In this paper, thermo–mechanical vibration analysis of carbon nanocones (CNCs) conveying fluid based on nonlocal elasticity theory is investigated. The governing equations are developed using Hamilton’s principle and a general eigenvalue problem is obtained by discretizing the resulting equations using the finite element method. In this paper, the non-uniform cross-section Timoshenko beam theory is utilized and the influences of apex angle, top radius, length, temperature change, thickness, small-scale parameter, and flow direction are surveyed on the fundamental frequency and the critical flow velocity associated with an instability condition. The results of the present study have been validated with available results in the literature. It is found that the apex angle has a considerable effect on the instability behavior of CNCs. Also, critical flow velocity is reduced by increasing the small-scale parameter. Furthermore, the direction of fluid has a crucial effect on both the fundamental frequency and critical flow velocity.
AjimaKYudasakaMMurakamiTMaigneAShibaIijimaS (2005) Carbon nanohorns as anticancer drug carriers. Molecular Pharmaceutics2(6): 475–480.
2.
AnsariRGholamiRRouhiH (2012) Vibration analysis of single-walled carbon nanotubes using different gradient elasticity theories. Composites: Part B43(8): 2985–2989.
3.
AskesHAifantisEC (2009) Gradient elasticity and flexural wave dispersion in carbon nanotubes. Physical Review B80(19): 195412–195420.
4.
BatraRCGuptaSS (2008) Wall thickness and radial breathing modes of single-walled carbon nanotubes. Journal of Applied Mechanics75(6): 061010–061011.
5.
CowperGR (1966) The shear coefficient in Timoshenko’s beam theory. Journal of Applied Mechanics33(2): 335–340.
6.
DockendorfCPRPoulikakosDHwangGNelsonBJGrigoropoulosCP (2007) Maskless writing of a flexible nanoscale transistor with Au-contacted carbon nanotube electrodes. Applied Physics Letters91(24): 243118–243120.
7.
EltaherMAAlshorbagyAEMahmoudFF (2013) Vibration analysis of Euler–Bernoulli nanobeams by using finite element method. Applied Mathematical Modeling37(7): 4787–4797.
8.
EringenAC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics54(9): 4703–4710.
9.
Farshidianfar A, Qassabi AA and Farshidianfar MH (2011) Transverse vibration of fluid conveying carbon nanotubes embedded in two-parameter elastic medium. In Proceedings of 18th International Congress on Sound and Vibration, Rio de Janeiro, Brazil, July 10–14.
10.
GeMSattlerK (1994) Observation of fullerene cones. Chemical Physics Letters220(3–5): 192–196.
11.
GhavanlooEFazelzadehSA (2011) Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid. Physica E44(1): 17–24.
12.
Ghorbanpour AraniAKolahchiRHaghighiSMosallaie BarzokiAA (2013) Nonlinear viscose flow induced nonlocal vibration and instability of embedded DWCNC via DQM. Journal of Mechanical Science and Technology27(1): 21–31.
13.
GuoSQYangSP (2012) Axial vibration analysis of nanocones based on nonlocal elasticity theory. Acta Mechanica Sinica28(3): 801–807.
14.
Hannoyer MJ (1977) Instabilities of slender, tapered tubular beams induced by internal and external axial flow. Ph.D. Thesis, Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada. pp.39–44.
IijimaS (1991) Helical microtubules of graphitic carbon. Nature354(6348): 56–58.
17.
KeLLWangYS (2011) Flow-induced vibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory. Physica E43(5): 1031–1039.
18.
KimS (2006) CNT sensors for detecting gases with low adsorption energy by ionization. Sensors6(5): 503–513.
19.
KrishnanADujardinETreacyMMJHugdahlJLynumSEbbesenTW (1997) Graphitic cones and the nucleation of curved carbon surfaces. Nature388(6641): 451–454.
LeeHLChangWJ (2008) Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory. Journal of Applied Physics103(2): 024302.
22.
LeeJHLeeBS (2012) Modal analysis of carbon nanotubes and nanocones using FEM. Computational Materials Science51(1): 30–42.
23.
LiangFSuY (2013) Stability analysis of a single-walled carbon nanotube conveying pulsating and viscous fluid with nonlocal effect. Applied Mathematical Modelling37(10–11): 6821–6828.
24.
MustaphaKBZhongZW (2010) Stability of single-walled carbon nanotubes and single-walled carbon nanocones under self-weight and an axial tip force. Computational Materials Science50(1): 742–751.
25.
NaessSNElgsaeterAHelgesenGKnudsenKD (2009) Carbon nanocones: wall structure and morphology. Science and Technology of Advanced Materials10(6): 65002–65005.
26.
PaidoussisMP (1998) Fluid-Structure Interactions: Slender Structures and Axial Flow, London: Academic Press, pp. 199–203.
27.
PaidoussisMPLaitheirBE (1976) Dynamics of Timoshenko beams conveying fluid. Journal of Mechanical Engineering Science18(4): 210–220.
28.
RafieiMMohebpourSRDaneshmandF (2012) Small-scale effect on the vibration of non-uniform carbon nanotubes conveying fluid and embedded in viscoelastic medium. Physica E44(7–8): 1372–1379.
29.
ReddyJN (2006) An Introduction to the Finite Element Method, New York: McGraw Hill, pp. 261–270.
30.
ReddyJNPangSD (2008) Nonlocal continuum theories of beams for the analysis of carbon nanotubes. Journal of Applied Physics103(2): 23511–23516.
31.
SoltaniPTaherianMMFarshidianfarA (2010) Vibration and instability of a viscous-fluid conveying single-walled carbon nanotube embedded in a visco-elastic medium. Journal of Physics D: Applied Physics43(42): 425401–425408.
32.
TianYWeiREichhornVFatikowSShirinzadehBZhangD (2012) Buckling and postbuckling behavior of carbon nanocones. Nanoscience and Nanotechnology Letters4(8): 766–774.
33.
WangL (2009) Vibration and instability analysis of tubular nano- and micro-beams conveying fluid using nonlocal elastic theory. Physica E41(10): 1835–1840.
34.
WangL (2010a) Wave propagation of fluid-conveying single-walled carbon nanotubes via gradient elasticity theory. Computational Materials Science49(4): 761–766.
35.
WangL (2010b) Vibration analysis of fluid conveying nanotubes with consideration of surface effects. Physica E43(1): 437–439.
36.
WeiCDeepakS (2004) Nanomechanics of carbon nanofibers: structural and elastic properties. Applied Physics Letters85(12): 2208–2210.
37.
YanJWLiewKMHeLH (2012) Predicting mechanical properties of single-walled carbon nanocones using a higher-order gradient continuum computational framework. Composite Structures94(11): 3271–3277.
38.
YangYZhangLLimCW (2012) Wave propagation in fluid-filled single walled carbon nanotube on analytically nonlocal Euler-Bernoulli beam model. Journal of Sound and Vibration331(7): 1567–1579.
39.
YaoXHanQ (2006) Buckling analysis of multiwalled carbon nanotubes under torsional load coupling with temperature change. Journal of Engineering Materials and Technology128(3): 419–427.
40.
YoonJRuCQMioduchowskiA (2005) Vibration and instability of carbon nanotubes conveying fluid. Composites Science and Technology65(9): 1326–1336.
41.
YoshitakeYTShimakawaYKuroshimaS (2002) Preparation of fine platinum catalyst supported on single-wall carbon nanohorns for fuel cell application. Physica B323(1–4): 124–126.
42.
ZhangYQLiuXZhaoJH (2008) Influence of temperature change on column buckling of multi-walled carbon nanotubes. Physics Letters A372(10): 1676–1681.
