In the present research, vibration and instability analysis of a viscoelastic Y-shaped single-walled carbon nanotube conveying fluid is carried out. The surrounding viscoelastic medium is simulated by various models such as Kelvin–Voigt, Maxwell, standard linear solid Reissner, and nonlocal models. The size effects are considered based on modified couple stress theory. In order to achieve more accurate results, fourth-order beam theory is utilized. Surface stress effects are considered based on Gurtin–Murdoch theory. In addition, effects of the asymmetry of Y-shaped single-walled carbon nanotube are also taken into account. Regarding fluid–structure interaction, the equations of motion as well as boundary conditions are derived using Hamilton’s principle and solved by means of hybrid analytical–numerical method. Regarding the temperature changes on visco-Pasternak foundation, the effects of different surrounding medium models are discussed in detail. The overall results indicated that the stability and vibration characteristics of Y-shaped single-walled carbon nanotube conveying fluid are strongly dependent on damping coefficient. The results of this work are hoped to be useful in design and manufacturing of nanodevices where Y-shaped nanotubes act as a basic element.
SattlerKD. Handbook of nanophysics: nanotubes and nanowires, United States: CRC Press, 2010.
2.
FilizSAydogduM. Axial vibration of carbon nanotube heterojunctions using nonlocal elasticity. Comput Mater Sci2010; 49: 619–627.
3.
LisenkovSVPonomarevaIVChernozatonskiiLA. Basic configuration of a single-wall carbon nanotube Y junction of D 3h symmetry: structure and classification. Phys Solid State2004; 46: 1577–1582.
4.
BiróLPHorváthZEMárkGI. Carbon nanotube Y junctions: growth and properties. Diam Relat Mater2004; 13: 241–249.
5.
BandaruPDaraioCJinS. Novel electrical switching behaviour and logic in carbon nanotube Y-junctions. Nat Mater2005; 4: 663–666.
ZhangJLuJXiaQ. Research on the valveless piezoelectric pump with Y-shape pipes. Front Mech Eng China2007; 2: 144–151.
8.
PakCHHongSCSYunYSY. On the vibrations of three-dimensional angled piping systems conveying fluid. KSME J1991; 5: 86–92.
9.
HellumAMukherjeeRHullAJ. Flutter instability of a fluid-conveying fluid-immersed pipe affixed to a rigid body. J Fluids Struct2011; 27: 1086–1096.
10.
LiuGLiSLiY. Vibration analysis of pipelines with arbitrary branches by absorbing transfer matrix method. J Sound Vib2013; 332: 6519–6536.
11.
KavianiFMirdamadiHR. Influence of Knudsen number on fluid viscosity for analysis of divergence in fluid conveying nano-tubes. Comput Mater Sci2012; 61: 270–277.
12.
MirramezaniMMirdamadiHR. The effect of Knudsen-dependent flow velocity on vibration of a nano-pipe conveying fluid. Arch Appl Mech2012; 82: 879–890.
13.
Ghorbanpour AraniAHaghparastEKhoddami MaraghiZ. Nonlocal vibration and instability analysis of embedded DWCNT conveying fluid under magnetic field with slip conditions consideration. Proc IMechE, Part C: J Mechanical Engineering Science2015; 229: 349–363.
14.
Sheikholeslami M, Mustafa MT and Domiri Ganji D. Effect of Lorentz forces on forced-convection nanofluid flow over a stretched surface. Particuology 2015, in press.
15.
HayatTWangYSiddiquiAM. Peristaltic transport of a third-order fluid in a circular cylindrical tube. Math Models Methods Appl Sci2002; 12: 1691–1706.
16.
NoreenSAhmedBHayatT. Mixed convection flow of nanofluid in presence of an inclined magnetic field. PLoS One2013; 8: 1–13.
17.
AvramidisIEMorfidisK. Bending of beams on three-parameter elastic foundation. Int J Solids Struct2006; 43: 357–375.
18.
ChallamelNMeftahSBernardF. Buckling of elastic beams on non-local foundation: a revisiting of Reissner model. Mech Res Commun2010; 37: 472–475.
19.
Qian D and Zhou Z. Visco-elastic properties of carbon nanotubes and their relation to damping. In: Time dependent constitutive behavior and fracture/failure processes, conference proceedings of the society for experimental mechanics series, 2011, pp.259–265. New York: Springer.
20.
ShenHS. A novel technique for nonlinear analysis of beams on two-parameter elastic foundations. Int J Struct Stab Dyn2011; 11: 999–1014.
21.
BesseghierATounsiAHouariMSA. Thermal effect on wave propagation in double-walled carbon nanotubes embedded in a polymer matrix using nonlocal elasticity. Phys E Low-Dimens Syst Nanostruct2011; 43: 1379–1386.
22.
FriswellMIAdhikariSLeiY. Vibration analysis of beams with nonlocal foundations using the finite element method. Int J Numer Methods Eng2007; 71: 1365–1386.
23.
FaillaGSantiniAZingalesM. A non-local two-dimensional foundation model. Arch Appl Mech2012; 83: 253–272.
24.
Kazemi-LariMAFazelzadehSAGhavanlooE. Non-conservative instability of cantilever carbon nanotubes resting on viscoelastic foundation. Phys E Low-Dimens Syst Nanostruct2012; 44: 1623–1630.
25.
ParkJHSinnottSBAluruNR. Ion separation using a Y-junction carbon nanotube. Nanotechnology2006; 17: 895–900.
26.
Ghorbanpour AraniAZareiMSh. Nonlinear nonlocal vibration of an embedded viscoelastic Y-SWCNT conveying viscous fluid under magnetic field using homotopy analysis method. J Solid Mech2014; 6: 173–193.
27.
Ghorbanpour AraniAZareiM.Sh. Nonlocal vibration of Y-shaped CNT conveying nanomagnetic viscous fluid under magnetic field. Ain Shams Eng J2015; 6: 565–575.
28.
WunderlichWPilkeyWD. Mechanics of structures: variational and computational methods, United States: CRC Press, 2002.
29.
YangFChongCMLamDCC. Couple stress based strain gradient theory for elasticity. Int J Solids Struct2002; 39: 2731–2743.
30.
Ghorbanpour AraniAAmirS. Electro-thermal vibration of visco-elastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory. Phys B Condens Matter2013; 419: 1–6.
31.
GurtinMEMMurdochAI. A continuum theory of elastic material surfaces. Arch Ration Mech Anal1975; 57: 291–323.
32.
Ghorbanpour AraniARoudbariMA. Surface stress, initial stress and Knudsen-dependent flow velocity effects on the electro-thermo nonlocal wave propagation of SWBNNTs. Phys B Condens Matter2014; 452: 159–165.
33.
Di PaolaMMarinoFZingalesM. A generalized model of elastic foundation based on long-range interactions: integral and fractional model. Int J Solids Struct2009; 46: 3124–3137.
34.
ZhangYCWangX. Thermal effects on interfacial stress transfer characteristics of carbon nanotubes/polymer composites. Int J Solids Struct2005; 42: 5399–5412.
35.
AoZLiS. Temperature- and thickness-dependent elastic moduli of polymer thin films. Nanoscale Res Lett2011; 6: 243–243.
36.
TorresJMStaffordCMVogtBD. Elastic modulus of amorphous polymer thin films: relationship to the glass transition temperature. ACS Nano2009; 3: 2677–2685.
37.
Khodami MaraghiZGhorbanpour AraniAKolahchiR. Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid. Compos Part B Eng2013; 45: 423–432.
