of a single-walled carbon nano-tube (SWCNT) conveying
viscous fluid embedded in an elastic medium. They revealed that
the frequency increased as the values of the viscosity parameter increased.
Soltani et al. [15] developed a transverse vibrational model
for a viscous fluid-conveying SWCNT embedded in biological soft
tissue. Their investigation determined that the structural instability
and the associated critical flow velocity could be affected by
the viscosity of the fluid and the nonlocal parameter. Khoddami
et al. [16] studied electro-thermo nonlinear vibration and instability
of embedded double-walled Boron Nitride nano-tubes

(DWBNNTs) conveying viscous fluid based on nonlocal piezoelasticity
theory. They reported that increasing the small scale parameter
decreased the real and imaginary parts of frequency and
critical fluid velocity. Furthermore, they concluded that the effect
of fluid viscosity on the vibration and instability of DWBNNTs
might be ignored. In many recent studies various size-dependent
continuum theories have been developed for vibration and stability
analysis of CNTs conveying fluid. Lee and Chang [17], Zhen
0927-0256/$ – see front matter  2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.commatsci.2013.04.047
⇑ Corresponding author. Tel.: +98 311 391 5248; fax: +98 311 391 2628.

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E-mail addresses: m.mirramezani@me.iut.ac.ir (M. Mirramezani), hrmirdamadi@
cc.iut.ac.ir (H.R. Mirdamadi), ghayour@cc.iut.ac.ir (M. Ghayour).
Computational Materials Science 77 (2013) 161–171
Contents lists available at SciVerse ScienceDirect
Computational Materials Science
journal homepage: www.elsevier.com/locate/commatsci
and Fang [18], Jannesari et al. [19] included the effect of small-size
into equations of motion by using nonlocal elasticity in their studies
and showed that increasing nonlocal parameter had the effect
of a decrease in the critical velocity of fluid. Ke and Wang [20]
investigated vibration and instability of fluid-conveying doublewalled
carbon nano-tubes based on modified couple stress theory.
They showed that the imaginary component of the frequency and
the critical flow velocity of the CNTs increased with an increase in