Nonlinear Vibration Analysis of Single-Walled Carbon Nanotube Conveying Fluid in Slip Boundary Conditions Using Variational Iterative Method

Document Type : Research Paper

Author

Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria

Abstract

In this paper, nonlinear dynamic behaviour of the carbon nanotube conveying fluid in slip boundary conditions is studied using the variation iteration method. The developed solutions are used to investigate the effects of various parameters on the nonlinear vibration of the nanotube. The results indicate that an increase in the slip parameter leads to a decrease in the frequency of vibration and the critical velocity, while the natural frequency and the critical fluid velocity increase as the stretching effect increases. Also, as the nonlocal parameter increases, the natural frequency and the critical velocity decreases. The analytical solutions help to have better insights and understand the relationship between the physical quantities of the problem.

Keywords

Main Subjects

  1. Iijima, S. Helical microtubules of graphitic carbon. Nature, London, Vol. 354, no. 6348, pp. 56–58, 1991.
  2. Yoon, G., Ru, C.Q., Mioduchowski, A. Vibration and instability of carbon nanotubes conveying fluid. Journal of Applied Mechanics, Transactions of the ASME, Vol. 65, no. 9, 1326–1336, 2005.
  3. Yan, Y., Wang, W.Q. and Zhang, L.X. Nonlocal effect on axially compressed buckling of triple-walled carbon nanotubes under temperature field.  Journal of Applied Math and Modelling, Vol. 34, pp. 3422–3429, 2010.
  4. Murmu, T., and Pradhan, S. C. Thermo-mechanical vibration of Single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory. Computational Material Science, Vol. 46, pp. 854–859, 2009.
  5. Yang, H. K. and Wang, X. Bending stability of multi-wall carbon nanotubes embedded in an elastic medium. Modeling and Simulation in Materials Sciences and Engineering, Vol. 14, pp. 99–116, 2006.
  6. Yoon, J. Ru, C.Q., Mioduchowski, A. Vibration of an embedded multiwall carbon nanotube. Composites Science and Technology, Vol. 63, no. 11, pp. 1533–1542, 2003.
  7. Lu, P. Lee, H.P., Lu, C. Zhang, P.Q. Application of nonlocal beam models for carbon nanotubes. International Journal of Solids and Structures, Vol. 44, no. 16, pp. 5289–5300, 2007.
  8. Zhang, Y., Liu, G., Han, X. Transverse vibration of double-walled carbon nanotubes under compressive axial load.  Applied Physics Letter A, Vol. 340, no. 1-4, pp. 258–266, 2005.
  9. GhorbanpourArani, M.S. Zarei, M. Mohammadimehr, A. Arefmanesh, M.R. Mozdianfard. The thermal effect on buckling analysis of a DWCNT embedded on the Pasternak foundation”, Physica E, Vol. 43, pp. 1642–1648, 2011.
  10. Sobamowo, M. G. Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation using Galerkin’s method of weighted residual. Applied Thermal Engineering Vol. 99, pp.1316–1330, 2016.
  11. Rafei, M. Ganji, D. D.  Daniali, H., Pashaei. H. The variational iteration method for nonlinear oscillators with discontinuities. J. Sound Vib. Vol. 305, pp. 614–620, 2007.
  12. S. S. Ganji, D. D. Ganji, D. D., H. Ganji, Babazadeh, Karimpour, S.: Variational approach method for nonlinear oscillations of the motion of a rigid rod rocking back and cubic-quintic duffing oscillators. Prog. Electromagn. Res. M Vol. 4, pp. 23–32, 2008.
  13. Liao, S. J. The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems,Ph. D. dissertation, Shanghai Jiao Tong University, 1992
  14. Zhou, J. K.  Differential Transformation and its Applications for Electrical Circuits. Huazhong University Press: Wuhan, China, 1986.
  15. Fernandez, A. On some approximate methods for nonlinear models. Appl Math Comput., Vol. 21., pp. 168-74, 2009
  16. Eringen, A. C. “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves”, Journal of Applied Physics, Vol. 54, no. 9, pp.4703–4710, 1983.
  17. Eringen, A. C. “Linear theory of nonlocal elasticity and dispersion of plane waves”, Inter- national Journal of Engineering Science, Vol. 10, no. (5), pp. 425–435, 1972.
  18. Eringen, A. C. and Edelen, D. G., B.  “On nonlocal elasticity”, International Journal of Engineering Science, Vol. 10(3), pp. 233–248, 1972.
  19. Eringen, A. C. “Nonlocal continuum field theories”, Springer, New York 2002.
  20. Ali-Asgari, M., Mirdamadi, H. R. and Ghayour, M.  Coupled effects of nano-size, stretching, and slip boundary conditions on nonlinear vibrations of nano-tube conveying fluid by the homotopy analysis method.Physica E, Vol. 52, pp. 77–85, 2013.
  21. Shokouhmand, H. Isfahani, A. H. M. and Shirani, E. “Friction and heat transfer coefficient in micro and nano channels with porous media for wide range of Knudsen number”, International Communication in Heat and Mass Transfer, Vol. 37, pp. 890-894, 2010.