Abstract
This work deals with the effect of agglomeration and distribution of carbon nanotube on the free vibration characteristics of a functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) by employing an equivalent fiber based on the Eshelby-Mori-Tanaka approach. Different SWCNTs distributions in the thickness directions are introduced to improve fundamental natural frequency of polymer composite beam. The micromechanics models used in the study include a two parameter model of agglomeration. An embedded carbon nanotube in a polymer matrix and its surrounding inter-phase is replaced with an equivalent fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. The system of equations of motion is derived by using the principle of virtual work under the assumptions of the Euler-Bernoulli beam theory. The finite element method is employed to obtain a numerical approximation of the motion equation. Numerical results are presented in both tabular and graphical forms to figure out the effects of nanotube agglomeration, CNTs distribution and boundary conditions on the dynamic characteristics of the beam. The above mentioned effects play very important role on the dynamic behavior of the beam.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. T. Lau, C. Gu and D. Hui, A critical review on nanotube and nanotube/nanoclay related polymer composite materials, Compos Part B, 37 (2006) 425–436.
G. M. Odegard, T. S. Gates, K. E. Wise, C. Park and E. J. Siochi, Constitutive modelling of nanotube-reinforced polymer composites, Compos Sci Technol, 63 (2003) 1671–1687.
R. Zhu, E. Pan and A. K. Roy, Molecular dynamics study of the stress-strain behavior of carbon-nanotube reinforced Epon 862, Compos. Mater. Sci Eng A, 447 (2007) 51–57.
D. L. Shi, X. Q. Feng, Y. Y. Huang, K. C. Hwang and H. Gao, The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube reinforced composites, J. Eng. Mater -Technol., 126 (2004) 250–257.
M. S. P. Shaffer and A. H. Windle, Fabrication and characterization of carbon nanotube/poly (vinyl alcohol) Compos. Adv. Mater. (Weinheim, Ger.), 11 (1999) 937–941.
B. Vigolo, A. P. Penicaud, C. Couloun, S. Sauder, R. Pailler, C. Journet, P. Bernier and P. Poulin, Macroscopic fibers and ribbons of oriented carbon nanotubes. Science, 290 (2000) 1331–1334.
M. Shokrieh and R. Rafiee, Prediction of mechanical properties of an embedded carbon nanotube in polymer matrix based on developing an equivalent long fiber, Mech. Res. Commun., 37 (2010) 235–240.
M. Shokrieh and R. Rafiee, On the tensile behavior of an embedded carbon nanotube in polymer matrix with nonbonded interphase region, Compos. Struct., 92 (2010) 647–652.
J. Wuite and S. Adali, Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis, Compos. Struct., 71 (2005) 388–396.
T. Vodenitcharova and L. C. Zhang, Bending and local buckling of a nanocomposite beam reinforced by a singlewalled carbon nanotube, Int. J. Solids Struct, 43 (2006) 3006–3024.
S. Sahmani and R. Ansari, Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions, Journal of Mechanical Science and Technology, 25(9) (2011) 2365–2375.
F. F. Mahmoud, M. A. Eltaher, A. E. Alshorbagy and E. I. Meletis, Static analysis of nanobeams including surface effects by nonlocal finite element, Journal of Mechanical Science and Technology, 26(11) (2012) 3555–3563.
L. L. Ke, J. Yang and S. Kitipornchai, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Compos. Struct., 92 (2010) 676–683.
M. H. Yas and M. Heshmati., Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Applied Mathematical Modelling, 36 (2012) 1371–1394.
T. Mori and K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall, 21 (1973) 571–574.
A. E. Alshorbagy, M. A. Eltaher and F. F. Mahmoud., Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35 (2011) 412–425.
L. Meirovitch, Methods of analytical dynamics, McGraw-Hill, Inc. (1970).
M. Aydogdu and V. Taskin, Free vibration analysis of functionally graded beams with simply supported edges, Materials and Design, 28 (2007) 1651–1656.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Jun-Sik Kim
M. Heshmati received his B.Sc. in Mechanical Engineering from Razi University of Kermanshah, Iran, 2005, M.Sc. in Mechanical Engineering from Shiraz University, Iran, in 2008. He is currently Ph.D student in Razi University of Kermanshah. His research fields are composite material, functionally graded material, nanomechancis, MEMS, NEMS, nonlocal elasticity, dynamic contact, vibrational analysis, plates and beams structures, and finite element analysis.
Rights and permissions
About this article
Cite this article
Heshmati, M., Yas, M.H. Free vibration analysis of functionally graded CNT-reinforced nanocomposite beam using Eshelby-Mori-Tanaka approach. J Mech Sci Technol 27, 3403–3408 (2013). https://doi.org/10.1007/s12206-013-0862-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-013-0862-8