Structural Engineering and Mechanics

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Nonlinear resonance of porous functionally graded nanoshells with geometrical imperfection

  • Wu-Bin Shan (Hunan Electrical College of Technology, School of Elevator Engineering) ;
  • Gui-Lin She (College of Mechanical and Vehicle Engineering, Chongqing University)
  • Received : 2023.04.11
  • Accepted : 2023.11.03
  • Published : 2023.11.25
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Abstract

Employing the non-local strain gradient theory (NSGT), this paper investigates the nonlinear resonance characteristics of functionally graded material (FGM) nanoshells with initial geometric imperfection for the first time. The effective material properties of the porous FGM nanoshells with even distribution of porosities are estimated by a modified power-law model. With the guidance of Love's thin shell theory and considering initial geometric imperfection, the strain equations of the shells are obtained. In order to characterize the small-scale effect of the nanoshells, the nonlocal parameter and strain gradient parameter are introduced. Subsequently, the Euler-Lagrange principle was used to derive the motion equations. Considering three boundary conditions, the Galerkin principle combined with the modified Lindstedt Poincare (MLP) method are employed to discretize and solve the motion equations. Finally, the effects of initial geometric imperfection, functional gradient index, strain gradient parameters, non-local parameters and porosity volume fraction on the nonlinear resonance of the porous FGM nanoshells are examined.

Keywords

References

  1. Affdl, J.C.H. and Kardos, J.L. (1976), "The Halpin-Tsai equations: A review", Polym. Eng. Sci., 16(5), 344-352. http://doi.org/10.1002/pen.760160512.
  2. Alazwari, M.A., Daikh, A.A., Houari, M.S., Tounsi, A. and Eltaher, M.A. (2021), "On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations", Steel. Compos. Struct., 40(3), 389-404. https://doi.org/10.12989/scs.2021.40.3.389.
  3. Belarbi, M.O., Li, L., Houari, M.S.A., Garg, A., Chalak, H.D., Dimitri, R. and Tornabene, F. (2022), "Nonlocal vibration of functionally graded nanoplates using a layerwise theory", Math. Mech. Solid., 27(12), 2634-2661. http://doi.org/10.1177/10812865221078571.
  4. Bezzina, S., Bessaim, A., Houari, M.S.A. and Azab, M. (2022), "A new quasi-3D plate theory for free vibration analysis of advanced composite nanoplates", Steel. Compos. Struct., 45(6), 839-850. http://doi.org/10.12989/scs.2022.45.6.839.
  5. Bouderba, B. and Madjid, B.H. (2022), "Bending analysis of PFGM plates resting on nonuniform elastic foundations and subjected to thermo-mechanical loading", Cogent Eng., 9(1), 2108576. http://doi.org/10.1080/23311916.2022.2108576.
  6. Chen, S.H. and Cheung, Y.K. (1996), "A modified Lindstedt-Poincare method for a strongly nonlinear system with quadratic and cubic nonlinearities", Shock Vib., 3(4), 279-285. http://doi.org/10.1155/1996/231241.
  7. Dehkordi, A.A., Goojani, R.J. and Beni, Y.T. (2022), "Porous flexoelectric cylindrical nanoshell based on the non-classical continuum theory", Appl. Phys. A, 128(6), 478. http://doi.org/10.1007/s00339-022-05584-z.
  8. Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates", Adv. Nano Res., 8(2), 115-134. http://doi.org/10.12989/anr.2020.8.2.115.
  9. Ding, H.X. and She, G.L. (2023a), "Nonlinear resonance of axially moving graphene platelet-reinforced metal foam cylindrical shells with geometric imperfection", Arch. Civil Mech. Eng., 23, 97. https://doi.org/10.1007/s43452-023-00634-6.
  10. Ding, H.X. and She, G.L. (2023b), "Nonlinear primary resonance behavior of graphene platelets reinforced metal foams conical shells under axial motion", Nonlin. Dyn., 111(15), 13723-13752. https://doi.org/10.1007/s11071-023-08564-x.
  11. Ding, H.X., Eltaher, M.A. and She, G.L. (2023), "Nonlinear low-velocity impact of graphene platelets reinforced metal foams cylindrical shell: Effect of spinning motion and initial geometric imperfections", Aerosp. Sci. Technol., 140, 108435. https://doi.org/10.1016/j.ast.2023.108435.
  12. Ding, H.X., She, G.L. and Zhang, Y.W. (2022a), "Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection", Eur. Phys. J. Plus, 137, 1329. https://doi.org/10.1140/epjp/s13360-022-03570-1.
  13. Ding, H.X., Zhang, Y.W. and She, G.L. (2022b), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concrete, 30(6), 433-443. https://doi.org/10.12989/cac.2022.30.6.433.
  14. Eipakchi, H. and Nasrekani, F.M. (2022), "Nonlinear static analysis of composite cylinders with metamaterial core layer, adjustable Poisson's ratio, and non-uniform thickness", Steel. Compos. Struct., 43(2), 241-256. https://doi.org/10.12989/scs.2022.43.2.241.
  15. Eskandary, K., Shishesaz, M. and Moradi, S. (2022), "Buckling analysis of composite conical shells reinforced by agglomerated functionally graded carbon nanotube", Arch. Civil Mech. Eng., 22(3), 132. http://doi.org/10.1007/s43452-022-00440-6.
  16. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. http://doi.org/10.1016/j.ijengsci.2018.08.007.
  17. Gan, L.L. and She, G.L. (2024), "Nonlinear low-velocity impact of magneto-electro-elastic plates with initial geometric imperfection", Acta Astronautica, 214, 11-29. https://doi.org/10.1016/j.actaastro.2023.10.016.
  18. Hadji, L., Avcar, M. and Civalek, O. (2021), "An analytical solution for the free vibration of FG nanoplates", J. Brazil. Soc. Mech. Sci. Eng., 43(9), 418. http://doi.org/10.1007/s40430-021-03134-x.
  19. Hendi, A., Eltaher, M.A, Mohamed, S.A. and Attia, M. (2022). "Nonlinear thermal vibration of pre/post-buckled two-dimensional FGM tapered microbeams based on a higher order shear deformation theory", Steel. Compos. Struct., 41(6), 787-802. http://doi.org/10.12989/scs.2021.41.6.787.
  20. Keleshteri, M.M. and Jelovica, J. (2022a), "Analytical assessment of nonlinear forced vibration of functionally graded porous higher order hinged beams", Compos. Struct., 298, 115994. https://doi.org/10.1016/j.compstruct.2022.115994.
  21. Keleshteri, M.M. and Jelovica, J. (2022b), "Analytical solution for vibration and buckling of cylindrical sandwich panels with improved FG metal foam core", Eng. Struct., 266, 114580. https://doi.org/10.1016/j.engstruct.2022.114580.
  22. 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. http://doi.org/10.12989/anr2020.9.4.237.
  23. Kumar, S. and Jana, P. (2019), "Application of dynamic stiffness method for accurate free vibration analysis of sigmoid and exponential functionally graded rectangular plates", Int. J. Mech. Sci., 163, 105105. https://doi.org/10.1016/j.ijmecsci.2019.105105.
  24. Kumar, S. and Jana, P. (2022), "Accurate solution for free vibration behaviour of stepped FGM plates implementing the dynamic stiffness method", Struct., 45, 1971-1989. https://doi.org/10.1016/j.istruc.2022.10.035.
  25. Kumar, S., Ranjan, V. and Jana, P. (2018), "Free vibration analysis of thin functionally graded rectangular plates using the dynamic stiffness method", Compos. Struct., 197, 39-53. https://doi.org/10.1016/j.compstruct.2018.04.085.
  26. Kumar, Y. and Gupta, A. (2022), "Size-dependent stochastic vibration response of compositionally graded nanoplates with system randomness using nonlocal continuum model with partial support", Arch. Appl. Mech., 92(3), 1053-1081. http://doi.org/10.1007/s00419-021-02092-z.
  27. Li, Q.X., Xie, B.H., Sahmani, S. and Safaei, B. (2020), "Surface stress effect on the nonlinear free vibrations of functionally graded composite nanoshells in the presence of modal interaction", J. Brazil. Soc. Mech. Sci. Eng., 42, 1-18. http://doi.org/10.1007/s40430-020-02317-2.
  28. Li, Q.Y., Wu, D., Chen, X.J., Liu, L., Yu, Y.G. and Gao, W. (2018), "Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler-Pasternak elastic foundation", Int. J. Mech. Sci., 148, 596-610. http://doi.org/10.1016/j.ijmecsci.2018.09.020.
  29. Li, Y.P., She, G.L., Gan, L.L. and Liu, H.B (2023), "Nonlinear thermal post-buckling analysis of graphene platelets reinforced metal foams plates with initial geometrical imperfection", Steel. Compos. Struct., 46(5), 649-658. https://doi.org/10.12989/scs.2023.46.5.649.
  30. Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling 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. Lu, L., Zhu, L., Guo, X.M., Zhao, J.Z. and Liu, G.Z. (2019), "A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells", Appl. Math. Mech., 40(12), 1695-1722. http://doi.org/10.1007/s10483-019-2549-7.
  32. Madjid, B.H. and Bouderba, B. (2022), "Buckling analysis of FGM plate exposed to different loads conditions", Mech. Bas. Des. Struct. Mach., 92, 104485. http://doi.org/10.1080/15397734.2022.2068576.
  33. Mehralian, F. and Beni, Y.T. (2017), "Thermo-electro-mechanical buckling analysis of cylindrical nanoshell on the basis of modified couple stress theory", J. Mech. Sci. Technol., 31, 1773-1787. http://doi.org/10.1007/s12206-017-0325-8.
  34. Mirjavadi, S.S., Forsat, M., Nia, A.F., Badnava, S. and Hamouda, A.M.S. (2020), "Nonlocal strain gradient effects on forced vibrations of porous FG cylindrical nanoshells", Adv. Nano Res., 8(2), 149-156. http://doi.org/10.12989/anr.2020.8.2.149.
  35. Phung-Van, P., Thai, C.H., Nguyen-Xuan, H. and Abdel-Wahab, M. (2019), "An isogeometric approach of static and free vibration analyses for porous FG nanoplates", Eur. J. Mech.-A/Solid., 78, 103851. http://doi.org/10.1016/j.euromechsol.2019.103851.
  36. Rabczuk, T. (2020), "Forced vibration analysis of functionally graded anisotropic nanoplates resting on Winkler/Pasternak-foundation", Comput. Mater. Continua, 62(2), 607-629. http://doi.org/10.32604/cmc.2020.08032.
  37. Rai, S., Kumar, S., Singh, R. and Gupta, A. (2023), "Effect of porosity inclusions on the natural frequencies of the FGM plates using dynamic stiffness method", Int. J. Interact. Des. Manuf., 17, 2723-2730. https://doi.org/10.1007/s12008-022-01170-y.
  38. Salari, E. and Vanini, S.A.S. (2022), "Nonlocal nonlinear static/dynamic snap-through buckling and vibration of thermally post-buckled imperfect functionally graded circular nanoplates", Wave. Random Complex Media, 1-47. http://doi.org/10.1080/17455030.2022.2055810.
  39. Salehipour, H., Shahsavar, A. and Civalek, O. (2019), "Free vibration and static deflection analysis of functionally graded and porous micro/nanoshells with clamped and simply supported edges", Compos. Struct., 221, 110842. http://doi.org/10.1016/j.compstruct.2019.04.014.
  40. Shakouri, P., Ghazavi, M.R., Shahgholi, M. and Mohamadi, A. (2022), "Linear dynamic analysis of axially moving cylindrical nanoshells considering surface energy effect with constant velocity", Acta Mechanica, 233(10), 4231-4246. http://doi.org/10.1007/s00707-022-03310-7.
  41. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stress., 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323.
  42. She, G.L. and Ding, H.X. (2023), "Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Acta Mechanica Sinica, 39, 522392. https://doi.org/10.1007/s10409-022-22392-x.
  43. She, G.L. and Li, Y.P. (2022), "Wave propagation in an FG circular plate in thermal environment", Geomech. Eng., 31(6), 615-622. https://doi.org/10.12989/gae.2022.31.6.615.
  44. She, G.L., Ding, H.X. and Zhang, Y.W. (2022), "Wave propagation in a FG circular plate via the physical neutral surface concept", Struct. Eng. Mech., 82(2), 225-232. https://doi.org/10.12989/sem.2022.82.2.225.
  45. 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.
  46. Van Tuyen, B. (2022), "Free vibration behaviors of nanoplates resting on viscoelastic medium", Arab. J. Sci. Eng., 1-14. http://doi.org/10.1007/s13369-022-07500-2.
  47. Vinh, P.V. and Tounsi, A. (2022), "Free vibration analysis of functionally graded doubly curved nanoshells using nonlocal first-order shear deformation theory with variable nonlocal parameters", Thin Wall. Struct., 174, 109084. http://doi.org/10.1016/j.tws.2022.109084.
  48. Vinh, P.V., Tounsi, A. and Belarbi, M.O. (2023), "On the nonlocal free vibration analysis of functionally graded porous doubly curved shallow nanoshells with variable nonlocal parameters", Eng. Comput., 39, 835-855. https://doi.org/10.1007/s00366-022-01687-6.
  49. Wei, H. and Mohammadi, R. (2021), "Hygro-thermo-mechanical bending and vibration analysis of the CNTRC doubly curved nanoshells with thickness stretching based on nonlocal strain gradient theory", Eur. Phys. J. Plus, 136, 1-23. http://doi.org/10.1140/epjp/s13360-021-01337-8.
  50. Wu, F. and She, G.L. (2023), "Wave propagation in double nano-beams in thermal environments using the Reddy's high-order shear deformation theory", Adv. Nano Res., 14(6), 495-506. https://doi.org/10.12989/anr.2023.14.6.495.
  51. Xiao, J. and Wang, J. (2022), "Nonlinear vibration of FGM sandwich nanoplates with surface effects", Acta Mechanica Solida Sinica, 36(2), 274-281. http://dx.doi.org/10.1007/s10338-022-00371-y.
  52. Xu, J.Q. and She, G.L. (2022), "Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection", Geomech. Eng., 31(3), 329-337. https://doi.org/10.12989/gae.2022.31.3.329.
  53. Xu, J.Q. and She, G.L. (2023a), "Thermal post-buckling of graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Struct. Eng. Mech., 87(1), 85-94. https://doi.org/10.12989/sem.2023.87.1.085.
  54. Xu, J.Q. and She, G.L. (2023b), "The effects of temperature and porosity on resonance behavior of graphene platelet reinforced metal foams doubly-curved shells with geometric imperfection", Geomech. Eng., 35(1), 81-93. https://doi.org/10.12989/gae.2023.35.1.081.
  55. Xu, J.Q., She, G.L., Li, Y.P. and Gan, L.L. (2023), "Nonlinear resonances of nonlocal strain gradient nanoplates made of functionally graded materials considering geometric imperfection", Steel. Compos. Struct., 47(6), 795-811. https://doi.org/10.12989/scs.2023.47.6.795.
  56. Yang, Y., Hu, Z.L. and Li, X.F. (2021), "Axisymmetric bending and vibration of circular nanoplates with surface stresses", Thin Wall. Struct., 166, 108086. http://doi.org/10.1016/j.tws.2021.108086.
  57. Zeighampour, H. and Shojaeian, M. (2017), "Size-dependent vibration of sandwich cylindrical nanoshells with functionally graded material based on the couple stress theory", J. Brazil. Soc. Mech. Sci. Eng., 39(7), 2789-2800. http://doi.org/10.1007/s40430-017-0770-4.
  58. Zhang, Y.F. and Zhang, F. (2019), "Vibration and buckling of shear deformable functionally graded nanoporous metal foam nanoshells", Nanomater., 9(2), 271. http://doi.org/10.3390/nano9020271.
  59. Zhang, Y.W. and She, G.L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel. Compos. Struct., 42(3), 397-405. https://doi.org/10.12989/scs.2022.42.3.397.
  60. Zhang, Y.W. and She, G.L. (2023a), "Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection", Nonlin. Dyn., 111(7), 6317-6334. https://doi.org/10.1007/s11071-022-08186-9.
  61. Zhang, Y.W. and She, G.L. (2023b), "Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment", Mech. Adv. Mater. Struct., 1-13. https://doi.org/10.1080/15376494.2023.2180556.
  62. Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stress., 45(12), 1029-1042. https://doi.org/10.1080/01495739.2022.2125137.
  63. Zhang, Y.W., Ding, H.X. and She, G.L. (2023a), "Wave propagation in spherical and cylindrical panels reinforced with carbon nanotubes", Steel. Compos. Struct., 46(1), 133-141. https://doi.org/10.12989/scs.2023.46.1.133.
  64. Zhang, Y.W., Ding, H.X., She, G.L. and Tounsi, A. (2023d), "Wave propagation of CNTRC beams resting on elastic foundation based on various higher-order beam theories", Geomech. Eng., 33(4), 381-391. https://doi.org/10.12989/gae.2023.33.4.381.
  65. Zhang, Y.W., She, G.L. and Ding, H.X. (2023b), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. A-Solid., 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887.
  66. Zhang, Y.W., She, G.L. and Eltaher, M.A. (2023d), "Nonlinear transient response of graphene platelets reinforced metal foams annular plate considering rotating motion and initial geometric imperfection", Aerosp. Sci. Technol., 108693. https://doi.org/10.1016/j.ast.2023.108693.
  67. Zhang, Y.W., She, G.L., Gan, L.L. and Li, Y.P. (2023c), "Thermal post-buckling behavior of GPLRMF cylindrical shells with initial geometrical imperfection", Geomech. Eng., 32(6), 615-625. https://doi.org/10.12989/gae.2023.32.6.615.
  68. Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTRC curved nanobeams considering surface effects", Steel. Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.
  69. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Luo, J. (2022a), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel. Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.
  70. Zhao, J.L., She, G.L., Wu, F., Yuan, S.J., Bai, R.Q., Pu, H.Y., Wang, S.L. and Luo, J. (2022b), "Guided waves of porous FG nanoplates with four edges clamped", Adv. Nano. Res., 13(5), 465-474. https://doi.org/10.12989/anr.2022.13.5.465.