Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T06:01:54.741Z Has data issue: false hasContentIssue false
  • English
  • Français

Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

Published online by Cambridge University Press:  03 June 2015

S. Jafari Mehrabadi ,
B. Sobhaniaragh  and
V. Pourdonya
S. Jafari Mehrabadi*
Affiliation:
Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran
B. Sobhaniaragh
Affiliation:
Young Researchers Club, Arak Branch, Islamic Azad University, Arak, Iran
V. Pourdonya
Affiliation:
Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran
*
*Corresponding author. Email: s-jafari@iau-arak.ac.ir
Get access

Abstract

Based on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton’s principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.

Keywords

35G0537N1574S30Carbon nanotube-reinforcedfunctionally gradedHamilton’s principleEshelby-Mori-Tanakasymmetric profilesextended rule of mixture
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 1 , February 2013 , pp. 90 - 112
Copyright
Copyright © Global-Science Press 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Thostenson, E. T., Ren, Z. and Chou, T. W., Advances in the science and technology of carbon nanotubes and their composites: a review, Compos. Sci. Tech., 61 (2001), pp. 1899–1912.CrossRefGoogle Scholar
[2]Stankovich, S., Dikin, D. A., Dommett, G. H. B., Kohlhaas, K. M., Zimney, E.J. and Stach, E. A. et al., Graphene-based composite materials, Nature, 442 (2006), pp. 282–286.Google Scholar
[3]Ramanathan, T., Abdala, A. A., Stankovich, S., Dikin, D. A., Herrera-Alonso, M. and Piner, R.D. et al., Functionalized graphene sheets for polymer nanocomposites, Nat. Nanotech., 3 (2008), pp. 327–331.CrossRefGoogle ScholarPubMed
[4]Qian, D., Wagner, G. J., Liu, W. K., Yu, M. F. and Ruoff, R. S., Mechanics of carbon nanotubes, Appl. Mech. Rev., 55 (2002), 495.Google Scholar
[5]Seymour, R.B, Polymeric Composites, VSP, the Netherlands, 1990.Google Scholar
[6]Morgan, P., Carbon Fibers and their Composites, CRC Press, Taylor and Francis Group, 2005.CrossRefGoogle Scholar
[7]Huit, J. A. H. and Rammerstorfer, K. G., Engineering Mechanics of Fiber Reinforced Polymers and Composite Structures, Springer Verlag, 1994.Google Scholar
[8]Fitzer, E. and Manocha, L. M., Carbon Reinforcements and Carbon/Carbon Composites, Springer-Verlag, 1998.Google Scholar
[9]Thostenson, E. T., Ren, Z. F. and Chou, T. W., Advances in the science and technology of carbon nanotubes and their composites: a review, Compos. Sci. Tech., 61(13) (2001), pp. 1899–1912.Google Scholar
[10]Moniruzzaman, M. and Winey, K. I., Polymer nanocomposites containing carbon nanotubes, Macromolecules, 39 (2006), pp. 5194–5205.CrossRefGoogle Scholar
[11]Bavastrello, V., Ram, M. K. and Nicolini, C., Synthesis of multiwalled carbon nanotubes and poly(o-anisidine) nanocomposite material: fabrication and characterization of its Langmuir-Schaefer films, Langmuir., 18 (2002), pp. 1535–1541.Google Scholar
[12]Qian, D., Dickey, E. C., Andrews, R. and Rantell, T., Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites, Appl. Phys. Lett., 76 (2000), pp. 2868–2670.CrossRefGoogle Scholar
[13]Shen, H. S., Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments, Compos. Struct., 91 (2009), pp. 9–19.Google Scholar
[14]Wang, Z. X. and Shen, H. S., Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets, Compos. Part B Eng., Article in Press, 2011, doi:10.1016/j.compositesb.2011.04.040.Google Scholar
[15]Shen, H. S. and Zhu, Z. H., Buckling and postbuckling behavior of functionally graded nanotube-reinforced composite plates in thermal environments, Comput. Mater. Continua., 18 (2010), pp. 155–182.Google Scholar
[16]Shen, H. S. and Zhang, C. L., Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates, J. Mater. Design, 31 (2010), pp. 3403–3411.CrossRefGoogle Scholar
[17]Ke, L. L., Yang, J. and Kitipornchai, S., Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Compos. Struct., 92 (2010), pp. 676–683.Google Scholar
[18]Yas, M. H. and Heshmati, M., Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Appl. Math. Model., 36 (2012), pp. 1371–1394.Google Scholar
[19]Moradi-Dastjerdi, R., Foroutan, M. and Pourasghar, A., Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method, J. Mater. Design, 44 (2013), pp. 256–266.Google Scholar
[20]Alibeigloo, A., Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity, Compos. Struct., http://dx.doi.org/10.1016/j.compstruct.2012.08.018.CrossRefGoogle Scholar
[21]Odegard, G. M., Gates, T. S., Wise, K. E., Park, C. and Siochi, E. J., Constitutive modeling of nanotubereinforced polymer composites, Compos. Sci. Tech., 63 (2003), pp. 1671–1687.Google Scholar
[22]Benveniste, Y., A new approach to the application of Mori-Tanaka’s theory in composite materials, Mech. Mater., 6 (1987), pp. 147–157.CrossRefGoogle Scholar
[23]Chen, C. H., Effective elastic moduli of misoriented short-fiber composites, Int. J. Solids Struct., 33 (1996), pp. 2519–2539.Google Scholar
[24]Shady, E. and Gowayed, Y., Effect of nanotube geometry on the elastic properties of nanocom-posites, Compos. Sci. Tech., 70 (2010), pp. 1476–1481.Google Scholar
[25]Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Royal Society London, Series A, 241 (1957), pp. 376–396.Google Scholar
[26]Eshelby, J. D., The elastic field outside an ellipsoidal inclusion, Proc. Royal Soc. A, 252 (1959), pp. 561–569.Google Scholar
[27]Giordano, S., Palla, P. L. and Colombo, L., Nonlinear elasticity of composite materials Landau coefficients in dispersions of spherical and cylindrical inclusions, Euro. Phys. J. B, 68 (2009), pp. 89–101.CrossRefGoogle Scholar
[28]Mori, T. and Tanaka, K., Average stress in matrix and average elastic energy of materials with misfit ting inclusions, Acta. Metall, 21 (1973), pp. 571–574.Google Scholar
[29]Formica, G., Lacarbonara, W. and Alessi, R., Vibrations of carbon nanotube-reinforced composites, J. Sound Vib., 329 (2010), pp. 1875–1889.CrossRefGoogle Scholar
[30]Shi, D. L., Feng, X. Q., Huang, Y. Y., Hwang, K. C. and Gao, H., The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites, J. Eng. Mater Tech., 126 (2004), pp. 250–257.Google Scholar
[31]Mura, T., Micromechanics of Defects in Solids, The Hague: Martinus Nijhoff; 1982.CrossRefGoogle Scholar
[32]Hill, R., A self-consistent mechanics of composite materials, J. Mech. Phys. Solids, 13 (1965), pp. 213–222.Google Scholar
[33]Mindlin, R. D., Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates, American Society of Mechanical Engineers, J. Appl. Mech., 18 (1951), pp. 31–38.CrossRefGoogle Scholar
[34]Norman, F., Knight, J. R. and Yunqian, Q., On a consistent first-order shear-deformation theory for laminated plates, Compos. Part B, 28(4) (1977), pp. 397–405.Google Scholar
[35]Fares, M. E., Non-linear bending analysis of composite laminated plates using a refined first-order theory, Compos. Struct., 46(3) (1999), pp. 257–266.Google Scholar
[36]Shu, C., Differential Quadrature and Its Application in Engineering, Springer, Berlin, 2000.CrossRefGoogle Scholar
[37]Shu, C. and Richards, B., Application of generalized differential quadrature to solve two-dimensional incompressible Navier Stockes equations, Int. J. Numer Meth. Fl., 15 (1992), pp. 791–798.Google Scholar
[38]Shu, C., Free vibration analysis of composite laminated conical shells by generalized differential quadrature, J. Sound Vib., 194 (1996), pp. 587–604.Google Scholar
[39]Reddy, J. N., Theory and Analysis of Elastic Plates, Taylor and Francis, Philadelphia, 1999.Google Scholar
[40]Yas, M. H. and Aragh, B. Sobhani, Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation, Int. J. Eng. Sci., 48 (2010), pp. 1881–1895.CrossRefGoogle Scholar
[41]Matsunaga, H., Free vibration and stability of functionally graded plates according to a 2D higherorder deformation theory, J. Compos. Struct., 82 (2008), pp. 499–512.Google Scholar
[42]Han, Y. and Elliott, J., Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Comput. Mater. Sci., 39 (2007), pp. 315–323.CrossRefGoogle Scholar