Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

The effect of carbon nanotubes agglomeration on vibrational response of thick functionally graded sandwich plates

  • Tahouneh, Vahid (Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University)
  • Received : 2017.01.25
  • Accepted : 2017.06.02
  • Published : 2017.08.30
⟨ Previous Next ⟩

Abstract

In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded (FG) nanocomposite sandwich plates resting on Pasternak foundation are presented. The volume fractions of randomly oriented agglomerated single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. To determine the effect of CNT agglomeration on the elastic properties of CNT-reinforced composites, a two-parameter micromechanical model of agglomeration is employed. In this research work, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented straight CNTs. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated FG nanocomposite plates are investigated. It is shown that the natural frequencies of structure are seriously affected by the influence of CNTs agglomeration. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated plates.

Keywords

References

  1. Anderson, T.A. (2003), "A 3-D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere", Compos. Struct., 60(3), 265-274. https://doi.org/10.1016/S0263-8223(03)00013-8
  2. 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. https://doi.org/10.12989/scs.2015.18.3.659
  3. 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. https://doi.org/10.12989/scs.2015.19.3.521
  4. 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. https://doi.org/10.12989/scs.2015.18.6.1493
  5. Chakraverty, S., Jindal, R. and Agarwal, V.K. (2007), "Effect of nonhomogeneity on natural frequencies of vibration of elliptic plates", Meccanica, 42(6), 585-599. https://doi.org/10.1007/s11012-007-9077-3
  6. Efraim, E. and Eisenberger, M. (2007), "Exact vibration analysis of variable thickness thick annular isotropic and FGM plates", J. Sound Vib., 299(4-5), 720-738. https://doi.org/10.1016/j.jsv.2006.06.068
  7. Endo, M., Hayashi, T., Kim, Y.A., Terrones, M. and Dresselhaus, M.S. (2004), "Applications of carbon nanotubes in the twentyfirst century", Phil. Trans. R. Soc. Lond. A, 362(1823), 2223-2238. https://doi.org/10.1098/rsta.2004.1437
  8. Heshmati, M. and Yas, M.H. (2013), "Free vibration analysis of functionally graded CNT-reinforced nanocomposite beam using Eshelby-Mori-Tanaka approach", J. Mech. Sci. Technol., 27(11), 3403-3408. https://doi.org/10.1007/s12206-013-0862-8
  9. Hosseini-Hashemi, Rokni Damavandi Taher, S.H. and Akhavan, H. (2010), "Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations", Compos. Struct., 92(7), 1734-1743. https://doi.org/10.1016/j.compstruct.2009.12.016
  10. Hosseini-Hashemi, S., Es'haghi, M. and Karimi, M. (2010), "Closed-form vibration analysis of thick annular functionally graded plates with integrated piezoelectric layers", Int. J. Mech. Sci., 52(3), 410-428. https://doi.org/10.1016/j.ijmecsci.2009.10.016
  11. Iijima, S. (1991), "Helical microtubes of graphitic carbon", Nature, 354, 56-58. https://doi.org/10.1038/354056a0
  12. Kamarian, S., Yas, M.H. and Pourasghar, A. (2013), "Free vibration analysis of three-parameter functionally graded material sandwich plates resting on Pasternak foundations", J. Sandw. Struct. Mater., 15(3), 292-308. https://doi.org/10.1177/1099636213487363
  13. Kamarian, S., Shakeri, M., Yas, M.H., Bodaghi, M. and Pourasghar, A. (2015), "Free vibration analysis of functionally graded nanocomposite sandwich beams resting on Pasternak foundation by considering the agglomeration effect of CNTs", J. Sandw. Struct. Mater., 17(6), 1-31.
  14. Kamarian, S., Salim, M., Dimitri, R. and Tornabene, F. (2016), "Free vibration analysis of conical shells reinforced with agglomerated carbon nanotubes", Int. J. Mech. Sci., 108(1), 157-165.
  15. Kashtalyan, M. and Menshykova, M. (2009), "Three-dimensional elasticity solution for sandwich panels with a functionally graded core", Compos. Struct., 87(1), 36-43. https://doi.org/10.1016/j.compstruct.2007.12.003
  16. Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams", Compos. Struct., 92(3), 676-683. https://doi.org/10.1016/j.compstruct.2009.09.024
  17. Koizumi, M. (1993), "The concept of FGM, ceramic transactions", Funct. Gradient. Mater., 34, 3-10.
  18. Li, Q., Iu, V. and Kou, K. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311(1-2), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018
  19. Marin, M. (2010), "A domain of influence theorem for microstretch elastic materials", Nonlinear Anal. Real World Appl., 11(5), 3446-3452. https://doi.org/10.1016/j.nonrwa.2009.12.005
  20. Marin, M. and Lupu, M. (1998), "On harmonic vibrations in thermoelasticity of micropolar bodies", J. Vib. Control, 4(5), 507-518. https://doi.org/10.1177/107754639800400501
  21. Malekzadeh, P., Golbahar Haghighi, M.R. and Atashi, M.M. (2011), "Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment", Meccanica, 46(5) 893-913. https://doi.org/10.1007/s11012-010-9345-5
  22. Matsunaga, H. (2000), "Vibration and stability of thick plates on elastic foundations", J. Eng. Mech. ASCE, 126, 27-34. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(27)
  23. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2D higher-order deformation theory", J. Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  24. Moniruzzaman, M. and Winey, K.I. (2006), "Polymer nanocomposites containing carbon nanotubes", Macromolecules, 39(16), 5194-5205. https://doi.org/10.1021/ma060733p
  25. Moradi-Dastjerdi, R., Pourasghar, A. and Foroutan, M. (2013), "The effects of carbon nanotube orientation and aggregation on vibrational behavior of functionally graded nanocomposite cylinders by a mesh-free method", Acta Mech., 224(11), 2817-2832. https://doi.org/10.1007/s00707-013-0897-z
  26. Nie, G.J. and Zhong, Z. (2008), "Vibration analysis of functionally graded annular sectorial plates with simply supported radial edges", Compos. Struct., 84(2), 167-176. https://doi.org/10.1016/j.compstruct.2007.07.003
  27. Odegard, G.M., Gates, T.S., Wise, K.E., Park, C. and Siochi, E.J. (2003), "Constitutive modelling of nanotube reinforced polymer composites", Compos. Sci. Technol., 63(11), 1671-1687. https://doi.org/10.1016/S0266-3538(03)00063-0
  28. Qian, D., Dickey, E.C., Andrews, R. and Rantell, T. (2000), "Load transfer and deformation mechanisms in carbon nanotubepolystyrene composites", Appl. Phys. Lett., 76(20), 2868-2870. https://doi.org/10.1063/1.126500
  29. Salvetat, D. and Rubio, A. (2002), "Mechanical properties of carbon nanotubes: a fiber digest for beginners", Carbon, 40(10), 1729-1734. https://doi.org/10.1016/S0008-6223(02)00012-X
  30. Seidel, G.D. and Lagoudas, D.C. (2006), "Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites", Mech. Mater., 38(8-10) 884-907. https://doi.org/10.1016/j.mechmat.2005.06.029
  31. Shaffer, M.S.P. and Windle, A.H. (1999), "Fabrication and Characterization of Carbon Nanotube/Poly (vinyl alcohol) Composites", Adv. Mater. (Weinheim, Ger.), 11(11), 937-941. https://doi.org/10.1002/(SICI)1521-4095(199908)11:11<937::AID-ADMA937>3.0.CO;2-9
  32. Sharma, K. and Marin, M. (2013), "Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space, U.P.B. Sci. Bull., Series A-Appl. Math. Phys., 75(2), 121-132.
  33. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  34. Shen, H.S. and Zhang, C.L. (2010), 'Thermal buckling and postbuckling behavior of functionally graded carbon nanotubereinforced composite plates', Mater. Des., 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048
  35. Shen, H.S. and Zhu, Z.H. (2010), "Buckling and postbuckling behavior of functionally graded nanotube-reinforced composite plates in thermal environments", Comput. Mater Continua., 18(2), 155-182.
  36. Shi, D.L., Feng, X.Q., Huang, Y.Y., Hwang, K.C. and Gao, H. (2004), "The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube reinforced composites", J. Eng. Mater. Technol., 126(3) 250-257. https://doi.org/10.1115/1.1751182
  37. Shokrieh, M.M. and Rafiee, R. (2010a), "Investigation of nanotube length effect on the reinforcement efficiency in carbon nanotube based composites", Compos. Struct., 92(10), 2415-2420. https://doi.org/10.1016/j.compstruct.2010.02.018
  38. Shokrieh, M.M. and Rafiee, R. (2010b), "Prediction of mechanical properties of an embedded carbon nanotube in polymer matrix based on developing an equivalent long fiber", Mech. Res. Commun., 37(2), 235-240. https://doi.org/10.1016/j.mechrescom.2009.12.002
  39. Shu, C. (2000), Differential Quadrature and its Application in Engineering, Springer Science & Business Media.
  40. Shu, C. and Richards, B.E. (1992), "Application of generalized differential quadrature to solve two dimensional incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluid, 15(7), 791-798. https://doi.org/10.1002/fld.1650150704
  41. Stephan, C., Nguyen, T.P., Chapelle, M.L. and Lefrant, S. (2000), "Characterization of single-walled carbon nanotubes-PMMA composite", Synth. Met., 108(2), 139-149. https://doi.org/10.1016/S0379-6779(99)00259-3
  42. Tahouneh, V. (2014a), "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. https://doi.org/10.12989/sem.2014.52.4.663
  43. Tahouneh, V. (2014b), "Free vibration analysis of thick CGFR annular sector plates resting on elastic foundations", Struct. Eng. Mech., Int. J., 50(6), 773-796. https://doi.org/10.12989/sem.2014.50.6.773
  44. Tahouneh, V. (2016), "Using an equivalent continuum model for 3D dynamic analysis of nanocomposite plates", Steel Compos. Struct., Int. J., 20(3), 623-649. https://doi.org/10.12989/scs.2016.20.3.623
  45. Tahouneh, V. and Naei, M.H. (2014), "A novel 2-D six-parameter power-law distribution for three-dimensional dynamic analysis of thick multi-directional functionally graded rectangular plates resting on a two-parameter elastic foundation", Meccanica, 49(1), 91-109. https://doi.org/10.1007/s11012-013-9776-x
  46. Tahouneh, V. and Naei, M.H. (2016), "Free vibration and vibrational displacements analysis of thick elastically supported laminated curved panels with power-law distribution functionally graded layers and finite length via 2D GDQ method", J. Sandw. Struct. Mater., 18(3), 263-293. https://doi.org/10.1177/1099636215600709
  47. Tahouneh, V. and Yas, M.H. (2012), "3-D free vibration analysis of thick functionally graded annular sector plates on Pasternak elastic foundation via 2-D differential quadrature method", Acta Mech., 223(9), 1879-1897. https://doi.org/10.1007/s00707-012-0648-6
  48. Tahouneh, V. and Yas, M.H. (2013), "Semi-analytical solution for three-dimensional vibration analysis of thick multidirectional functionally graded annular sector plates under various boundary conditions", J. Eng. Mech., 140(1), 31-46.
  49. Tahouneh, V., Yas, M.H., Tourang, H. and Kabirian, M. (2013), "Semi-analytical solution for three-dimensional vibration of thick continuous grading fiber reinforced (CGFR) annular plates on Pasternak elastic foundations with arbitrary boundary conditions on their circular edges", Meccanica, 48(6), 1313-1336. https://doi.org/10.1007/s11012-012-9669-4
  50. Thostenson, E.T., Ren, Z.F. and Chou, T.W. (2001), "Advances in the Science and Technology of Carbon Nanotubes and their Composites: A Review", Compos. Sci. Technol., 61(13), 1899-1912. https://doi.org/10.1016/S0266-3538(01)00094-X
  51. Tornabene, F. and Viola, E. (2009), "Free vibration analysis of four-parameter functionally graded parabolic panels and shells of revolution", Eur. J. Mech. A/Solid, 28(5), 991-1013. https://doi.org/10.1016/j.euromechsol.2009.04.005
  52. Tornabene, F., Fantuzzi, N. and Ubertini, F. (2015), "Strong formulation finite element method based on differential quadrature: A survey", Appl. Mech. Rev., 67(2), 1-55.
  53. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2016), "Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells", Compos. Part B, 89(1), 187-218. https://doi.org/10.1016/j.compositesb.2015.11.016
  54. Tsai, S.W., Hoa, C.V. and Gay, D. (2003), Composite Materials, Design and Applications, CRC Press, Boca Raton, CA, USA.
  55. Valter, B., Ram, M.K. and Nicolini, C. (2002), "Synthesis of multiwalled carbon nanotubes and poly (o-anisidine) nanocomposite material: Fabrication and characterization its langmuir-schaefer films", Langmuir, 18(5), 1535-1541. https://doi.org/10.1021/la0104673
  56. Vigolo, B., Penicaud, A.P., Couloun, C., Sauder, S., Pailler, R., Journet, C., Bernier, P. and Poulin, P. (2000), "Macroscopic fibers and ribbons of oriented carbon nanotubes", Science, 290(5495), 1331-1334. https://doi.org/10.1126/science.290.5495.1331
  57. 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. https://doi.org/10.1063/1.120680
  58. Wang, Z.X. and Shen, H.S. (2011), "Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets", Compos. Part B, 43(2), 411-421. https://doi.org/10.1016/j.compositesb.2011.04.040
  59. Wernik, J.M. and Meguid, S.A. (2011), "Multiscale modeling of the nonlinear response of nano-reinforced polymers", Acta. Mech., 217(1), 1-16. https://doi.org/10.1007/s00707-010-0377-7
  60. Wuite, J. and Adali, S. (2005), "Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis", Compos. Struct., 71(3-4), 388-396. https://doi.org/10.1016/j.compstruct.2005.09.011
  61. Yas, M.H. and Sobhani Aragh, B. (2010), "Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation", Int. J. Eng. Sci., 48(12), 1881-1895. https://doi.org/10.1016/j.ijengsci.2010.06.015
  62. Yas, M.H. and Tahouneh, V. (2012), "3-D free vibration analysis of thick functionally graded annular plates on Pasternak elastic foundation via differential quadrature method (DQM)", Acta Mech., 223(1), 43-62. https://doi.org/10.1007/s00707-011-0543-6
  63. Yokozeki, T., Iwahori, Y. and Ishiwata, S. (2007), "Matrix cracking behaviors in carbon fiber/epoxy laminates filled with cup-stacked carbon nanotubes (CSCNTs)", Compos. Part A, 38(3), 917-924. https://doi.org/10.1016/j.compositesa.2006.07.005
  64. Zenkour, A. (2005a), "A comprehensive analysis of functionally graded sandwich plates, Part 1-Deflection and stresses", Int. J. Solids Struct., 42(18-19), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
  65. Zenkour, A. (2005b), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. J. Solids Struct., 42(18-19), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016
  66. Zhou, D., Cheung, Y.K., Lo, S.H. and Au, F.T.K. (2004), "Threedimensional vibration analysis of rectangular thick plates on Pasternak foundation", Int. J. Numer. Methods Eng., 59(10), 1313-1334. https://doi.org/10.1002/nme.915

Cited by

  1. Vibrational characteristic of FG porous conical shells using Donnell's shell theory vol.35, pp.2, 2017, https://doi.org/10.12989/scs.2020.35.2.249
  2. Influence of internal pores and graphene platelets on vibration of non-uniform functionally graded columns vol.35, pp.2, 2017, https://doi.org/10.12989/scs.2020.35.2.295
  3. Vibration analysis of sandwich sector plate with porous core and functionally graded wavy carbon nanotube-reinforced layers vol.37, pp.6, 2017, https://doi.org/10.12989/scs.2020.37.6.711
  4. The effect of agglomeration and slightly weakened CNT-matrix interface on free vibration response of cylindrical nanocomposites vol.232, pp.6, 2021, https://doi.org/10.1007/s00707-020-02933-y