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Vibration and mode shape analysis of sandwich panel with MWCNTs FG-reinforcement core

  • Tahouneh, Vahid (Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University)
  • Received : 2017.04.08
  • Accepted : 2017.07.11
  • Published : 2017.10.30

Abstract

The goal of this study is to fill this apparent gap in the area about vibration analysis of multiwalled carbon nanotubes (MWCNTs) curved panels by providing 3-D vibration analysis results for functionally graded multiwalled carbon nanotubes (FG-MWCNTs) sandwich structure with power-law distribution of nanotube. The effective material properties of the FG-MWCNT structures are estimated using a modified Halpin-Tsai equation. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of MWCNT/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 MWCNTs wt% range considered. Also, the mass density and Poisson's ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. Parametric studies are carried out to highlight the influence of MWCNT volume fraction in the thickness, different types of CNT distribution, boundary conditions and geometrical parameters on vibrational behavior of FG-MWCNT thick curved panels. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. For an overall comprehension on 3-D vibration analysis of sandwich panel, some mode shape contour plots are reported in this research work.

Keywords

References

  1. Abrate, S. (1998), "Impact on composite structures", Cambridge UK: Cambridge University Press.
  2. Affdl Halpin, J.C. and Kardos, J.L. (1976), "The Halpin-Tsai equations: A review", Polym. Eng. Sci., 16(5), 344-352. https://doi.org/10.1002/pen.760160512
  3. Anderson, T.A. (2003), "3D 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
  4. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659
  5. Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperaturedependent sandwich FGM plates resting on Pasternak elastic foundation", Steel Compos. Struct., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.091
  6. Bellman, R. and Casti, J. (1971), "Differential quadrature and long term integration", J. Math. Anal. Appl., 34(2), 235-238. https://doi.org/10.1016/0022-247X(71)90110-7
  7. 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.,, 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  8. 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., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  9. Bouguenina, O., Belakhdar, K., Tounsi, A. and Bedia, E.A.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., 19(3), 679-695. https://doi.org/10.12989/scs.2015.19.3.679
  10. Brischetto, S., Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2015), "Refined 2D and exact 3D shell models for the free vibration analysis of single- and double-walled carbon nanotubes", Technologies, 3(4), 259-284. https://doi.org/10.3390/technologies3040259
  11. Cai, J.B., Chen W.Q., Ye, G.R. and Ding, H.J. (2000), "On natural frequencies of a transversely isotropic cylindrical panel on a kerr foundation", J. Sound Vib., 232(5), 997-1004. https://doi.org/10.1006/jsvi.1999.2703
  12. Chen, C.S., Liu, F.H. and Chen, W.R. (2017), "vibration and stability of initially stressed sandwich plates with FGM face sheets in thermal environments", Steel Compos. Struct., 23(3), 251-261. https://doi.org/10.12989/scs.2017.23.3.251
  13. Chen, W.Q., Bian, Z.G. and Ding, H.U., (2004), "Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells", Int. J. Mech. Sci., 46(1), 159-171. https://doi.org/10.1016/j.ijmecsci.2003.12.005
  14. Civalek, O. (2005), "Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of HDQ-FD methods", Int. J. Press Vessel Pip., 82(6), 470-479. https://doi.org/10.1016/j.ijpvp.2004.12.003
  15. Fantuzzi, N., Tornabene, F., Bacciocchi, M. and Dimitri, R., (2016), "Free vibration analysis of arbitrarily shaped functionally carbon nanotube-reinforced plates", Composites: Part B, 115(1), 384-408.
  16. 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. https://doi.org/10.1016/j.compositesa.2005.02.006
  17. Gang, S.W., Lam, K.Y. and Reddy, J.N. (1999), "The elastic response of functionally graded cylindrical shells to low-velocity", Int. J. Impact Eng., 22(4), 397-417. https://doi.org/10.1016/S0734-743X(98)00058-X
  18. Ghavamian, A., Rahmandoust, M. and O chsner, 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. https://doi.org/10.1016/j.commatsci.2012.05.003
  19. 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(15-16), 2300-2313. https://doi.org/10.1016/j.compscitech.2005.04.021
  20. Gunawan, H. and Sato, M. (2006), "Free vibration characteristics of cylindrical shells partially buried in elastic foundations", J. Sound Vib., 290(3-5), 785-793. https://doi.org/10.1016/j.jsv.2005.04.014
  21. Halpin, J.C. and Tsai, S.W. (1969), "Effects of environmental factors on composite materials", AFML-TR-67-423.
  22. 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. https://doi.org/10.1016/j.matdes.2012.10.002
  23. Hong, M. and Lee, U. (2015), "Dynamics of a functionally graded material axial bar, Spectral element modeling and analysis", Composites: Part B, 69, 427-434. https://doi.org/10.1016/j.compositesb.2014.10.022
  24. Kamarian, S., Yas, M.H., and Pourasghar, A. (2013), "Free vibration analysis of three-parameter functionally graded material sandwich plates resting on Pasternak foundations", Sandw. Strut. Mater., 15(3) 292-308.
  25. 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
  26. Li, Q., Iu, V.P. and Kou, K.P. (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
  27. Loy, C.T., Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41(3), 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X
  28. 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
  29. 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
  30. Marin, M. and Marinescu, C. (1998), "Thermoelasticity of initially stressed bodies. Asymptotic equipartition of energies", Int. J. Eng. Sci., 36(1), 73-86. https://doi.org/10.1016/S0020-7225(97)00019-0
  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. https://doi.org/10.1016/j.compscitech.2011.04.002
  32. Matsunaga, H. (2008), "Free vibration and stability of functionally graded shallow shells according to a 2-D higher-order deformation theory", Compos. Struct., 84(2), 132-146. https://doi.org/10.1016/j.compstruct.2007.07.006
  33. Montazeri, A., Javadpour, J., Khavandi, A., Tcharkhtchi, A. and Mohajeri, A. (2010), "Mechanical properties of multi-walled carbon nanotube/epoxy composites", Mater. Des., 31, 4202-4208. https://doi.org/10.1016/j.matdes.2010.04.018
  34. Moradi-Dastjerdi, R. and Momeni-Khabisi, H. (2016), "Dynamic analysis of functionally graded nanocomposite plates reinforced by wavy carbon nanotube", Steel Compos. Struct., 22(2), 277-299. https://doi.org/10.12989/scs.2016.22.2.277
  35. Paliwal, D.N., Kanagasabapathy, H. and Gupta, K.M. (1995), "The large deflection of an orthotropic cylindrical shell on a Pasternak foundation", Compos. Struct., 31, 31-37. https://doi.org/10.1016/0263-8223(94)00068-9
  36. Paliwal, D.N., Pandey, R.K. and Nath, T. (1996), "Free vibration of circular cylindrical shell on Winkler and Pasternak foundation", Int. J. Press. Vessel Pip., 69(1), 79-89. https://doi.org/10.1016/0308-0161(95)00010-0
  37. Park, W.T., Han, S.C., Jung, W.Y. and Lee, W.H. (2016), "Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory", Steel Compos. Struct., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239
  38. Patel, B.P., Gupta, S.S., Loknath, M.S.B. and Kadu, C.P. (2005), "Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory", Compos. Struct., 69(3), 259-270. https://doi.org/10.1016/j.compstruct.2004.07.002
  39. 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. https://doi.org/10.1016/j.ijsolstr.2005.03.079
  40. Pradhan, S.C., Loy, C.T., Lam, K.Y., Reddy, J.N. (2000). "Vibration characteristic of functionally graded cylindrical shells under various boundary conditions", Appl. Acoust., 61(1), 119-129.
  41. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded panels using higher-order finiteelement formulation", J. Sound Vib., 318(1-2), 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  42. Shakeri, M., Akhlaghi, M. and Hosseini, S.M. (2006), Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder", J Compos. Struct., 76(1), 174-181. https://doi.org/10.1016/j.compstruct.2006.06.022
  43. Shu, C. (2000), Differential quadrature and its application in engineering. Springer, Berlin.
  44. Sobhani Aragh, B. and Yas, M.H. (2010), "Static and free vibration analyses of continuously graded fiber-reinforced cylindrical shells using generalized power-law distribution", Acta Mech., 215(1), 155-173. https://doi.org/10.1007/s00707-010-0335-4
  45. Sobhani Aragh, B. and Yas, M.H. (2010), "Three dimensional free vibration of functionally graded fiber orientation and volume fraction of cylindrical panels", Mater. Des., 31(9), 4543-4552. https://doi.org/10.1016/j.matdes.2010.03.055
  46. Tahouneh, V. (2014), "Free vibration analysis of bidirectional functionally graded annular plates resting on elastic foundations using differential quadrature method", Struct. Eng. Mech., 52(4), 663-686. https://doi.org/10.12989/sem.2014.52.4.663
  47. Tahouneh, V. (2016), "Using an equivalent continuum model for 3D dynamic analysis of nanocomposite plates", Steel Compos. Struct., 20(3), 623-649. https://doi.org/10.12989/scs.2016.20.3.623
  48. 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
  49. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical cylindrical shell and annular plate structures with a fourparameter power-law distribution", Comput. Meth. Appl. Mech. Eng., 198(37), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011
  50. Tornabene, F. and Ceruti, A. (2013), "Mixed static and dynamic optimization of four-parameter functionally graded completely doubly curved and degenerate shells and panels using GDQ method", Math. Probl. Eng., 1-33.
  51. 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", Composites: Part B, 67(1), 490-509. https://doi.org/10.1016/j.compositesb.2014.08.012
  52. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2016b), "Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes", Composites: Part B, 115(1), 449-476.
  53. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2016a), "Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells", Composites: Part B, 89(1), 187-218. https://doi.org/10.1016/j.compositesb.2015.11.016
  54. Viola, E., and Tornabene, F. (2009), "Free vibrations of threeparameter functionally graded parabolic panels of revolution", Mech. Res. Commun., 36(5), 587-594. https://doi.org/10.1016/j.mechrescom.2009.02.001
  55. 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
  56. Wu, C.P. and Liu, Y.C. (2016), "A state space meshless method for the 3D analysis of FGM axisymmetric circular plates", Steel Compos. Struct., 22(1), 161-182. https://doi.org/10.12989/scs.2016.22.1.161
  57. Yang, J. and Shen, S.H. (2003), "Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels", J. Sound Vib., 261(5), 871-893. https://doi.org/10.1016/S0022-460X(02)01015-5
  58. Yang, R., Kameda, H. and Takada, S. (1998), "Shell model FEM analysis of buried pipelines under seismic loading", Bull Disaster Prev Res. Inst., 38, 115-146.
  59. 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. https://doi.org/10.1016/j.carbon.2005.07.005
  60. Zenkour, A.M. (2005a), "A comprehensive analysis of functionally graded sandwich plates. Part 1-deflection and stresses", Int. J. Solid Struct., 42(1), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
  61. Zenkour, A.M. (2005b), "A comprehensive analysis of functionally graded sandwich plates. Part 1-buckling and free vibration deflection and stresses", Int. J. Solid Struct., 42(18), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016

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