Longitudinal Wave Propagation Analysis of Stationary and Axially Moving Carbon Nanotubes Conveying Fluid


1 MSc Student, Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch, Isfahan, Iran.

2 Associated Prof., Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch, Isfahan, Iran

3 Assistant Prof., Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch, Isfahan, Iran


In this study, the effect of small-scale of both nanostructure and nano-fluid flowing through it on the natural frequency and longitudinal wave propagation are investigated. Here, the stationary and axially moving single-walled carbon nanotube conveying fluid are studied. The boundary conditions for the stationary nanotube is considering clamped-clamped and pined-pined and for the axially moving SWCNT is simply supported end where the left-end has been restrained. To apply the nano-scale for fluid the Knudsen number and to apply the structure the nano-rod model and nonlocal theory are utilized. Next, using the approximate Galerkin method the governing equation of motion is discretized and solved. In addition, the ratio of the natural frequency and phase velocity to the wave number and also the influence of velocities of flowing fluid and axially moving structure on the natural frequency would be studied. It can be shown that the natural frequency and wave propagation velocity are depending to the nano-scale of the structure and fluid flowing through it. So that, by increasing the nonlocal parameter, the natural frequency is decreased and by increasing the Knudsen number the system frequency is increased hence, leading to a bigger wave


[1] Iijima S., Helical microtubules of graphitic carbon, Nature, 345, 1991, pp. 56-58.

[2] Hummer, J. C., Rasaiah J. C., Noworyta J. P., Water conduction through the hydrophobic channel of a carbon nanotube, Nature, Vol 414, 2001, pp 188-190.

[3] Craighead H.G., Nanoelectromechanical Systems, Science, Vol 290, 2000, pp 1532-1535.

[4] Yoon J., Ru C.Q., Mioduchowski A., Vibration and instability of carbon nanotubes conveying fluid, Composites Science and Technology, Vol 65, 2005, pp 1326-1336.

[5] Wang L., Ni Q., Li M., A reappraisal of the computational modeling of carbon nanotubes conveying viscous fluid, Cumputational Materials Science,Vol 44, 2008, p 821.

[6] Wang Q., Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied Physics, Vol 98, 2005, p 124301.

[7] Reddy J.N., Nonlocal continuum theories of beams for the analysis of carbon nanotubes, Journal of Applied Physics, Vol 103, 2008, p 023511.

[8] Rashidi V., Mirdamadi H.R., Shirani E., A Novel Model for Vibrations of Nanotubes Conveying Nanoflow, Computational Materials Science, 51, Vol. 1, 2012, pp 347–352.

[9] Kaviani F., Mirdamadi H.R., Wave propagation analysis of carbon nano-tube conveying fluid including slip boundary condition and strain/inertia gradient theory, Computers and Structures, Vol 116, 2013, pp 75-87.

[10] Aydogdu M., Longitudinal wave propagation in multi-walled carbon nanotubes, Composite Structures, Vol 107, 2014, pp 578–584.

[11] Eringen A.C., Nonlocal continuum field theories, Springer-Verlag Inc, New York, 2002.

[12] Paidoussis M.P., Price S.J., de Langre E., Fluid-Structure Interactions: Cross-Flow-Induced Instabilities, Cambridge University Press, New York, USA, 2005.

[13] اویسی س، تحلیل انتشار موج تنش و ارتعاشات در نانولوله‏های کربنی حاوی سیال براساس تئوری غیرمحلی، دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی واحد خمینی شهر، 1393.