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On vibrations of functionally graded carbon nanotube (FGCNT) nanoplates under moving load

  • Alaa A. Abdelrahman (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University) ;
  • Ismail Esen (Department of Mechanical Engineering, Karabuk University) ;
  • Mohammed Y. Tharwan (Mechanical Engineering Department, Faculty of Engineering, Jazan University) ;
  • Amr Assie (Mechanical Engineering Department, Faculty of Engineering, Jazan University) ;
  • Mohamed A Eltaher (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University)
  • 투고 : 2022.06.08
  • 심사 : 2024.03.07
  • 발행 : 2024.04.25

초록

This article develops a nonclassical size dependent nanoplate model to study the dynamic response of functionally graded carbon nanotube (FGCNT) nanoplates under a moving load. Both nonlocal and microstructure effects are incorporated through the nonlocal strain gradient elasticity theory. To investigate the effect of reinforcement orientation of CNT, four different configurations are studied and analysed. The FGM gradation thorough the thickness direction is simulated using the power law. In the context of the first order shear deformation theory, the dynamic equations of motion and the associated boundary conditions are derived by Hamilton's principle. An analytical solution of the dynamic equations of motion is derived based on the Navier methodology. The proposed model is verified and compared with the available results in the literature and good agreement is found. The numerical results show that the dynamic performance of FGCNT nanoplates could be governed by the reinforcement pattern and volume fraction in addition to the non-classical parameters and the moving load dimensionless parameter. Obtained results are reassuring in design and analysis of nanoplates reinforced with CNTs.

키워드

과제정보

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number ISP23-49.

참고문헌

  1. Abdelrahman, A.A., Esen, I., Ozarpa, C., Shaltout, R., Eltaher, M.A. and Assie, A.E. (2021a), "Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory", Smart Struct. Syst., 28(4), 515-533. https://doi.org/10.12989/sss.2021.28.4.515 
  2. Abdelrahman, A.A., Esen, I., Daikh, A.A. and Eltaher, M.A. (2021b), "Dynamic analysis of FG nanobeam reinforced by carbon nanotubes and resting on elastic foundation under moving load", Mech. Based Des. Struct., 1-24. https://doi.org/10.1080/15397734.2021.1999263 
  3. Abdelrahman, A., Shanab, R.A., Esen, I. and Eltaher, M.A. (2022), "Effect of moving load on dynamics of nanoscale Timoshenko CNTs embedded in elastic media based on doublet mechanics theory", Steel Compos. Struct., 44(2), 255. https://doi.org/10.12989/scs.2022.44.2.255 
  4. Alazwari, M.A., Daikh, A.A. and Eltaher, M.A. (2022), "Novel quasi 3D theory for mechanical responses of FG-CNTs reinforced composite nanoplates", Adv. Nano Res., 12(2), 117. https://doi.org/10.12989/anr.2022.12.2.117 
  5. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Modell., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006 
  6. Ansari, R., Shahabodini, A. and Shojaei, M.F. (2016), "Vibrational analysis of carbon nanotube-reinforced composite quadrilateral plates subjected to thermal environments using a weak formulation of elasticity", Compos. Struct., 139, 167-187. https://doi.org/10.1016/j.compstruct.2015.11.079 
  7. Assie, A., Akbas, S.D., Bashiri, A.H., Abdelrahman, A.A. and Eltaher, M.A. (2021), "Vibration response of perforated thick beam under moving load", Eur. Phys. J. Plus, 136(3), 1-15. https://doi.org/10.1140/epjp/s13360-021-01224-2 
  8. Barati, M.R. (2017), "Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities", Adv. Nano Res., 5(4), 393. https://doi.org/10.12989/anr.2017.5.4.393 
  9. Bouafia, H., Chikh, A., Bousahla, A. A., Bourada, F., Heireche, H., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Hussain, M. (2021), "Natural frequencies of FGM nanoplates embedded in an elastic medium", Adv. Nano Res., 11(3), 239. https://doi.org/10.12989/anr.2021.11.3.239 
  10. Daikh, A.A., Belarbi, M.O., Salami, S.J., Ladmek, M., Belkacem, A., Houari, M.S.A., Ahmed, H.M. and Eltaher, M.A. (2023), "A three-unknown refined shear beam model for the bending of randomly oriented FG-CNT/fiber-reinforced composite laminated beams rested on a new variable elastic foundation", Acta Mechanica, 234(10), 5171-5186. https://doi.org/10.1007/s00707-023-03657-5 
  11. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. http://doi.org/10.12989/sem.2021.80.1.063. 
  12. Drai, A., Daikh, A.A., Belarbi, M.O., Houari, M.S.A., Aour, B., Hamdi, A. and Eltaher, M.A. (2023), "Bending of axially functionally graded carbon nanotubes reinforced composite nanobeams", Adv. Nano Res., 14(3), 211. https://doi.org/10.12989/anr.2023.14.3.211 
  13. Eltaher, M.A., Abdelrahman, A.A. and Esen, I. (2021), "Dynamic analysis of nanoscale Timoshenko CNTs based on doublet mechanics under moving load", Eur. Phys. J. Plus, 136(7), 1-21. https://doi.org/10.1140/epjp/s13360-021-01682-8 
  14. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2020), "Dynamics analysis of timoshenko perforated microbeams under moving loads", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-020-01212-7 
  15. Esen, I., Daikh, A.A. and Eltaher, M.A. (2021a), "Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load", Eur. Phys. J. Plus, 136(4), 1-22. https://doi.org/10.1140/epjp/s13360-021-01419-7 
  16. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2021b), "On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load", Int. J. Mech. Mater. Des., 1-22. https://doi.org/10.1007/s10999-021-09555-9 
  17. Farahmand, H. (2021), "A variational approach for analytical buckling solution of moderately thick microplate using strain gradient theory incorporating two-variable refined plate theory: a benchmark study", J. Brazil. Soc. Mech. Sci. Eng., 43(3), 1-11. https://doi.org/10.1007/s40430-020-02766-9 
  18. Farzam, A. and Hassani, B. (2018), "Thermal and mechanical buckling analysis of FG carbon nanotube reinforced composite plates using modified couple stress theory and isogeometric approach", Compos. Struct., 206, 774-790. https://doi.org/10.1016/j.compstruct.2018.08.030 
  19. Ghorbanpour Arani, A., Rousta Navi, B. and Mohammadimehr, M. (2016), "Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches", Adv. Compos. Mater., 25(5), 423-441. https://doi.org/10.1080/09243046.2015.1052189 
  20. Griebel, M. and Hamaekers, J. (2004), "Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites", Comput. Meth. Appl. Mech. Eng., 193(17-20), 1773-1788. https://doi.org/https://doi.org/10.1016/j.cma.2003.12.025 
  21. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39(2), 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011 
  22. Karami, B. and Karami, S. (2019), "Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials", Adv. Nano Res., 7(1), 51. https://doi.org/10.12989/anr.2019.7.1.051 
  23. 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/https://doi.org/10.1016/j.compstruct.2009.09.024 
  24. Kolahdouzan, F., Mosayyebi, M., Ghasemi, F.A., Kolahchi, R. and Panah, S.R.M. (2020), "Free vibration and buckling analysis of elastically restrained FG-CNTRC sandwich annular nanoplates", Adv. Nano Res., 9(4), 237-250. https://doi.org/10.12989/anr.2020.9.4.237 
  25. Lei, Z. X., Liew, K. M. and Yu, J. L. (2013), "Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method", Compos. Struct., 98, 160-168. https://doi.org/10.1016/j.compstruct.2012.11.006. 
  26. Liew, K.M., Lei, Z.X., Yu, J.L. and Zhang, L. (2014), "Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach", Comput. Meth. Appl. Mech. Eng., 268, 1-17. https://doi.org/10.1016/j.cma.2013.09.001 
  27. Lim, C.W., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001 
  28. Lin, F. and Xiang, Y. (2014), "Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories", Appl. Math. Modell., 38(15-16), 3741-3754. https://doi.org/10.1016/j.apm.2014.02.008 
  29. Liu, H., Zhang, Q., Yang, X. and Ma, J. (2021), "Size-dependent vibration of laminated composite nanoplate with piezo-magnetic face sheets", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-021-01285-y 
  30. Lu, L., She, G.L., and Guo, X. (2021), "Size-dependent post-buckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428. 
  31. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58.  https://doi.org/10.1038/354056a0
  32. Mahesh, V. and Harursampath, D. (2020), "Nonlinear deflection analysis of CNT/magneto-electro-elastic smart shells under multi-physics loading", Mech. Adv. Mater. Struct., 1-25. https://doi.org/10.1080/15376494.2020.1805059 
  33. Mirzaei, M. and Kiani, Y. (2015), "Thermal buckling of temperature dependent FG-CNT reinforced composite conical shells", Aerosp. Sci. Technol., 47, 42-53.  https://doi.org/10.1016/j.ast.2015.09.011
  34. Mirzaei, M. and Kiani, Y. (2016), "Thermal buckling of temperature dependent FG-CNT reinforced composite plates", Meccanica, 51(9), 2185-2201.  https://doi.org/10.1007/s11012-015-0348-0
  35. Mohammadimehr, M., Arshid, E., Alhosseini, S.M.A.R., Amir, S. and Arani, M.R.G. (2019), "Free vibration analysis of thick cylindrical MEE composite shells reinforced CNTs with temperature-dependent properties resting on viscoelastic foundation", Struct. Eng. Mech., 70(6), 683-702. https://doi.org/10.12989/sem.2019.70.6.683 
  36. Mohammadimehr, M. and Mostafavifar, M. (2016), "Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT", Compos. Part B Eng., 94, 253-270. https://doi.org/10.1016/j.compositesb.2016.03.030 
  37. Mohammadimehr, M., Navi, B.R. and Arani, A.G. (2015), "Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671. https://doi.org/10.1016/j.compstruct.2015.05.077 
  38. Mohammadimehr, M., Salemi, M. and Navi, B.R. (2016a), "Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermomechanical loadings using DQM", Compos. Struct., 138, 361-380. https://doi.org/10.1016/j.compstruct.2015.11.055 
  39. Mohammadimehr, M., Navi, B.R. and Arani, A.G. (2016b), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B Eng., 87, 132-148. https://doi.org/10.1016/j.compositesb.2015.10.007 
  40. Mohammadimehr, M., Navi, B.R. and Arani, A.G. (2017), "Dynamic stability of MSGT sinusoidal viscoelastic piezoelectric polymeric FG-SWNT reinforced nanocomposite plate considering surface stress and agglomeration effects under hydro-thermo-electro-magneto-mechanical loadings", Mech. Adv. Mater. Struct, 24(16), 1325-1342. http://doi.org/10.1080/15376494.2016.1227507 
  41. Nguyen, H.X., Nguyen, T.N., Abdel-Wahab, M., Bordas, S.P., Nguyen-Xuan, H. and Vo, T.P. (2017), "A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory", Comput. Meth. Appl. Mech. Eng., 313, 904-940. https://doi.org/10.1016/j.cma.2016.10.002 
  42. Phung-Van, P., Abdel-Wahab, M., Liew, K.M., Bordas, S.P.A. and Nguyen-Xuan, H. (2015), "Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory", Compos. Struct., 123, 137-149. https://doi.org/10.1016/j.compstruct.2014.12.021 
  43. Phung-Van, P., Lieu, Q.X., Nguyen-Xuan, H. and Wahab, M.A. (2017), "Size-dependent isogeometric analysis of functionally graded carbon nanotube-reinforced composite nanoplates", Compos. Struct., 166, 120-135. http://doi.org/10.1016/j.compstruct.2017.01.049. 
  44. Rafiee, M., He, X.Q. and Liew, K.M. (2014), "Non-linear dynamic stability of piezoelectric functionally graded carbon nanotube-reinforced composite plates with initial geometric imperfection", Int. J. Non-Linear Mech., 59, 37-51. https://doi.org/10.1016/j.ijnonlinmec.2013.10.011 
  45. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press.
  46. Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004 
  47. Salari, E., Ashoori, A. and Vanini, S.A.S. (2019), "Porosity-dependent asymmetric thermal buckling of inhomogeneous annular nanoplates resting on elastic substrate", Adv. Nano Res., 7(1), 25. https://doi.org/10.12989/anr.2019.7.1.025 
  48. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stresses, 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323 
  49. She, G.L., Liu, H.B., and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407 
  50. 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 
  51. Shen, H.S. (2011), "Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells", Compos. Struct., 93(8), 2096-2108.  https://doi.org/10.1016/j.compstruct.2011.02.011
  52. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Des., 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048 
  53. Shen, H.S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Meth. Appl. Mech. Eng., 213, 196-205. https://doi.org/10.1016/j.compstruct.2011.02.011 
  54. Shen, H.S. and Zhu, Z. (2012), "Postbuckling of sandwich plates with nanotube-reinforced composite face sheets resting on elastic foundations", Eur. J. Mech. A Solids, 35, 10-21. https://doi.org/10.1016/j.euromechsol.2012.01.005 
  55. Shen, H.S. and Xiang, Y. (2013), "Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments", Eng. Struct., 56, 698-708. https://doi.org/10.1016/j.engstruct.2013.06.002 
  56. Shen, H.S. and Xiang, Y. (2014), "Nonlinear bending of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments", Eng. Struct., 80, 163-172. https://doi.org/10.1016/j.engstruct.2014.08.038 
  57. Thai, C.H., Ferreira, A.J.M., Nguyen-Xuan, H., Nguyen, L.B. and Phung-Van, P. (2021), "A nonlocal strain gradient analysis of laminated composites and sandwich nanoplates using meshfree approach", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-021-01501-9 
  58. Tharwan, M.Y., Daikh, A.A., Assie, A.E., Alnujaie, A. and Eltaher, M.A. (2023), "Refined quasi-3D shear deformation theory for buckling analysis of functionally graded curved nanobeam rested on Winkler/Pasternak/Kerr foundation", Mech. Based Des. Struct. Mach., 1-24. https://doi.org/10.1080/15397734.2023.2270043 
  59. Wattanasakulpong, N. and Ungbhakorn, V. (2013), "Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation", Comput. Mater. Sci., 71, 201-208. https://doi.org/10.1016/j.commatsci.2013.01.028 
  60. Xu, C., Qu, J., Rong, D., Zhou, Z. and Leung, A.Y.T. (2021), "Theory and modeling of a novel class of nanoplate-based mass sensors with corner point supports", Thin Wall. Struct., 159, 107306. https://doi.org/10.1016/j.tws.2020.107306 
  61. Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Press. Vess. Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012 
  62. Zhang, L.W., Liew, K.M. and Reddy, J. (2016), "Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression", Comput. Meth. Appl. Mech. Eng., 298, 1-28. https://doi.org/10.1016/j.cma.2015.09.016 
  63. Zhang, L.W. and Liew, K.M. (2015), "Geometrically nonlinear large deformation analysis of functionally graded carbon nanotube reinforced composite straight-sided quadrilateral plates", Comput. Meth. Appl. Mech. Eng., 295, 219-239. https://doi.org/10.1016/j.cma.2015.07.006 
  64. Zhang, L.W., Song, Z.G. and Liew, K.M. (2015), "State-space Levy method for vibration analysis of FG-CNT composite plates subjected to in-plane loads based on higher-order shear deformation theory", Compos. Struct., 134, 989-1003. https://doi.org/10.1016/j.compstruct.2015.08.138 
  65. Zhang, Y.Y., Wang, Y.X., Zhang, X., Shen, H.M., and She, G.L., (2021), "On snap-buckling of FGCNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. http://doi.org/10.12989/scs.2021.38.3.293 
  66. Zhang, Y.W., She, G.L. and Eltaher, M.A. (2023), "Nonlinear transient response of graphene platelets reinforced metal foams annular plate considering rotating motion and initial geometric imperfection", Aerosp. Sci. Technol., 142, 108693. https://doi.org/10.1016/j.ast.2023.108693 
  67. Zhu, P., Lei, Z.X. and Liew, K.M. (2012a), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010 
  68. Zhu, P., Lei, Z.X. and Liew, K.M. (2012b), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010