This work reports the effect of nanotube aspect ratio on the free vibration characteristics of a functionally graded nanocomposite cylinders reinforced by wavy single-walled carbon nanotubes (CNTs) based on mesh-free method. In this simulation, an axisymmetric model is used and axisymmetric natural frequencies of CNT reinforced composite cylinders are presented. The material properties of functionally graded CNT reinforced composites are assumed to be graded in the thickness direction and are estimated by a micromechanical model. The effect of the waviness of the CNTs and its parameters are studied. In the mesh-free analysis, moving least squares shape functions are used for approximation of displacement field in the weak form of motion equation, and the transformation method is used for the imposition of essential boundary conditions. It is observed that the waviness significantly reduces the effective reinforcement of the nanocomposites. The effective moduli and frequency response are very sensitive to the waviness but this sensitivity decreases with the increase of the waviness. The validity of the Young's modulus and the frequency response were assessed by a comparison with available literature data, providing a good agreement.
EsawiAMKFaragMM. Carbon nanotube reinforced composites: potential and current challenges. Mater Design2007; 28: 2394–2401.
2.
ThostensonETRenZFChouTW. Advances in the science and technology of carbon nanotubes and their composites: a review. Compos Sci Technol2001; 61: 1899–1912.
3.
DaiH. Carbon nanotubes: opportunities and challenges. Surf Sci2002; 500: 218–241.
4.
KangIHeungYKimJ. Introduction to carbon nanotube and nanofiber smart materials. Compos Part B2006; 37: 382–394.
5.
LauKTGuCHuiD. A critical review on nanotube and nanotube/nanoclay related polymer composite materials. Compos Part B2006; 37: 425–436.
6.
GojnyFHWichmannMHGFiedlerB. Influence of different carbon nanotubes on the mechanical properties of epoxy matrix composites – a comparative study. Compos Sci Technol2005; 65: 2300–2313.
7.
FidelusJDWieselEGojnyFH. Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites. Compos Part A2005; 36: 1555–1561.
8.
HanYElliottJ. Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Comput Mater Sci2007; 39: 315–323.
9.
ManchadoMALValentiniLBiagiottiJ. Thermal and mechanical properties of single-walled carbon nanotubes-polypropylene composites prepared by melt processing. Carbon2005; 43: 1499–1505.
10.
MokashiVVQianDLiuYJ. A study on the tensile response and fracture in carbon nanotube-based composites using molecular mechanics. Compos Sci Technol2007; 67: 530–540.
11.
ZhuRPanERoyAK. Molecular dynamics study of the stress–strain behavior of carbon-nanotube reinforced Epon 862 composites. Mater Sci Eng A2007; 447: 51–57.
12.
ShenHS. Nonlinear bending of functionally graded carbon nanotube reinforced composite plates in thermal environments. Compos Struct2009; 91: 9–19.
13.
ShenHS. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: axially-loaded shells. Compos Struct2011; 93: 2096–2108.
14.
TsaiCZhangCJackDA. The effect of inclusion waviness and waviness distribution on elastic properties of fiber-reinforced composites. Compos Part B2011; 42: 62–70.
15.
MontazeriAJavadpourJKhavandiA. Mechanical properties of multi-walled carbon nanotube/epoxy composites. Mater Design2010; 31: 4202–4208.
16.
MartoneFGAntonucciVGiordanoM. The effect of the aspect ratio of carbon nanotubes on their effective reinforcement modulus in an epoxy matrix. Compos Sci Technol2011; 71: 1117–1123.
17.
PradhanSCLoyCTReddyJN. Vibration characteristics of functionally graded cylindrical shells under various boundary conditions. Appl Acoust2000; 61: 111–129.
18.
AnsariRDarvizehM. Prediction of dynamic behavior of FGM shells under arbitrary boundary conditions. Compos Struct2008; 85: 284–292.
19.
Sobhani AraghBYasMH. Static and free vibration analyses of continuously graded fiber-reinforced cylindrical shells using generalized power-law distribution. Acta Mech2010; 215: 155–173.
20.
Sobhani AraghBYasMH. Three-dimensional free vibration of functionally graded fiber orientation and volume fraction cylindrical panels. Mater Design2010; 31: 4543–4552.
21.
HosseiniSMAkhlaghiMShakeriM. Dynamic response and radial wave propagation velocity in thick hollow cylinder made of functionally graded materials. Eng Comput2007; 24: 288–303.
22.
JamJEPourasgharAKamarianS. The effect of the aspect ratio and waviness of CNTs on the vibrational behavior of functionally graded nanocomposite cylindrical panels. Polym Compos2012; 33: 2036–2044.
23.
Moradi-DastjerdiRForoutanMPourasgharA. Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method. Mater Design2013; 44: 256–266.
24.
ForoutanMMoradi-DastjerdiRSotoodeh-BahreiniR. Static analysis of FGM cylinders by a mesh-free method. Steel Compos Struct2012; 12: 1–11.
25.
MollaraziHRForoutanMMoradi-DastjerdiR. Analysis of free vibration of functionally graded material (FGM) cylinders by a meshless method. J Compos Mater2011; 46: 507–515.
26.
ForoutanMMoradi-DastjerdiR. Dynamic analysis of functionally graded material cylinders under an impact load by a mesh-free method. Acta Mech2011; 219: 281–290.
27.
LancasterPSalkauskasK. Surface generated by moving least squares methods. Math Comput1981; 37: 141–158.
28.
ZhouDCheungYKLoSH. 3D vibration analysis of solid and hollow circular cylinders via Chebyshev–Ritz method. Comput Meth Appl Mech Eng2003; 192: 1575–1589.
29.
HutchinsonJR. Comments on “Accurate vibration frequencies of circular cylinders from three-dimensional analysis”. J Acoust Soc Am1996; 98: 2136–2141.
30.
HutchinsonJR. Comments on “Accurate vibration frequencies of circular cylinders from three-dimensional analysis”. J Acoust Soc Am1995; 100: 1894–1895.
31.
LeissaAWSoJ. Accurate vibration frequencies of circular cylinders from three dimensional analysis. J Acoust Soc Am1995; 98: 2136–2141.
32.
SongYSYounJR. Modeling of effective elastic properties for polymer based carbon nanotube composites. Polymer2006; 47: 1741–1748.
33.
ShenHSZhangCL. Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates. Mater Design2010; 31: 3403–3411.
