DOI QR코드

DOI QR Code

Strain gradient theory for vibration analysis of embedded CNT-reinforced micro Mindlin cylindrical shells considering agglomeration effects

  • Tohidi, H. (Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University) ;
  • Hosseini-Hashemi, S.H. (Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University) ;
  • Maghsoudpour, A. (Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University) ;
  • Etemadi, S. (Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University)
  • 투고 : 2016.12.27
  • 심사 : 2017.03.30
  • 발행 : 2017.06.10

초록

Based on the strain gradient theory (SGT), vibration analysis of an embedded micro cylindrical shell reinforced with agglomerated carbon nanotubes (CNTs) is investigated. The elastic medium is simulated by the orthotropic Pasternak foundation. The structure is subjected to magnetic field in the axial direction. For obtaining the equivalent material properties of structure and considering agglomeration effects, the Mori-Tanaka model is applied. The motion equations are derived on the basis of Mindlin cylindrical shell theory, energy method and Hamilton's principal. Differential quadrature method (DQM) is proposed to evaluate the frequency of system for different boundary conditions. The effects of different parameters such as CNTs volume percent, agglomeration of CNTs, elastic medium, magnetic field, boundary conditions, length to radius ratio and small scale parameter are shown on the frequency of the structure. The results indicate that the effect of CNTs agglomeration plays an important role in the frequency of system so that considering agglomeration leads to lower frequency. Furthermore, the frequency of structure increases with enhancing the small scale parameter.

키워드

참고문헌

  1. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity", Struct. Eng. Mech., 48(2), 195-205. https://doi.org/10.12989/sem.2013.48.2.195
  2. Alibeigloo, A. (2014), "Free vibration analysis of functionally graded carbon nanotube reinforced composite cylindrical panel embedded in piezoelectric layers by using theory of elasticity", Eur. J. Mech. A/Solids, 44, 104-115. https://doi.org/10.1016/j.euromechsol.2013.10.002
  3. Ansari, R., Gholami, R. and Norouzzadeh, A. (2016), "Sizedependent thermo-mechanical vibration and instability of conveying fluid functionally graded nanoshells based on Mindlin's strain gradient theory", Thin-Wall. Struct., 105, 172-184. https://doi.org/10.1016/j.tws.2016.04.009
  4. Ayatollahi, M.R., Naeemi A.R. and Alishahi, E. (2015), "Effects of mixed contents of carbon nanoreinforcements on the impact resistance of epoxy-based nanocomposites", Struct. Eng. Mech., 56(2), 157-167. https://doi.org/10.12989/sem.2015.56.2.157
  5. Changcheng, D. and Yinghui, L. (2013), "Nonlinear resonance behavior of functionally graded cylindrical shells in thermal environments", Compos. Struct., 102, 164-174. https://doi.org/10.1016/j.compstruct.2013.02.028
  6. Civalek, E. (2016), "Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method", Compos. Part B, 111, 45-59.
  7. Gharib, A., Karimi, M.S. and Ghorbanpour Arani, A. (2016), "Vibration analysis of the embedded piezoelectric polymeric nano-composite panels in the elastic substrate", Compos. Part B, 101, 64-76. https://doi.org/10.1016/j.compositesb.2016.06.077
  8. Gholami, R., Darvizeh, A., Ansari, R. and Sadeghi, F. (2016), "Vibration and buckling of first-order shear deformable circular cylindrical micro-/nano-shells based on Mindlin's strain gradient elasticity theory", Eur. J. Mech. A/Solids, 58, 76-88. https://doi.org/10.1016/j.euromechsol.2016.01.014
  9. Ghorbanpour Arani, A., Kolahchi, R. and Vossough, H. (2012), "Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory", Physica B, 407(21), 4281-4286. https://doi.org/10.1016/j.physb.2012.07.018
  10. Guo, S., He, Y., Liu, D., Lei, J., Shen, L. and Li, Zh. (2016), "Torsional vibration of carbon nanotube with axial velocity and velocity gradient effect", Int. J. Mech. Sci., 119, 88-96. https://doi.org/10.1016/j.ijmecsci.2016.09.036
  11. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58. https://doi.org/10.1038/354056a0
  12. Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032
  13. Kolahchi, R., Safari, M. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
  14. Lei, J., He, Y., Guo, S., Li, Zh. and Liu, D. (2016), "Sizedependent vibration of nickel cantilever microbeams: Experiment and gradient elasticity", AIP Adv., 6(10), 105202. https://doi.org/10.1063/1.4964660
  15. Li, S. and Wang, G. (2008), Introduction to Micromechanics and Nanomechanics, World Scientific Publication, Singapore.
  16. Li, C. (2013), "Size-dependent thermal behaviors of axially traveling nanobeams based on a strain gradient theory", Struct. Eng. Mech., 48(3), 415-434. https://doi.org/10.12989/sem.2013.48.3.415
  17. Li, L. and Hu, Y. (2016), "Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory", Comput. Mat. Sci., 112, 282-288. https://doi.org/10.1016/j.commatsci.2015.10.044
  18. Mirzaei, M. and Kiani, Y. (2016), "Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels", Compos. Struct., 142, 45-56. https://doi.org/10.1016/j.compstruct.2015.12.071
  19. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall. et Mater., 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  20. Paliwal, D., Pandey, R.K. and Nath, T. (1996), "Free vibrations of circular cylindrical shell on Winkler and Pasternak foundations", Int. J. Press. Vessel. Pip., 69(1), 79-89. https://doi.org/10.1016/0308-0161(95)00010-0
  21. Qian, D., Dickey, E.C., Andrews, R. and Rantell, T. (2000), "Load transfer and deformation mechanisms in carbon nanotubepolystyrene composites", Appl. Phy. Lett., 76(20), 2868-2870. https://doi.org/10.1063/1.126500
  22. Qian, D., Wagner, G.J., Liu, W.K., Yu, M.F. and Ruoff, R.S. (2002), "Mechanics of carbon nanotubes", Appl. Mech. Rev., 55(6), 495-533. https://doi.org/10.1115/1.1490129
  23. Razavi, H., Faramarzi Babadi, A. and Tadi Beni, Y. (2016), "Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory", Compos. Struct., 160, 1299-1309.
  24. Reddy, J.N. (2002), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition, CRC Press.
  25. Rogacheva, N. (1988), "Forced vibrations of a piezoceramic cylindrical shell with longitudinal polarization", J. Appl. Math. Mech., 52(5), 641-646. https://doi.org/10.1016/0021-8928(88)90114-1
  26. Saito, R., Dresselhaus, G. and Dresselhaus, M.S. (1998), Physical Properties of Carbon Nanotubes, Imperial College Press, London.
  27. Shen, H.S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Methods Appl. Mech. Eng., 213-216, 196-205. https://doi.org/10.1016/j.cma.2011.11.025
  28. Shen, H.S. and Xiang, Y. (2014), "Nonlinear vibration of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments", Compos. Struct., 111, 291-300. https://doi.org/10.1016/j.compstruct.2014.01.010
  29. Shi, D.L. and Feng, X.Q. (2004), "The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composties", J. Eng. Mat. Tech., ASME, 126, 250-270. https://doi.org/10.1115/1.1751182
  30. Song, Z.G., Zhang, L.W. and Liew, K.M. (2016), "Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments", Int. J. Mech. Sci., 115, 339-347.
  31. Tadi Beni, Y., Mehralian, F. and Razavi, H. (2014), "Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of the modified couple stress theory", Compos. Struct., 120, 65-78.
  32. Yas, M.H., Pourasghar, A., Kamarian, S. and Heshmati, M. (2013), "Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube", Mat. Des., 49, 583-590. https://doi.org/10.1016/j.matdes.2013.01.001
  33. Zeighampour, H. and Tadi Beni, Y. (2014), "Cylindrical thin-shell model based on modified strain gradient theory", Int. J. Eng. Sci., 78, 27-47. https://doi.org/10.1016/j.ijengsci.2014.01.004
  34. Zhang, L.W., Cui W.C. and Liew, K.M. (2015a), "Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges", Int. J. Mech. Sci., 103, 9-21. https://doi.org/10.1016/j.ijmecsci.2015.08.021
  35. Zhang, B., He, Y., Liu, D., Shen, L. and Lei, J. (2015b), "Free vibration analysis of four-unknown shear deformable functionally graded cylindrical microshells based on the strain gradient elasticity theory", Compos. Struct., 119, 578-597. https://doi.org/10.1016/j.compstruct.2014.09.032
  36. Zhang, B., He, Y., Liu, D., Shen, L. and Lei, J. (2015c), "An efficient size-dependent plate theory for bending, buckling and free vibration analyses of functionally graded microplates resting on elastic foundation", Appl. Math. Model., 39(13), 3814-3845. https://doi.org/10.1016/j.apm.2014.12.001