Assessment of timoshenko beam models for vibrational behavior of single-walled carbon nanotubes using molecular dynamics

Advances in Applied Mathematics and Mechanics

Volumn 1, Issue 1, 2009, Pages 89-106

  Zhang, Y Y ^a   Wang, C M ^a   Tan, V B C ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Carbon nanotubes; Molecular dynamics; Timoshenko beam models; Vibration

Indexed keywords

EID: 77950520777     PISSN: 20700733     EISSN: 20751354     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. M. M. J. Treacy, T. W. Ebbesen and J. M. Gibson, Exceptionally high Young's modulus observed for individual carbon nanotubes, Nature, 381 (1996), pp. 678-680.
2. A. Krishnan, E. Dujardin, T. W. Ebbesen, P. N. Yianilos and M. M. J. Treacy, Young's modulus of single-walled nanotubes, Phys. Rev. B, 58 (1998), pp. 14013-19.
3. P. Poncharal, Z. L. Wang, D. Ugarte and W. A. De Heer, Electrostatic deflection and electromechanical resonators, Science, 283 (1999), pp. 1513-6.
4. Q. Zhao, Z. H. Gan and O. K. Zhuang, Electrochemical sensors based on carbon nanotubes, Electroanalysis, Electroanal., 14 (2002), pp. 1609-13.
5. N. Yao and V. Lordi, Young's modulus of single-walled carbon nanotubes, J. Appl. Phys., 84 (1998), pp. 1939-43.
6. B. I. Yakobson, C. J. Brabec and J. Bernholc, Nanomechanics of carbon tubes: Instabilities beyond linear response, Phys. Rev. Lett., 76 (1996), pp. 2511-2514.
7. C. F. Cornwell and L. T. Wille, Elastic properties of single-walled carbon nanotubes in compression, Solid State, Commun., 101 (1997), pp. 555-558.
8. M. J. Buehler, J. Kong and H. J. Gao, Deformation mechanism of very long single-wall carbon nanotubes subject to compressive loading, J. Eng. Mate. Tech., 126 (2004), pp. 245-249.
9. B. I. Yakobson, M. P. Campbell, C. J. Brabec and J. Bernholc, High strain rate fracture and C-chain unraveling in carbon nanotubes, Comp. Mater. Sci., 8(1997), pp. 341-348.
10. G. X. Cao and X. Chen, Buckling of single-walled carbon nanotubes upon bending: Molecular dynamics simulations and finite element method, Phys. Rev. B, 73 (2006), 155435.
11. Y. Y. Zhang, V. B. C. Tan and C. M. Wang, Effect of chirality on buckling behavior of single-walled carbon nanotubes, J. Appl. Phys., 100 (2006), 074304.
12. Y. Y. Zhang, V. B. C. Tan and C. M. Wang, Effect of strain rate on the buckling behavior of single-and double-walled carbon nanotubes, Carbon, 45 (2007), pp. 514-523.
13. J. Yoon, C. Q. Ru and A. Mioduchowski, Vibration of an embedded multiwall carbon nanotube, Compos. Sci. Technol., 63(2003), pp. 1533-42.
14. A. C. Eringen, Nonlocal polar elastic continua, Int. J. Eng. Sci., 10 (1972), pp. 1-16.
15. Y. Q. Zhang, G. R. Liu and X. Y. Xie, Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity, Phys. Rev. B, 71 (2005), pp. 195404.
16. S. Timoshenko, Vibration Problems in Engineering, Wiley, New York, 1974.
17. C. M. Wang, V. B. C. Tan and Y. Y. Zhang, Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes, J. Sound. Vib., 294 (2006), pp. 1060-1072.
18. C. M. Wang, Y. Y. Zhang and X. Q. He, Vibration of nonlocal Timoshenko beams, Nanotechnology, 18 (2007), pp. 105401.
19. M. C. Ece and M. Aydogdu, Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nanotubes, Acta Mechanica, 190 (2007), pp. 185-195.
20. J. N. Reddy and S. D. Pang, Nonlocal continuum theories of beams for the analysis of carbon nanotubes, J. Appl. Phys., 103 (2008), pp. 023511.
21. C. Y. Li, Single-walled carbon nanotubes as ultrahigh frequency nanomechanical resonators, Phys. Rev. B, 68, 2003 (073405), pp. .
22. C. Y. Li and T. W. Chou, Vibrational behaviors of multiwalled-carbon-nanotube-based nanomechanical resonators, Appl. Phys. Lett., 84 (2003), pp. 121-123.
23. C. Y. Li and T. W. Chou, Strain and pressure sensing using single-walled carbon nanotubes, Nanotechnology, 15 (2004), pp. 1493-1496.
24. G. X. Cao, X. Chen and J. W. Kysar, Thermal vibration and apparent thermal contraction of single-walled carbon nanotubes, J. Mech. Phys. Solids, 54 (2006), pp. 1206-1236.
25. V. Sazonova, Y. Yaish, H. Ustunel, D. Roundy, T. A. Arias and P. L. Mceuen, A tunable carbon nanotube electromechanical oscillator, Nature, 431 (2004), pp. 284.
26. G. X. Cao, X. Chen and J. W. Kysar, Strain sensing of carbon nanotubes: Numerical analysis of the vibrational frequency of deformed sing-wall carbon nanotubes, Phys. Rev. B, 72 (2005,) pp. 195412.
27. D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni and S. B. Sinnott, A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, J. Phys.: Condens. Matter., 14 (2002), pp. 783-802.
28. P. Kim and C. M. Lieber, Nanotube nanotweezers, Science, 286 (1999), pp. 2148-2150.
29. E. S. Snow, P. M. Campbel and J. P. Novak, Single-wall nanotubes atomic force microscope probes, Appl. Phys. Lett., 80 (2002), pp. 2002-2004.
30. D.W. Brenner, Empirical potential for hydrocarbons for use in simulation the chemical vapor deposition of diamond films, Phys. Rev. B, 42 (1990), pp. 3877.
31. O. A. Shenderova, D. W. Brenner, A. Omeltchenko, X. Su, L. H. Yang, Atomistic modeling of the fracture of polycrystalline diamond, Phys. Rev. B, 61, (2000), pp.3877.
32. Y. Y. Zhang, C. M. Wang and V. B. C. Tan, Examining the effects of wall numbers on buckling behavior and mechanical properties of MWCNTs based on MDS results, J. Appl. Phys., 103 (2008), pp. 053505.
33. H. J. C. Brendsen, J. P. M. Postma, W. F. Van Gunsteren, A. Dinola and J. R. Haak, Molecular dynamics with coupling to an external bath, J. Chem. Phys., 81 (1984), pp. 3684-3690.
34. Y. Huang, J. Wu and K. C. Hwang, Thickness of graphene and single-wall carbon nanotubes, Phys. Rev. B, 74 (2006), pp. 245413.
35. D. J. Inman, Engineering Vibration, Prentice Hall, 2000.
36. S. T. Purcell, P. Vincent, C. Journet and V. T. Binh, Tuning of nanotube mechanical resonances by electric field pulling, Phys. Rev. Lett., 89 (2002), pp. 276103.
37. H. Jiang, M. F. Yu, B. Liu and Y. Huang, Intrinsic energy loss mechanisms in a clamped- free carbon nanotube beam oscillator, Phys. Rev. Lett., 93 (2004), pp. 185501.
38. S. S. Rao, Mechanical Vibrations, Prentice-Hall, Englewood Cliffs, NJ, 2002.
39. W. H. Duan, C. M. Wang and Y. Y. Zhang, Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics, J. Appl. Phys., 101 (2007), pp. 024305.
40. P. Hauptmann, Resonant sensors and applications, Sensors and Actuators A-Physical, 26 (1991), pp. 371-377.