Structural Engineering and Mechanics

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Investigation of nonlinear free vibration of FG-CNTRC cylindrical panels resting on elastic foundation

  • J.R. Cho (Department of Naval Architecture and Ocean Engineering, Hongik University)
  • Received : 2023.06.08
  • Accepted : 2023.11.15
  • Published : 2023.12.10
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Abstract

Non-linear vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) cylindrical shell panel on elastic foundation have not been sufficiently examined. In this situation, this study aims at the profound numerical investigation of the non-linear vibration response of FG-CNTRC cylindrical panels on Winkler-Pasternak foundation by introducing an accurate and effective 2-D meshfree-based non-linear numerical method. The large-amplitude free vibration problem is formulated according to the first-order shear deformation theory (FSDT) with the von Karman non-linearity, and it is approximated by Laplace interpolation functions in 2-D natural element method (NEM) and a non-linear partial derivative operator HNL. The complex and painstaking numerical derivation on the curved surface and the crucial shear locking are overcome by adopting the geometry transformation and the MITC3+ shell elements. The derived nonlinear modal equations are iteratively solved by introducing a three-step iterative solving technique which is combined with Lanczos transformation and Jacobi iteration. The developed non-linear numerical method is estimated through the benchmark test, and the effects of foundation stiffness, CNT volume fraction and functionally graded pattern, panel dimensions and boundary condition on the non-linear vibration of FG-CNTRC cylindrical panels on elastic foundation are parametrically investigated.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1100924). This work was supported by the 2023 Hongik University Research Fund.

References

  1. Ansari, R., Hasrati, E. and Torabi, J. (2019), "Non-linear vibration response of higher-order shear deformable FG-CNTRC conical shells", Compos. Struct., 222, 110906. https://doi.org/10.1016/j.compstruct.2019.110906.
  2. Arani, A.G., Pourjamshidian, M. and Arefi, M. (2018), "Nonlinear free and forced vibration analysis of sandwich nano-beam with FG-CNTRC face-sheets based on nonlocal strain gradient theory", Smart Struct. Syst., 22(1), 105-120. https://doi.org/10.12989/sss.2018.22.1.105.
  3. Au, F.T.K. and Cheung, Y.K. (1996), "Free vibration and stability analysis of shells by the isoparametric spline finite strip method", Thin Wall. Struct., 24, 53-82. https://doi.org/10.1016/0263-8231(95)00040-2.
  4. Avey, M., Fantuzzi, N., Sofiyev, A.H. and Kuruogdu, N. (2021 "Nonlinear vibration of multilayer shell-type structural elements with double curvature consisting of CNT patterned layers within different theories", Compos. Struct., 275, 114401. https://doi.org/10.1016/j.compstruct.2021.114401.
  5. Avey, M., Fantuzzi, N., Sofiyev, A.H. and Kuruogdu, N. (2022), "Influences of elastic foundations on the nonlinear free vibration of composite shells containing carbon nanotubes within shear deformation theory", Compos. Struct., 236, 115288. https://doi.org/10.1016/j.compstruct.2022.115288.
  6. Bakshi, S.R., Lahiri, D. and Agarwal, A. (2010), "Carbon nanotube reinforced metal matrix composites-A review", Int. Mater. Rev., 55(1), 41-64. https://doi.org/10.1179/095066009X12572530170543.
  7. Chau-Dinh, T. (2023), "Analysis of shell structures by an improved 3-node triangular flat shell element with a bubble function and cell-based smoothing", Thin Wall. Struct., 182, 110222. https://doi.org/10.1016/j.tws.2022.110222.
  8. Cho, J.R. (2022a), "Non-linear free vibration of functionally graded CNT-reinforced composite plates", Compos. Struct., 281, 115101. https://doi.org/10.1016/j.compstruct.2021.115101.
  9. Cho, J.R. (2022b), "Buckling analysis of functionally graded plates resting on elastic foundation by natural element method", Steel Compos. Struct., 44(2), 157-167. https://doi.org/10.12989/scs.2022.44.2.157.
  10. Cho, J.R. and Ahn, Y.J. (2022), "Investigation of mechanical behaviors of functionally graded CNT-reinforced composite plates", Polym., 14, 2664. https://doi.org/10.3390/polym14132664.
  11. Cho, J.R. and Lee, H.W. (2006), "A Petrov-Galerkin natural element method securing the numerical integration accuracy", J. Mech. Sci. Technol., 20(1), 94-109. https://doi.org/10.1007/BF02916204.
  12. Cho, J.R. and Oden, J.T. (1997), "Locking and boundary layer in hierarchical models for thin elastic structures", Comput. Meth. Appl. Mech. Eng., 149, 33-48. https://doi.org/10.1016/S0045-7825(97)00057-1.
  13. Cho, J.R. and Oden, J.T. (2000), "Functionally graded material: a parametric study on thermal-stress characteristics using the Crack-Nicolson-Galerkin scheme", Comput. Meth. Appl. Mech. Eng., 188, 17-38. https://doi.org/10.1016/S0045-7825(99)00289-3.
  14. Curtin, W.A. and Sheldon, B.W. (2004), "CNT-reinforced ceramics and metals", Mater. Today, 7(11), 44-49. https://doi.org/10.1016/S1369-7021(04)00508-5.
  15. Deb Nath, J.M. (1969), "Dynamics of rectangular curved plate", PhD Thesis, Southampton University, UK.
  16. Deniz, A., Fantuzzi, N., Sofiyev, A.H. and Kuruoglu, N. (2021), "Modeling and solution of large amplitude vibration problem of construction elements made of nanocomposites using shear deformation theory", Mater., 14, 3843. https://doi.org/0.3390ma14143843.
  17. Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: Potential and current channenges", Mater. Des., 28, 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022.
  18. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube-reinforced composites", J. Sound Vib., 329, 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020.
  19. Foroutan, K., Ahmadi, H. and Carrera, E. (2019), "Non-linear vibration of imperfect FG-CNTRC cylindrical shell panels under external pressure in the thermal environement", Compos. Struct., 227, 111310. https://doi.org/10.1016/j.compstruct.2019.111310.
  20. Gia Phi, G., Van Hieu, D., Sedighi, H.M. and Sofiyev, A.H. (2022), "Size-dependent nonlinear vibration of functionally graded composite micro-beams reinforced by carbon nanotubes with piezoelectric layers in thermal environments", Acta Mechanica, 233, 2249-2270. https://doi.org/10.1007/s00707-022-03224-4.
  21. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanobute composites", Comput. Mater. Sci., 39, 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011.
  22. Harris, P.J.F. (2001) Carbon Nanotubes and Related Structures: New Materials for the Twenty-first Century, Cambridge University Press.
  23. Hu, N., Fugunaga, H., Lu, C., Kameyama, M. and Yan, B. (2005), "Prediction of elastic properties of carbon nanotube reinforced composites", Proc. R. Soc. A, 461, 1685-1710. https://doi.org/10.1098/rspa.2004.1422.
  24. Kar, V.R. and Panda, S.K. (2016), "Non-linear free vibration of functionally graded doubly curved shear deformable panels using finite element method", J. Vib. Control, 22, 1935-1949. https://doi.org/10.1177/1077546314545102.
  25. Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "Non-linear free vibration of functionally graded carbon nanotube-reinforced composite beams", Compos. Struct., 92(3), 676-683. https://doi.org/10.1016/j.compstruct.2009.09.024.
  26. Lee, H.W., Cho, J.R. and Kim, D.Y. (2020), "Locking-free robust finite element approximation of thin shell-like structures", J. Mech. Sci. Technol., 34(9), 3701-3708. https://doi.org/10.1007/s12206 -020-0822-z.
  27. Lee, P.S. and Bathe, K.J. (2004), "Development of MITC isotropic triangular shell finite elements", Comput. Struct., 82, 945-962. https://doi.org/10.1016/j.compstruc.2004.02.004.
  28. Lee, Y., Lee, P.S. and Bathe, K.J. (2014), "The MITC3+shell finite element and its performance", Comput. Struct., 138, 12-23. https://doi.org/10.1016/j.compstruc.2014.02.005.
  29. Liew, K.M., Pan, Z. and Zhang, L.W. (2020), "The recent progress of functionally graded CNT reinforced composites and structures", Sci. China Phys. Mech. Astronomy, 63(3), 234601. https://doi.org/10.1007/s11433-019-1457-2.
  30. Lyly, M., Stenberg, R. and Vihinen, T. (1993), "A stable bilinear element for the Reissner-mindlin plate model", Comput. Meth. Appl. Mech. Eng., 110, 343-357. https://doi.org/10.1016/0045-7825(93)90214-I.
  31. Meguid, S.A. and Sun, Y. (2004), "On the tensile and shear strength of nano-reinforced composite interfaces", Mater. Des., 25, 289-296. https://doi.org/10.1016/j.matdes.2003.10.018.
  32. Mehar, K. and Panda, S.K. (2016), "Geometrical non-linear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038.
  33. Mirzaei, M. and Kiani, Y. (2017), "Non-linear free vibration of FG-CNT reinforced composite plates", Struct. Eng. Mech., 64(3), 381-390. https://doi.org/10.12989/sem.2017.64.3.381.
  34. Mohammadzadeh-Keleshteri, M., Asadi, H. and Aghdam, M.M. (2017), "Geometrical non-linear free vibration responses of FGCNTRC reinforced composite annular sector plates integrated with piezoelectric layers", Compos. Struct., 171, 100-112. https://doi.org/10.1016/j.compstruct.2017.01.048.
  35. Nguyen, V.T., Nguyen, D.K., Ngo, D.T., Tran, P. and Nguyen, D.C. (2017), "Non-linear dynamic response and vibration of functionally graded nanotubes reinforced composite (FGCNTRC) shear deformable plates with temperature dependence material properties and surrounded on elastic foundations", J. Therm. Stress., 40(10), 1254-1274. https://doi.org/10.1177/1099636219847191.
  36. Nguyen-Thoi, T., Phung-Van, P., Thai-Hoang, C. and Nguyen- Xuan, H. (2013), "A cell-based smoothed discrete shear gap method (CS-DSG3) using triangular elements for static and free vibration analyses of shell structures", Int. J. Mech. Sci., 74, 32-45. https://doi.org/10.1016/j.ijmecsci.2013.04.005.
  37. Ninh, D.G. and Bich, D.H. (2018), "Characteristics of non-linear vibration of nanocomposite cylindrical shells with piezoelectric actuators under thermo-mechanical loads", Aero. Sci. Technol., 77, 595-609. https://doi.org/10.1016/j.ast.2018. 04.008.
  38. Pitkaranta, J. (1992), "The problem of membrane locking in finite element analysis of cylindrical shells", Numner. Math., 61, 523-542. https://doi.org/10.1007/BF01385524.
  39. Shen, H.S. (2009), "Non-linear bending of functionally graded carbon nanotubereinforced composite plates in thermal environments", Compos. Struct., 91, 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026.
  40. Shen, H.S. and Reddy, J.N. (2020), "Large amplitude vibration of FG-CNTRC laminated cylindrical shells with negative Poisson's ratio", Comput. Meth. Appl. Mech. Eng., 360, 112727. https://doi.org/10.1016/j.cma.2019.112727.
  41. Shen, H.S. and Xiang, Y. (2012), "Non-linear vibration of nanotube-reinforced composite cylindrical shells in thermal environements", Comput. Meth. Appl. Mech. Eng., 213-216, 196-205. https://doi.org/10.1016/j.cma.2011.11.025.
  42. Shen, H.S., Xiang, Y., Fan, Y. and Hui, D. (2018), "Non-linear vibration of functionally graded graphene-reinforced composite cylindrical shell panels resting on elastic foundations in thermal environements", Compos. Part B, 136, 177-186. https://doi.org/10.1016/j.compositesb.2017.10.032.
  43. Shen, S.H. and Xiang, Y. (2014), "Non-linear vibration of nanotube-reinforced composite cylindrical shell panels resting on elastic foundations in thermal environments", Compos. Struct., 111, 291-300. https://doi.org/10.1016/j.compstruct.2014.01.010.
  44. Shin, D.K. (1997), "Large amplitude free vibration behavior of doubly curved shallow open shells with simply-supported edges", Comput. Struct., 62(1), 35-49. https://doi.org/10.1016/S0045-7949(96)00215-5.
  45. Sofiyev, A.H. (2019), "Review of research on the vibration and buckling of the FGM conical shells", Compos. Struct., 211, 301-317. https://doi.org/10.1016/j.compstruct.2018.12.047.
  46. Sofiyev, A.H. (2020), "On the vibration and stability behaviors of heterogeneous CNTRC-truncated conical shells under axial load in the context of FSDT", Thin Wall. Struct., 151, 106747. https://doi.org/10.1016/j.tws.2020.106747.
  47. Sofiyev, A.H. (2023), "Nonlinear forced response of doublycurved laminated panels composed of CNT patterned layers within first order shear deformation theory", Thin Wall. Struct., 193, 111227. https://doi.org/10.1016/j.tws.2023.111227.
  48. Sofiyev, A.H., Mammadov, Z., Dimitri, R. and Tornabene, F. (2020), "Vibration analysis of shear deformable carbon nanotubes-based functionally graded conical shells resting on elastic foundation", Math. Meth. Appl. Sci., 2020, 1-16. https://doi.org/10.1002/mma.6674.
  49. Sukumar, N., Moran, B. and Belytschko, T. (1998), "The natural element method in solid mechanics", Int. J. Numer. Meth. Eng., 43(5), 839-887. https://doi.org/10.1002/(SICI)1097-0207(19981115)43:5<839::AID-NME423>3.0.CO;2-R.
  50. Thai, H.T. and Kim, S.E. (2013), "Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation", Int. J. Mech. Sci., 75, 34-44. https://doi.org/10.1016/j.ijmecsci.2013.06.007.
  51. Thostenson, E.T., Ren, Z.F. and Chou, T.W. (2001), "Advances in the science and technology of carbon nanotubes and their composites: a review", Compos. Sci. Technol., 61, 1899-1912. https://doi.org/10.1016/S0266-3538(01)00094-X.
  52. Wang, Z.X. and Shen, S.H. (2011), "Non-linear vibration of nanotube-reinforced composite plates in thermal environments", Comput. Mater. Sci., 50(8), 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005.
  53. Wong, M., Paramsothy, M., Xu, X.J., Ren, Y., Li, S. and Liao, K. (2003), "Physical interactions at carbon-nanotube-polymer interface", Polym., 44, 7757-7764. https://doi.org/10.1016/j.polymer.2003.10.011.
  54. Wuite, J. and Adali, S. (2005), "Deflection and stress behavior of nanocomposite reinforced beams using a multiscale amalysis", Compos. Struct., 71, 388-396. https://doi.org/10.1016/j.compstruct.2005.09.011.