Steel and Composite Structures

  • 재36권6호
  • /
  • Pages.711-727
  • /
  • 2020
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibration of FG-GPLRC spherical shell on two parameter elastic foundation

  • Eyvazian, Arameh (Institute of Research and Development, Duy Tan University) ;
  • Musharavati, Farayi (Department of Mechanical and Industrial Engineering, College of Engineering, Qatar University) ;
  • Talebizadehsardari, Pouyan (Metamaterials for Mechanical, Biomechanical and Multiphysical Applications Research Group, Ton Duc Thang University) ;
  • Sebaey, Tamer A. (Engineering Management Department, College of Engineering, Prince Sultan University)
  • 투고 : 2019.12.08
  • 심사 : 2020.08.24
  • 발행 : 2020.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

In the present research, the free vibration analysis of functionally graded (FG) nanocomposite deep spherical shells reinforced by graphene platelets (GPLs) on elastic foundation is performed. The elastic foundation is assumed to be Winkler-Past ernak-type. It is also assumed that graphaene platelets are randomly oriented and uniformly dispersed in each layer of the nanocomposite shell. Volume fraction of the graphene platelets as nanofillers may be different in the layers. The modified HalpinTsai model is used to approximate the effective mechanical properties of the multilayer nanocomposite. With the aid of the first order shear deformation shell theory and implementing Hamilton's principle, motion equations are derived. Afterwards, the generalized differential quadrature method (GDQM) is utilized to study the free vibration characteristics of FG-GPLRC spherical shell. To assess the validity and accuracy of the presented method, the results are compared with the available researches. Finally, the natural frequencies and corresponding mode shapes are provided for different boundary conditions, GPLs volume fraction, types of functionally graded, elastic foundation coefficients, opening angles of shell, and thickness-to-radius ratio.

키워드

참고문헌

  1. Affdl, J.H. and Kardos, J.L. (1976), "The HalpinTsai equations: a review", Polym. Eng. Sci., 16(5), 344-352. https://doi.org/10.1002/pen.760160512.
  2. Akbarov, S.D., Guliyev, H.H. and Yahnioglu, N. (2016), "Natural vibration of the three-layered solid sphere with middle layer made of FGM: three-dimensional approach", Struct. Eng. Mech., 57(2), 239-263. http://dx.doi.org/10.12989/sem.2016.57.2.239.
  3. Anirudh, B., Ganapathi, M., Anant, C. and Polit, O. (2019), "A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: Bending, vibration and buckling", Compos. Struct., 222, p.110899. https://doi.org/10.1016/j.compstruct.2019.110899.
  4. Ansari, R., Torabi, J. and Shojaei, M.F. (2016), "Vibrational analysis of functionally graded carbon nanotube-reinforced composite spherical shells resting on elastic foundation using the variational differential quadrature method", Eur. J. Mech. A-Solid., 60, 166-182. https://doi.org/10.1016/j.euromechsol.2016.07.003.
  5. Artioli, E. and Viola, E. (2005), "Static analysis of shear-deformable shells of revolution via GDQ method", Struct. Eng. Mech., 19(4), 459-475. https://doi.org/10.12989/sem.2005.19.4.459.
  6. Artioli, E. and Viola, E. (2006), "Free vibration analysis of spherical caps using a GDQ numerical solution", J. Press. Vess-T. Asme., 128(3), 370-378. https://doi.org/10.1115/1.2217970.
  7. Cadelano, E., Palla, P.L., Giordano, S. and Colombo, L., (2009), "Nonlinear elasticity of monolayer graphene", Phys. Rev. Lett., 102(23), p.235502. https://doi.org/10.1103/PhysRevLett.102.235502.
  8. Chandra, Y., Chowdhury, R., Scarpa, F., Adhikari, S., Sienz, J., Arnold, C., Murmu, T. and Bould, D. (2012), "Vibration frequency of graphene based composites: a multiscale approach", Mat. Sci. Eng. B-Adv., 177(3), 303-310. https://doi.org/10.1016/j.mseb.2011.12.024.
  9. Dong, Y.H., Zhu, B., Wang, Y., Li, Y.H. and Yang, J. (2018), "Nonlinear free vibration of graded graphene reinforced cylindrical shells: Effects of spinning motion and axial load", J. Sound. Vib., 437, 79-96. https://doi.org/10.1016/j.jsv.2018.08.036.
  10. Dong, Y.H., Li, Y.H., Chen, D. and Yang, J. (2018), "Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion", Compos. Part. B-Eng., 145, 1-13. https://doi.org/10.1016/j.compositesb.2018.03.009.
  11. Feng, C., Kitipornchai, S. and Yang, J. (2017), "Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs)", Eng. Struct., 140, 110-119. https://doi.org/10.1016/j.engstruct.2017.02.052.
  12. Gao, K., Gao, W., Chen, D. and Yang, J. (2018), "Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation", Compos. Struct., 204, 831-846. https://doi.org/10.1016/j.compstruct.2018.08.013.
  13. Gholami, R. and Ansari, R. (2018), "Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates", Eng. Struct., 156, 197-209. https://doi.org/10.1016/j.engstruct.2017.11.019.
  14. Gholami, R. and Ansari, R. (2019), "Nonlinear stability and vibration of pre/post-buckled multilayer FG-GPLRPC rectangular plates", Appl. Math. Model., 65, 627-660. https://doi.org/10.1016/j.apm.2018.08.038.
  15. Guo, H., Cao, S., Yang, T. and Chen, Y. (2018), "Vibration of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method", Int. J. Mech. Sci., 142, 610-621. https://doi.org/10.1016/j.ijmecsci.2018.05.029.
  16. Javani, M., Kiani, Y., Sadighi, M. and Eslami, M.R. (2019), "Nonlinear vibration behavior of rapidly heated temperature-dependent FGM shallow spherical shells", AIAA. J., 57(9), 4071-4084. https://doi.org/10.2514/1.J058240.
  17. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel. Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693.
  18. Kiani, Y. (2018), "Isogeometric large amplitude free vibration of graphene reinforced laminated plates in thermal environment using NURBS formulation", Comput. Method. Appl. M., 332, 86-101. https://doi.org/10.1016/j.cma.2017.12.015.
  19. Kiani, Y. and Mirzaei, M. (2019), "Isogeometric thermal postbuckling of FG-GPLRC laminated plates", Steel and Compos. Struct., 32(6), 821-832. https://doi.org/10.12989/scs.2019.32.6.821.
  20. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Design., 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.
  21. Kulkarni, Dhaval D., Ikjun Choi, Srikanth S. Singamaneni, and Vladimir V. Tsukruk. (2010) "Graphene oxide- polyelectrolyte nanomembranes", ACS. Nano., 4(8) 4667-4676. https://doi.org/10.1021/nn101204d.
  22. Liu, D., Kitipornchai, S., Chen, W. and Yang, J. (2018), "Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell", Compos. Struct., 189, 560-569. https://doi.org/10.1016/j.compstruct.2018.01.106.
  23. Malekzadeh, P., Setoodeh, A.R. and Shojaee, M. (2018), "Vibration of FG-GPLs eccentric annular plates embedded in piezoelectric layers using a transformed differential quadrature method", Comput. Method. Appl. M., 340, 451-479. https://doi.org/10.1016/j.cma.2018.06.006.
  24. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.Z. and Koratkar, N. (2009), "Enhanced mechanical properties of nanocomposites at low graphene content", ACS Nano., 3(12), 3884-3890. https://doi.org/10.1021/nn9010472.
  25. Reddy, C.D., Rajendran, S. and Liew, K.M. (2006), "Equilibrium configuration and continuum elastic properties of finite sized graphene", Nanotechnology, 17(3), p.864. https://doi.org/10.1088/0957-4484/17/3/042.
  26. Reddy, J.N. (2006), Theory and analysis of elastic plates and shells, CRC press.
  27. Saidi, A.R., Bahaadini, R. and Majidi-Mozafari, K. (2019), "On vibration and stability analysis of porous plates reinforced by graphene platelets under aerodynamical loading", Compos. Part. B-Eng., 164, 778-799. https://doi.org/10.1016/j.compositesb.2019.01.074.
  28. Scarpa, F., Adhikari, S. and Phani, A.S. (2009), "Effective elastic mechanical properties of single layer graphene sheets", Nanotechnology, 20(6), p.065709. https://doi.org/10.1088/0957-4484/20/6/065709
  29. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V. and Firsov, A.A. (2004), "Electric field effect in atomically thin carbon films", Science, 306(5696), 666-669. https://doi.org/1126/science.1102896. https://doi.org/10.1126/science.1102896
  30. Potts, J.R., Dreyer, D.R., Bielawski, C.W. and Ruoff, R.S. (2011), "Graphene-based polymer nanocomposites", Polymer, 52(1), 5-25. https://doi.org/10.1016/j.polymer.2010.11.042.
  31. Qu, Y., Long, X., Yuan, G. and Meng, G. (2013), "A unified formulation for vibration analysis of functionally graded shells of revolution with arbitrary boundary conditions", Compos. Part. B-Eng., 50, 381-402. https://doi.org/10.1016/j.compositesb.2013.02.028.
  32. Shen, H.S., Lin, F. and Xiang, Y. (2017), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations in thermal environments", Nonlinear. Dynam., 90(2), 899-914. https://doi.org/10.1007/s11071-017-3701-0.
  33. Shen, H.S., Xiang, Y. and Fan, Y., (2019), "Nonlinear vibration of thermally postbuckled FG-GRC laminated beams resting on elastic foundations", Int. J. Struct. Stab. Dy., 25(9), 1507-1520. https://doi.org/10.1142/S0219455419500512.
  34. Shen, H.S., Xiang, Y. and Fan, Y. (2019), "Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations", J. Vib. Control., 19(6), p.1950051. https://doi.org/10.1177/1077546319825671.
  35. Shen, H.S., Xiang, Y. and Lin, F. (2017), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments", Comput. Method. Appl. M., 319, 175-193. https://doi.org/10.1016/j.cma.2017.02.029.
  36. Shen, H.S., Xiang, Y. and Fan, Y. (2017), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical shells in thermal environments", Compos. Struct., 182, 447-456. https://doi.org/10.1016/j.compstruct.2017.09.010.
  37. Shen, H.S., Xiang, Y., Fan, Y. and Hui, D. (2018), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical panels resting on elastic foundations in thermal environments", Compos. Part. B-Eng., 136, 177-186. https://doi.org/10.1016/j.compositesb.2017.10.032.
  38. Song, M., Kitipornchai, S. and Yang, J. (2017), "Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Struct., 159, 579-588. https://doi.org/10.1016/j.compstruct.2016.09.070.
  39. Stankovich, S., Dikin, D.A., Dommett, G.H., Kohlhaas, K.M., Zimney, E.J., Stach, E.A., Piner, R.D., Nguyen, S.T. and Ruoff, R.S. (2006), "Graphene-based composite materials", Nature, 442(7100), p.282. https://doi.org/10.1038/nature04969
  40. Thai, C.H., Ferreira, A.J.M., Tran, T.D. and Phung-Van, P. (2019), "Free vibration, buckling and bending analyses of multilayer functionally graded graphene nanoplatelets reinforced composite plates using the NURBS formulation", Compos. Struct., 220, 749-759. https://doi.org/10.1016/j.compstruct.2019.03.100.
  41. Tornabene, F. and Viola, E. (2007), "Vibration analysis of spherical structural elements using the GDQ method", Comput. Math. Appl., 53(10), 1538-1560. https://doi.org/10.1016/j.camwa.2006.03.039.
  42. Wang, M., Xu, Y.G., Qiao, P. and Li, Z.M. (2019), "A two-dimensional elasticity model for bending and free vibration analysis of laminated graphene-reinforced composite beams", Compos. Struct., 211, 364-375. https://doi.org/10.1016/j.compstruct.2018.12.033.
  43. Wang, Y., Xie, K., Fu, T. and Shi, C. (2019), "Vibration response of a functionally graded graphene nanoplatelet reinforced composite beam under two successive moving masses", Compos. Struct., 209, 928-939. https://doi.org/10.1016/j.compstruct.2018.11.014.
  44. Wang, A., Chen, H., Hao, Y. and Zhang, W. (2018), "Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets", Results. Phys., 9, 550-559. https://doi.org/10.1016/j.rinp.2018.02.062.
  45. Wu, H., Kitipornchai, S. and Yang, J. (2017), "Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates", Mater. Design., 132, 430-441. https://doi.org/10.1016/j.matdes.2017.07.025.
  46. Zhang, Y.Y., Wang, C.M., Cheng, Y. and Xiang, Y. (2011), "Mechanical properties of bilayer graphene sheets coupled by sp3 bonding", Carbon, 49(13), 4511-4517. https://doi.org/10.1016/j.carbon.2011.06.058.
  47. Zhao, X., Zhang, Q., Chen, D. and Lu, P. (2010), "Enhanced mechanical properties of graphene-based poly (vinyl alcohol) composites", Macromolecules, 43(5), 2357-2363. https://doi.org/10.1021/ma902862u.
  48. Zhao, Z., Feng, C., Wang, Y. and Yang, J. (2017), "Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs)", Compos. Struct., 180, 799-808. https://doi.org/10.1016/j.compstruct.2017.08.044.

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