Steel and Composite Structures

  • 제23권6호
  • /
  • Pages.657-668
  • /
  • 2017
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

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)
  • 투고 : 2016.10.27
  • 심사 : 2017.02.19
  • 발행 : 2017.04.30
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  1. 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
  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. 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. https://doi.org/10.12989/sem.2015.56.1.085
  4. 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
  5. 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
  6. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: A review", Appl. Mech. Rev., 49, 1-27. https://doi.org/10.1115/1.3101882
  7. 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
  8. 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. https://doi.org/10.1016/j.matdes.2008.03.001
  9. 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. https://doi.org/10.1016/j.matdes.2009.07.025
  10. 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
  11. 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. https://doi.org/10.1016/j.commatsci.2012.05.003
  12. 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. https://doi.org/10.1016/j.compscitech.2005.04.021
  13. 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. https://doi.org/10.1016/j.jsv.2006.05.030
  14. 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. https://doi.org/10.12989/sem.2016.57.2.315
  15. Halpin, J.C. and Tsai, S.W. (1969), "Effects of environmental factors on composite materials", AFML-TR-67-423.
  16. 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
  17. 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. https://doi.org/10.1002/pc.22346
  18. 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. https://doi.org/10.1006/jsvi.1999.2623
  19. 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. https://doi.org/10.1016/0020-7403(95)00062-3
  20. 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. https://doi.org/10.1016/S0045-7825(98)00376-4
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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. https://doi.org/10.1016/j.matdes.2010.04.018
  26. 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. https://doi.org/10.12989/sem.2016.57.3.441
  27. 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. https://doi.org/10.1016/j.cma.2007.06.028
  28. Nie, G.J. and Zhong, Z. (2010), "Dynamic analysis of multidirectional functionally graded annular plates", Appl. Math. Model., 34(3), 608-616. https://doi.org/10.1016/j.apm.2009.06.009
  29. 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
  30. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press Inc., (2nd Revised Edition).
  31. 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
  32. Shu, C. (2000), Differential Quadrature and Its Application in Engineering, Springer, Berlin.
  33. 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. https://doi.org/10.12989/sem.2014.52.4.663
  34. 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
  35. 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.
  36. 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. https://doi.org/10.1002/pc.22818
  37. 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. https://doi.org/10.1016/j.compositesb.2014.08.012
  38. Viola, E. and Tornabene, F. (2009), "Free vibrations of three parameter functionally graded parabolic panels of revolution", Mech. Res. Commun., 36(5), 587-594. https://doi.org/10.1016/j.mechrescom.2009.02.001
  39. 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
  40. 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. https://doi.org/10.1016/j.cma.2004.02.010
  41. 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

피인용 문헌

  1. Free vibration analysis of carbon nanotube RC nanobeams with variational approaches vol.11, pp.2, 2021, https://doi.org/10.12989/anr.2021.11.2.157