Abstract
An analytical method to investigate wave propagation in single- and double- walled carbon nanotubes under initial compression stress is presented. The nanotube structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. The governing equations are derived based on Flügge equations of motion. Frequency equations of wave propagation in single and double wall carbon nanotubes are described through the effects of initial compression stress and van der Waals force. To show the effects of Initial compression stress on the wave propagation in nanotubes, the symmetrical mode can be analyzed based on the present elastic continuum model. It is shown that the wave speed are sensitive to the compression stress especially for the lower frequencies.
Similar content being viewed by others
References
S. Iijima, Nature 354, 56 (1991)
R.H. Baughman, A.A. Zakhidov, W.A. de Heer, Nature 414, 142 (2002)
D. Qian, J.G. Wagner, W.K. Liu, M.F. Yu, R.S. Ruoff, Appl. Mech. Rev. 55, 495 (2002)
Q. Wang, V.K. Varadan, Smart Mater. Struct. 14, 281 (2005)
D. Baowan, J.M. Hill, Int. J. Solids Struct. 44, 8297 (2007)
C. Li, T.-W. Chou, Int. J. Solids Struct. 40, 2487 (2003)
L. Shen, J. Li, Phys. Rev. B 69, 045414 (2004)
L. Shen, J. Li, Phys. Rev. B 71, 035412 (2005)
Q. Wang, T. Hu, G. Chen, Q. Jiang, Phys. Rev. B 71, 045403 (2005)
J. Yoon, C.Q. Ru, A. Mioduchowski, J. Appl. Phys. 93, 04801 (2003)
J. Yoon, C.Q. Ru, A. Mioduchowski, Compos. Sci. Technol. 63, 1533 (2003)
Q. Wang, V.K. Varadan, Int. J. Solids Struct. 43, 254 (2006)
T. Natsuki, T. Hayashi, M. Endo, J. Appl. Phys. 97, 044307 (2005)
T. Natsuki, Q.-Q. Ni, J. Appl. Phys. 101, 034319 (2007)
T. Natsuki, Q.-Q. Ni, M. Endo, Appl. Phys. A 90, 441 (2008)
K. Dong, B.Y. Liu, X. Wang, Comput. Mater. Sci. 42, 139 (2008)
K. Dong, S.Q. Zhu, X. Wang, Compos. Struct. 82, 1 (2008)
T. Natsuki, Q.-Q. Ni, T. Hayashi, M. Endo, J. Appl. Phys. 103, 094312 (2008)
Y. Zhang, G. Liu, X. Han, Phys. Lett. A 340, 258 (2005)
H. Cai, X. Wang, Nanotechnology 17, 45 (2006)
X. Wang, H. Cai, Acta Mater. 54, 2067 (2006)
K. Liu, C. Sun, Solid State Communication 143, 202 (2007)
X. Chen, X. Wang, Phys. Scr. 78, 015601 (2008)
M.M.J. Treacy, Ebbesen, J.M. Gibson, Nature ( London) 381, 678 (1996)
M.F. Yu, O. Lourie, M.J. Dyer, K. Moloni, T.F. Kelly, R.S. Ruoff, Science 287, 637 (2000)
D. Kahn, K.W. Kim, M.A. Stroscio, J. Appl. Phys. 89, 05107 (2001)
C.Y. Wang, C.Q. Ru, A. Mioduchowski, Phys. Rev. B 72, 075414 (2005)
T. Natsuki, M. Endo, H. Tsuda, J. Appl. Phys. 99, 034311 (2006)
W. Flügge, Statik und Dynamik der Schalen (Berlin, Springer, 1934)
C.Q. Ru, Phys. Rev. B 62, 16962 (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Selim, M., Abe, S. & Harigaya, K. Effects of initial compression stress on wave propagation in carbon nanotubes. Eur. Phys. J. B 69, 523–528 (2009). https://doi.org/10.1140/epjb/e2009-00184-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2009-00184-5