Advertisement

Acta Mechanica Solida Sinica

, Volume 27, Issue 6, pp 568–578 | Cite as

Vibration of Fluid-Filled Multi-Walled Carbon Nanotubes Seen via Nonlocal Elasticity Theory

  • Qingtian Deng
  • Zhichun Yang
Article

Abstract

Vibration characteristics of fluid-filled multi-walled carbon nanotubes are studied by using nonlocal elastic Flügge shell model. Vibration governing equations of an N-layer carbon nanotube are formulated by considering the scale effect. In the numerical simulations, the effects of different theories, small-scale, variation of wavenumber, the innermost radius and length of double-walled and triple-walled carbon nanotubes are considered. Vibrational frequencies decrease with an increase of scale coefficient, the innermost radius, length of nanotube and effects of wall number are negligible. The results show that the cut-off frequencies can be influenced by the wall number of nanotubes.

Key Words

vibration multi-walled carbon nanotubes fluid-filled nonlocal elastic theory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Tuzun, R.E., Noid, D.W., Sumpter, B.G. and Merkle, R.C., Dynamics of fluid flow inside carbon nanotubes. Nanotechnology, 1996, 7: 241–246.CrossRefGoogle Scholar
  2. 2.
    Yan, Y., He, X.Q., Zhang, L.X. and Wang, C.M., Dynamic behavior of triple-walled carbon nanotubes conveying fluid. Journal of Sound and Vibration, 2009, 319: 1003–1018.CrossRefGoogle Scholar
  3. 3.
    Yan, Y., Wang, W.Q. and Zhang, L.X., Free vibration of the fluid-filled single-walled carbon nanotube based on a double shell-potential flow model. Applied Mathematical Modelling, 2012, 36: 6146–6153.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Eringen, A.C., Nonlocal Continuum Field Theories. Springer, 2002.Google Scholar
  5. 5.
    Mirramezani, M. and Mirdamadi, H.R., Effects of nonlocal elasticity and Knudsen number on fluid-structure interaction in carbon nanotube conveying fluid. Physica E, 2012, 44: 2005–2015.CrossRefGoogle Scholar
  6. 6.
    Wang, L., Dynamical behavior of double-walled carbon nanotubes conveying fluid accounting for the role of small length scale. Computational Materials Science, 2009, 45: 584–588.CrossRefGoogle Scholar
  7. 7.
    Wang, L., Size-dependent vibration characteristics of fluid-conveying microtubes. Journal of Fluid and Structures, 2010, 26: 675–684.CrossRefGoogle Scholar
  8. 8.
    Xia, W. and Wang, L., Vibration characteristics of fluid-conveying carbon nanotubes with curved longitudinal shape. Computational Materials Science, 2010, 49: 99–103.CrossRefGoogle Scholar
  9. 9.
    Narendar, S. and Gopalakrishnan, S., Terahertz wave characteristics of a single-walled carbon nanotube containing a fluid flow using the nonlocal Timoshenko beam model. Physica E, 2010, 42: 1706–1712.CrossRefGoogle Scholar
  10. 10.
    Yang, Y., Zhang, L.X. and Lim, C.W., Wave propagation in fluid-filled single-walled carbon nanotube on analytically nonlocal Euler-Bernoulli beam model. Journal of Sound and Vibration, 2012, 331: 1567–1579.CrossRefGoogle Scholar
  11. 11.
    Rashidi, V., Mirdamadi, H.R. and Shirani, E., A novel model for vibrations of nanotubes conveying nanoflow. Computational Materials Science, 2012, 51: 347352.CrossRefGoogle Scholar
  12. 12.
    Arani, A.G., Zarei, M.Sh., Amir, S. and Maraghi, Z.K., Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model. Physica B, 2013, 410: 188–196.CrossRefGoogle Scholar
  13. 13.
    Chang, T.P. and Liu, M.F., Small scale effect on flow-induced instability of double-walled carbon nanotubes. European Journal of Mechanics A/Solids, 2011, 30: 992–998.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Rafiei, M., Mohebpour, S.R. and Daneshmand, F., Small-scale effect on the vibration of non-uniform carbon nanotubes conveying fluid and embedded in viscoelastic medium. Physica E, 2012, 44: 1372–1379.CrossRefGoogle Scholar
  15. 15.
    Soltani, P. and Farshidianfar, A., Periodic solution for nonlinear vibration of a fluid-conveying carbon nanotube, based on the nonlocal continuum theory by energy balance method. Applied Mathematical Modeling, 2012, 36: 3712–3724.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P., Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 2002, 39: 2731–2743.CrossRefGoogle Scholar
  17. 17.
    Wang, L., Size-dependent vibration characteristics of fluid-conveying microtubes. Journal of Fluids and Structures, 2010, 26: 675–684.CrossRefGoogle Scholar
  18. 18.
    Ke, L.L. and Wang, Y.S., Flow-induced vibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory. Physica E, 2011, 43: 1031–1039.CrossRefGoogle Scholar
  19. 19.
    Askes, H. and Aifantis, E.C., Gradient elasticity and flexural wave dispersion in carbon nanotbes. Physical Review B, 2009, 80: 195412–195412.CrossRefGoogle Scholar
  20. 20.
    Wang, L., Wave propagation of fluid-conveying single-walled carbon nanotubes via gradient elasticity theory. Computational Materials Science, 2010, 49: 761–766.CrossRefGoogle Scholar
  21. 21.
    Ansari, R., Gholami, R. and Rouhi, H., Vibration analysis of single-walled carbon nanotubes using different gradient elasticity theories. Composite: Part B, 2012, 43: 2985–2989.CrossRefGoogle Scholar
  22. 22.
    Kaviani, F. and Mirdamadi, H.R., Wave propagation analysis of carbon nano-tube conveying fluid including slip boundary condition and strain/inertial gradient theory. Computers and Structures, 2013, 116: 75–87.CrossRefGoogle Scholar
  23. 23.
    Wang, L.F., Guo, W.L. and Hu, H.Y., Flexural wave displacement in multi-walled carbon nanotubes conveying fluids. Acta Mechanica Solida Sinica, 2009, 22(6): 623–629.CrossRefGoogle Scholar
  24. 24.
    Duan, W.H., Wang, C.M. and Zhang, Y.Y., Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics. Journal of Applied Physics, 2007, 101: 02430.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

Authors and Affiliations

  1. 1.School of ScienceChang’an UniversityXi’anChina
  2. 2.School of AeronauticsNorthwestern Polytechnical UniversityXi’anChina

Personalised recommendations