Transverse vibration and instability of fluid conveying triple-walled carbon nanotubes based on strain-inertia gradient theory


1 Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch, 84175/119, Khomeinishahr, Isfahan, Iran

2 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran


In this paper, the transverse vibration of a triple-walled carbon nanotube (TWCNT) conveying fluid flow is studied based on the strain/inertia gradient theory with van der Waals interaction taken into consideration. The nanotube is modelled using Euler-Bernoulli beam model and the Galerkin’s method is employed to obtain the CNT complex valued Eigen-frequencies. The effects of the fluid flow thorough the innermost tube and the van der Waals force interaction between any two walls on the instability of the nanotube are studied. In addition, the effects of the nano-flow size, the characteristic lengths and the aspect ratio on the critical flow velocities are investigated. Results indicate that due to the fluid flow the nanotube natural frequencies decrease. By considering the size effect of the fluid flow, frequencies decrease more rapidly causing reduction of the stability region. Moreover, it is shown that the length of the nanotube can play an important role in the vibration response.


Main Subjects

[1] G. Hummer, J.C. Rasaiah, J.P. Noworyta, Water conduction through the hydrophobic channel of a carbon nanotube, Nature, 414 (2001) 188-190.

[2] D. Mattia, Y. Gogotsi, Review: static and dynamic behavior of liquids inside carbon nanotubes, Microfluid Nanofluid, 5 (2008) 289-305.

[3] C.N.R. Rao, A.K. Cheetham, Science and technology of nanomaterials: current status and future prospects, Journal of Materials Chemistry, 11 (2001) 2887-2894.

[4] K. Dong, B.Y. Liu, X. Wang, Wave propagation in fluid-filled multi-walled carbon nanotubes embedded in elastic matrix, Computational Materials Science, 42 (2008) 139-148.

[5] W.J. Chang, H.L. Lee, Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model, Physics Letters A, 373 (2009) 982-985.

[6] Y. Yan, W.Q. Wang, J.M. Zhang, L.X. Zhang, Free vibration of the water-filled single-walled carbon nanotubes, Procedia Engineering, 31 (2012) 647-653.

[7] M. Rafiei, S.R. Mohebpour, F. Daneshmand, Small-scale effect on the vibration of non-uniform carbon nanotubes conveying fluid and embedded in viscoelastic medium, Physica E: Low-dimensional Systems and Nanostructures, 44 (2012) 1372-1379.

[8] L. Wang, Vibration analysis of fluid-conveying nanotubes with consideration of surface effects, Physica E: Low-dimensional Systems and Nanostructures, 43 (2010) 437-439.

[9] J. Yoon, C.Q. Ru, A. Mioduchowski, Sound wave propagation in multiwall carbon nanotubes, Journal of Applied Physics, 93 (2003) 4801-4806.

[10] Y. Yan, W.Q. Wang, L.X. Zhang, Dynamical behaviors of fluid-conveyed multi-walled carbon nanotubes, Applied Mathematical Modelling, 33 (2009) 1430-1440.

[11] V. Rashidi, H.R. Mirdamadi, E. Shirani, A novel model for vibrations of nanotubes conveying nanoflow, Computational Materials Science, 51 (2012) 347-352.

[12] H. Askes, E.C. Aifantis, Gradient elasticity and flexural wave dispersion in carbon nanotubes, Physical Review B, 80 (2009) 195412.

[13] M. Mirramezani, H.R. Mirdamadi, M. Ghayour, Innovative coupled fluid–structure interaction model for carbon nano-tubes conveying fluid by considering the size effects of nano-flow and nano-structure, Computational Materials Science, 77 (2013) 161-171.

[14] W.G. Polard, R.D. Present, On gaseous self-diffusion in long capillary tubes, Physical Review, 73 (1948) 762.

[15] M.P. Paidoussis, Fluid-structure interactions: slender structures and axial flow, Academic press, 1998.