soc 117: 5179–97.
  • Xiao, J. R., Gama, B. A., and Gillespie, J. W. Jr (2005) An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes. Int J Solids Struct 42: 3075–3092.
  • Popov, V. N., Van Doren, V. E., and Balkanski, M. (2000) Elastic properties of single-walled carbon nanotubes. Phys. Rev. B 61: 3078–3084.
  • Jiang, H., Liu, R., Huang, Y., and Hwang, K. C. (2004) Thermal expansion of single wall carbon nanotubes. J. Eng. Mater. Technol. 126: 265–270.
  • Yao, X. H., and Han, Q. (2006) Buckling analysis of multiwalled carbon nanotubes under torsional load coupling with temperature change. J. Eng. Mater. Technol. 128: 419–427.
  • Yao, X. H., and Han, Q. (2007) Investigation of axially compressed buckling of a multi-walled carbon nanotube under temperature field. Compos. Sci. Technol. 67: 125–134.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.