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http://dx.doi.org/10.12989/scs.2017.23.6.657

Using modified Halpin-Tsai approach for vibrational analysis of thick functionally graded multi-walled carbon nanotube plates  

Tahouneh, Vahid (Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University)
Publication Information
Steel and Composite Structures / v.23, no.6, 2017 , pp. 657-668 More about this Journal
Abstract
In the most of previous studies, researchers have restricted their own studies to consider the effect of single walled carbon nanotubes as a reinforcement on the vibrational behavior of structures. In the present work, free vibration characteristics of functionally graded annular plates reinforced by multi-walled carbon nanotubes resting on Pasternak foundation are presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of the multi-walled carbon nanotube/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the multi-walled carbon nanotubes wt% range considered. The 2-D generalized differential quadrature method as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the plates are investigated. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of annular plates.
Keywords
multi-walled carbon nanotubes; vibration; thick plates; modified Halpin-Tsai equation;
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Times Cited By KSCI : 8  (Citation Analysis)
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1 Tahouneh, V. and Naei, M.H. (2015), "3D free vibration analysis of elastically supported thick nanocomposite curved panels with finite length and different boundary conditions via 2-D GDQ method", Mech. Adv. Mater. Struct., 23(10), 1216-1235.
2 Tahouneh, V. and Yas, M.H. (2014), "Influence of equivalent continuum model based on the Eshelby-Mori-Tanaka scheme on the vibrational response of elastically supported thick continuously graded carbon nanotube-reinforced annular plates", Polym. Compos., 35(8), 1644-1661.   DOI
3 Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2014), "Free vibrations of free-form doubly curved shells made of functionally graded materials using higher-order equivalent single layer theories", Compos. Part B, 67, 490-509.   DOI
4 Viola, E. and Tornabene, F. (2009), "Free vibrations of three parameter functionally graded parabolic panels of revolution", Mech. Res. Commun., 36(5), 587-594.   DOI
5 Wagner, H.D., Lourie, O. and Feldman, Y. (1997), "Stress-induced fragmentation of multiwall carbon nanotubes in a polymer matrix", Appl. Phys. Lett., 72(2), 188-190.   DOI
6 Wang, X. and Wang, Y. (2004), "Free vibration analyses of thin sector plates by the new version of differential quadrature method", Comput. Methods Appl. Mech. Eng., 193(36), 3957-3971.   DOI
7 Yeh, M.K., Tai, N.H. and Liu, J.H. (2006), "Mechanical behavior of phenolic-based composites reinforced with multi-walled carbon nanotubes", Carbon, 44(1), 1-9.   DOI
8 Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical postbuckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., Int. J., 56(1), 85-106.   DOI
9 Affdl Halpin, J.C. and Kardos, J.L. (1976), "The Halpin-Tsai equations: A review", Polym. Eng. Sci., 16(5), 344-352.   DOI
10 Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections', Steel Compos. Struct., Int. J., 18(3), 659-672.   DOI
11 Bellman, R. and Casti, J. (1971), "Differential quadrature and long term integration", J. Math. Anal. Appl., 34(2), 235-238.   DOI
12 Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higherorder shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546.   DOI
13 Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: A review", Appl. Mech. Rev., 49, 1-27.   DOI
14 Bouchafa, A., Bouiadjra, M.B., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515.   DOI
15 Gupta, U.S., Lal, R. and Sharma, S. (2006), "Vibration analysis of non-homogeneous circular plate of nonlinear thickness variation by differential quadrature method", J. Sound Vib., 298(4), 892-906.   DOI
16 Dong, C.Y. (2008), "Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev-Ritz method", Mater. Des., 29(8), 1518-1525.   DOI
17 Farid, M., Zahedinejad, P. and Malekzadeh, P. (2010), "Three dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two parameter elastic foundation using a hybrid semi-analytic, differential quadrature method", J. Mater. Des., 31(1), 2-13.   DOI
18 Fidelus, J.D., Wiesel, E., Gojny, F.H., Schulte, K. and Wagner, H.D. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites", Composites Part A, 36(11), 1555-1561.   DOI
19 Ghavamian, A., Rahmandoust, M. and Ochsner, A. (2012), "A numerical evaluation of the influence of defects on the elastic modulus of single and multi-walled carbon nanotubes", Comput. Mater. Sci., 62, 110-116.   DOI
20 Gojny, F.H., Wichmann, M.H.G., Fiedler, B. and Schulte, K. (2005), "Influence of different carbon nanotubes on the mechanical properties of epoxy matrix composites-A comparative study", Compos. Sci. Technol., 65(15), 2300-2313.   DOI
21 Hadji, L., Hassaine Daouadji, T., Ait Amar Meziane, M., Tlidji, Y. and Adda Bedia, E.A. (2016), "Analysis of functionally graded beam using a new first-order shear deformation theory", Struct. Eng. Mech., Int. J., 57(2), 315-325.   DOI
22 Halpin, J.C. and Tsai, S.W. (1969), "Effects of environmental factors on composite materials", AFML-TR-67-423.
23 Heshmati, M. and Yas, M.H. (2013), "Vibrations of non-uniform functionally graded MWCNTs-polystyrene nanocomposite beams under action of moving load", Mater. Des., 46, 206-218.   DOI
24 Liu, F.L. and Liew, K.M. (1999), "Free vibration analysis of Mindlin sector plates numerical solutions by differential quadrature method", Comput. Methods Appl. Mech. Eng., 177(1-2), 77-92.   DOI
25 Jam, J.E., Pourasghar, A. and Kamarian, S. (2012), "The effect of the aspect ratio and waviness of CNTs on the vibrational behavior of functionally graded nanocomposite cylindrical panels", Polym. Compos., 33(11), 2036-2044.   DOI
26 Liew, K.M. and Liu, F.L. (2000), "Differential quadrature method for vibration analysis of shear deformable annular sector plates", J. Sound Vib., 230(2), 335-356.   DOI
27 Liew, K.M., Han, J.B., Xiao, Z.M. and Du, H. (1996), "Differential quadrature method for Mindlin plates on Winkler foundation", Int. J. Mech. Sci., 38(4), 405-421.   DOI
28 Marin, M. (2010), "A domain of influence theorem for microstretch elastic materials", Nonlinear Anal. Real World Appl., 11(5), 3446-3452.   DOI
29 Marin, M. and Lupu, M. (1998), "On harmonic vibrations in thermoelasticity of micropolar bodies", J. Vib. Control, 4(5), 507-518.   DOI
30 Marin, M. and Marinescu, C. (1998), "Thermoelasticity of initially stressed bodies. Asymptotic equipartition of energies", Int. J. Eng. Sci., 36(1), 73-86.   DOI
31 Martone, A., Faiella, G., Antonucci, V., Giordano, M. and Zarrelli, M. (2011), "The effect of the aspect ratio of carbon nanotubes on their effective reinforcement modulus in an epoxy matrix", Compos. Sci. Technol., 71(8), 1117-1123.   DOI
32 Montazeri, A., Javadpour, J., Khavandi, A., Tcharkhtchi, A. and Mohajeri, A. (2010), "Mechanical properties of multi-walled carbon nanotube/epoxy composites", Mater. Des., 31(9), 4202-4208.   DOI
33 Pelletier Jacob, L. and Vel Senthil, S. (2006), "An exact solution for the steady state thermo elastic response of functionally graded orthotropic cylindrical shells", Int. J. Solid Struct., 43(5), 1131-1158.   DOI
34 Moradi-Dastjerdi, R. (2016), "Wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube", Struct. Eng. Mech., Int. J., 57(3), 441-456.   DOI
35 Nie, G.J., and Zhong, Z. (2007), "Semi-analytical solution for three-dimensional vibration of functionally graded circular plates", Comput. Methods Appl. Mech. Eng., 196(49), 4901-4910.   DOI
36 Nie, G.J. and Zhong, Z. (2010), "Dynamic analysis of multidirectional functionally graded annular plates", Appl. Math. Model., 34(3), 608-616.   DOI
37 Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press Inc., (2nd Revised Edition).
38 Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19.   DOI
39 Shu, C. (2000), Differential Quadrature and Its Application in Engineering, Springer, Berlin.
40 Tahouneh, V. (2014), "Free vibration analysis of bidirectional functionally graded annular plates resting on elastic foundations using differential quadrature method", Struct. Eng. Mech., Int. J., 52(4), 663-686.   DOI
41 Tahouneh, V. (2016), "Using an equivalent continuum model for 3D dynamic analysis of nanocomposite plates", Steel Compos. Struct., Int. J., 20(3), 623-649.   DOI