DOI QR코드

DOI QR Code

Free vibration analysis of FG porous spherical cap reinforced by graphene platelet resting on Winkler foundation

  • Xiangqian Shen (XiHua University) ;
  • Tong Li (XiHua University) ;
  • Lei Xu (XiHua University) ;
  • Faraz Kiarasi (Department of Mechanical Engineering, University of Eyvanekey) ;
  • Masoud Babaei (Department of Mechanical Engineering, University of Eyvanekey) ;
  • Kamran Asemi (Department of Mechanical Engineering, Islamic Azad University)
  • 투고 : 2022.12.11
  • 심사 : 2023.10.30
  • 발행 : 2024.01.25

초록

In this study, free vibration analysis of FG porous spherical cap reinforced by graphene platelets resting on Winkler-type elastic foundation has been surveyed for the first time. Three different types of porosity patterns are considered for the spherical cap whose two types of porosity patterns in the metal matrix are symmetric and the other one is uniform. Besides, five GPL patterns are assumed for dispersing of GPLs in the metal matrix. Tsai-Halpin and extended rule of the mixture are used to determine the Young modulus and mass density of the shell, respectively. Employing 3D FEM elasticity in conjunction with Hamilton's Principle, the governing motion equations of the structure are obtained and solved. The impact of various parameters including porosity coefficient, various porosity distributions in conjunction with different GPL patterns, the weight fraction of graphene Nano fillers, polar angles and stiffness coefficient of elastic foundation on natural frequencies of FG porous spherical cap reinforced by GPLs have been reported for the first time.

키워드

참고문헌

  1. Akbas, S.D. (2021), "Dynamic analysis of axially functionally graded porous beams under a moving load", Steel Compos. Struct., 39(6), 811-821. https://doi.org/10.12989/scs.2021.39.6.811
  2. Al-Furjan, M.S.H., Habibi, M., Ghabussi, A., Safarpour, H., Safarpour, M. and Tounsi, A. (2021), "Non-polynomial framework for stress and strain response of the FG-GPLRC disk using three-dimensional refined higher-order theory", Eng. Struct., 228, 111496. https://doi.org/10.1016/j.engstruct.2020.111496
  3. Al-Furjan, M.S.H., Habibi, M., Ni, J., Jung, D.W. and Tounsi, A. (2022a), "Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems", Eng. Comput., 38(Suppl 5), 3725-3741. https://doi.org/10.1007/s00366-020-01200-x
  4. Al-Furjan, M.S.H., Habibi, M., Jung, D.W., Sadeghi, S., Safarpour, H., Tounsi, A. and Chen, G. (2022b), "A computational framework for propagated waves in a sandwich doubly curved nanocomposite panel", Eng. Comput., 38(2), 1679-1696. https://doi.org/10.1007/s00366-020-01130-8
  5. Al-Osta, M.A., Saidi, H., Tounsi, A., Al-Dulaijan, S.U., AlZahrani, M.M., Sharif, A. and Tounsi, A. (2021), "Influence of porosity on the hygro-thermo-mechanical bending response of an AFG ceramic-metal plates using an integral plate model", Smart Struct. Syst., 28(4), 499-513. https://doi.org/10.12989/sss.2021.28.4.499
  6. Ansari, R., Hassani, R., Gholami, R. and Rouhi, H. (2021), "Buckling and postbuckling of plates made of FG-GPL-reinforced porous nanocomposite with various shapes and boundary conditions", Int. J. Struct. Stabil. Dyn., 21(5), 2150063. https://doi.org/10.1142/S0219455421500632
  7. Arshid, E., Khorasani, M., Soleimani-Javid, Z., Amir, S. and Tounsi, A. (2021), "Porosity-dependent vibration analysis of FG microplates embedded by polymeric nanocomposite patches considering hygrothermal effect via an innovative plate theory", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-021-01382-y
  8. Artioli, E. and Viola, E. (2006), "Free vibration analysis of spherical caps using a GDQ numerical solution", J. Press. Vessel Technol., 128(3), 370-378. https://doi.org/10.1115/1.2217970
  9. Asadzadeh, Z. and Eslami, M.R. (2018), "Nonlinear axisymmetric, thermally induced vibrations of a functionally graded spherical cap", J. Mech. Eng. Transact. ISME, 20(3), 133-169.
  10. Babaei, M., Kiarasi, F., Hossaeini Marashi, S.M., Ebadati, M., Masoumi, F. and Asemi, K. (2021), "Stress wave propagation and natural frequency analysis of functionally graded graphene platelet-reinforced porous joined conical-cylindrical-conical shell", Waves Random Complex Media, 1-33. https://doi.org/10.1080/17455030.2021.2003478
  11. Bahaadini, R., Saidi, A.R., Arabjamaloei, Z. and Ghanbari-Nejad-Parizi, A. (2019), "Vibration analysis of functionally graded graphene reinforced porous nanocomposite shells", Int. J. Appl. Mech., 11(7), 1950068. https://doi.org/10.1142/S1758825119500686
  12. Barzegar, A.R. and Fadaee, M. (2018), "Thermal vibration analysis of functionally graded shallow spherical caps by introducing a decoupling analytical approach", Appl. Math. Modell., 58, 473-486. https://doi.org/10.1016/j.apm.2018.02.018
  13. Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H. and Al-Zahrani, M.M. (2020), "Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory", Comput. Concr., 26(5), 439-450. http://doi.org/10.12989/cac.2020.26.5.439
  14. Bellifa, H., Chikh, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K. H. and Tounsi, A. (2021), "Influence of porosity on thermal buckling behavior of functionally graded beams", Smart Struct. Syst., 27(4), 719-728. https://doi.org/10.12989/sss.2021.27.4.719
  15. Bouafia, H., Chikh, A., Bousahla, A.A., Bourada, F., Heireche, H., Tounsi, A. and Hussain, M. (2021), "Natural frequencies of FGM nanoplates embedded in an elastic medium", Adv. Nano Res., 11(3), 239-249. http://doi.org/10.12989/anr.2021.11.3.239
  16. Bot, I.K., Bousahla, A.A., Zemri, A., Sekkal, M., Kaci, A., Bourada, F. and Mahmoud, S.R. (2022), "Effects of Pasternak foundation on the bending behavior of FG porous plates in hygrothermal environment", Steel Compos. Struct., 43(6), 821-837. https://doi.org/10.12989/scs.2022.43.6.821
  17. Cuong-Le, T., Nguyen, K. D., Le-Minh, H., Phan-Vu, P., Nguyen-Trong, P. and Tounsi, A. (2022), "Nonlinear bending analysis of porous sigmoid FGM nanoplate via IGA and nonlocal strain gradient theory", Adv. Nano Res., 12(5), 441. https://doi.org/10.12989/anr.2022.12.5.441
  18. Du, Y., Huo, R., Pang, F., Li, S., Huang, Y. and Zhang, H (2019), "Free vibration of spherical cap subjected to various boundary conditions", Adv. Mech. Eng., 11(9), 1687814019879261. https://doi.org/10.1177/1687814019879261
  19. Du, Y., Sun, L., Miao, X., Pang, F., Li, H. and Wang, S. (2019), "A unified formulation for free vibration of spherical cap based on the Ritz method", Shock Vib., 18. https://doi.org/10.1155/2019/7470460
  20. Ebrahimi, F., Seyfi, A., Dabbagh, A. and Tornabene, F. (2019), "Wave dispersion characteristics of porous graphene platelet-reinforced composite shells", Struct. Eng. Mech., 71(1), 99-107. https://doi.org/10.12989/sem.2019.71.1.099
  21. Faghidian, S.A. and Tounsi, A. (2022), "Dynamic characteristics of mixture unified gradient elastic nanobeams", Facta Universitatis, Series Mech. Eng., 20(3), 539-552. https://doi.org/10.22190/FUME220703035F
  22. Flis, J. and Muc, A. (2021), "Influence of coupling effects on analytical solutions of functionally graded (FG) spherical shells of revolution", Rev. Adv. Mater. Sci., 60(1), 761-770. https://doi.org/10.1515/rams-2021-0064
  23. Gao, C., Pang, F., Li, H. and Li, L. (2020), "An approximate solution for vibrations of uniform and stepped functionally graded spherical cap based on Ritz method", Compos. Struct., 233, 111640. https://doi.org/10.1016/j.compstruct.2019.111640
  24. Gautham, B.P. and Ganesan, N. (1992), "Free vibration analysis of thick spherical shells", Comput. Struct., 45(2), 307-313. https://doi.org/10.1016/0045-7949(92)90414-U
  25. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S.R. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38(1), 1. https://doi.org/10.12989/scs.2021.38.1.001
  26. Hadji, M., Bouhadra, A., Mamen, B., Menasria, A., Bousahla, A.A., Bourada, F., Bourada, M., Benrahou, K.H., Tounsi, A. (2023), "Combined influence of porosity and elastic foundation parameters on the bending behavior of advanced sandwich structures", Steel Compos. Struct., 46(1), 1-13. https://doi.org/10.12989/scs.2023.46.1.001
  27. Heidari, F., Taheri, K., Sheybani, M., Janghorban, M. and Tounsi, A. (2021), "On the mechanics of nanocomposites reinforced by wavy/defected/aggregated nanotubes", Steel Compos. Struct., 38(5), 533-545. http://doi.org/10.12989/scs.2021.38.5.533
  28. Huang, Y., Karami, B., Shahsavari, D. and Tounsi, A. (2021), "Static stability analysis of carbon nanotube reinforced polymeric composite doubly curved micro-shell panels", Arch. Civil Mech. Eng., 21(4), 139. https://doi.org/10.1007/s43452-021-00291-7
  29. Katiyar, V., Gupta, A. and Tounsi, A. (2022), "Microstructural/ geometric imperfection sensitivity on the vibration response of geometrically discontinuous bi-directional functionally graded plates (2D-FGPs) with partial supports by using FEM", Steel Compos. Struct., 45(5), 621-640. https://doi.org/10.12989/scs.2022.45.5.621
  30. Khinchi, A. and Sharma, P, (2020), "Free vibration analysis of isotropic spherical cap and FG-spherical cap with cut-out using COMSOL", AIP Conference Proceedings, 2220(1), 130074. https://doi.org/10.1063/5.0001299
  31. Khinchi, A. and Sharma, P. (2019), "Review on vibration analysis of functionally graded material (FGM) spherical shell", 14th ICRTESM, 96-101.
  32. Kiarasi, F., Babaei, M., Mollaei, S., Mohammadi, M. and Asemi, K. (2021), "Free vibration analysis of FG porous joined truncated conical-cylindrical shell reinforced by graphene platelets", Adv. Nano Res., 11(4), 361-380. https://doi.org/10.12989/anr.2021.11.4.361
  33. Kitipornchai, S., Chen, D., and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Des., 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061
  34. Kong, F., Dong, F., Duan, M., Habibi, M., Safarpour, H. and Tounsi, A. (2022), "On the vibrations of the Electrorheological sandwich disk with composite face sheets considering pre and post-yield regions", Thin Wall. Struct., 179, 109631. https://doi.org/10.1016/j.tws.2022.109631
  35. Kumar, Y., Gupta, A. and Tounsi, A. (2021), "Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model", Adv. Nano Res., 11(1), 1. http://doi.org/10.12989/anr.2021.11.1.001
  36. Li, H., Pang, F., Ren, Y., Miao, X. and Ye, K. (2019), "Free vibration characteristics of functionally graded porous spherical shell with general boundary conditions by using first-order shear deformation theory", Thin Wall. Struct., 144, 106331. https://doi.org/10.1016/j.tws.2019.106331
  37. Liu, G., Wu, S., Shahsavari, D., Karami, B. and Tounsi, A. (2022), "Dynamics of imperfect inhomogeneous nanoplate with exponentially-varying properties resting on viscoelastic foundation", Eur. J. Mech. A Solids, 95, 104649. https://doi.org/10.1016/j.euromechsol.2022.104649
  38. Madenci, E. and Ozkilic, Y.O. (2021), "Free vibration analysis of open-cell FG porous beams: Analytical, numerical and ANN approaches", Steel Compos. Struct., 40(2), 157-173. https://doi.org/10.12989/scs.2021.40.2.157
  39. Mangalasseri, A.S., Mahesh, V., Mukunda, S., Mahesh, V., Ponnusami, S.A., Harursampath, D., Tounsi, A. (2023), "Vibration based energy harvesting performance of magneto-electro-elastic beams reinforced with carbon nanotubes", Adv. Nano Res., 14(1), 27-43. https://doi.org/10.12989/anr.2023.14.1.027
  40. Minh, T.Q., Dong, D.T., Duc, V.M., Tien, N.V., Phuong, N.T. and Nam, V.H. (2022), "Nonlinear axisymmetric vibration of sandwich FGM shallow spherical caps with lightweight porous core", In CIGOS 2021, Emerging Technologies and Applications for Green Infrastructure, Springer, Singapore, 203, 381-389. https://doi.org/10.1007/978-981-16-7160-9_38
  41. Mirjavadi, S.S., Forsat, M., Barati, M.R. and Hamouda, A.S. (2021), "Geometrically nonlinear vibration analysis of eccentrically stiffened porous functionally graded annular spherical shell segments", Mech. Based Des. Struct., 50(6), 1-15. https://doi.org/10.1080/15397734.2020.1771729
  42. Moradi-Dastjerdi, R. and Behdinan, K. (2021), "Stress waves in thick porous graphene-reinforced cylinders under thermal gradient environments", Aerosp. Sci. Technol., 110, 106476. https://doi.org/10.1016/j.ast.2020.106476
  43. Nejadi, M.M., Mohammadimehr, M. and Mehrabi, M. (2021), "Free vibration and stability analysis of sandwich pipe by considering porosity and graphene platelet effects on conveying fluid flow", Alexandria Eng. J., 60(1), 1945-1954. https://doi.org/10.1016/j.aej.2020.11.042
  44. Nguyen, Q.H., Nguyen, L.B., Nguyen, H.B. and Nguyen-Xuan, H. (2020), "A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets", Compos. Struct., 245, 112321. https://doi.org/10.1016/j.compstruct.2020.112321
  45. Pang, F., Gao, C., Cui, J., Ren, Y., Li, H. and Wang, H. (2019), "A semianalytical approach for free vibration characteristics of functionally graded spherical shell based on first-order shear deformation theory", Shock Vib., 2019, 18. https://doi.org/10.1155/2019/7352901
  46. Pourjabari, A., Hajilak, Z.E., Mohammadi, A., Habibi, M. and Safarpour, H. (2019), "Effect of porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures", Comput. Math. Appl., 77(10), 2608-2626. https://doi.org/10.1016/j.camwa.2018.12.041
  47. Prakash, T., Singh, M.K. and Ganapathi, M. (2006), "Vibrations and thermal stability of functionally graded spherical caps", Struct. Eng. Mech., 24(4), 447-461. https://doi.org/10.12989/sem.2006.24.4.447
  48. Punera, D. and Kant, T. (2019), "A critical review of stress and vibration analyses of functionally graded shell structures", Compos. Struct., 210, 787-809. https://doi.org/10.1016/j.compstruct.2018.11.084
  49. Ram, K.S. and Babu, T.S. (2002), "Free vibration of composite spherical shell cap with and without a cutout", Comput. Struct., 80(23), 1749-1756. https://doi.org/10.1016/S0045-949(02)00210-9
  50. Rouabhia, A., Chikh, A., Bousahla, A.A., Bourada, F., Heireche, H., Tounsi, A. and Structures, C. (2020), "Physical stability response of a SLGS resting on viscoelastic medium using nonlocal integral first-order theory", Steel Compos. Struct., 37(6), 695-709. https://doi.org/10.12989/scs.2020.37.6.695
  51. Sadd, M.H. (2009). Elasticity: theory, applications, and numerics. Academic Press.
  52. Safarpour, M., Rahimi, A. and Alibeigloo, A. (2020), "Static and free vibration analysis of graphene platelets reinforced composite truncated conical shell, cylindrical shell, and annular plate using theory of elasticity and DQM", Mech. Based Des. Struct., 48(4) 496-524. https://doi.org/10.1016/j.compstruct.2018.03.090
  53. Salehi, M., Gholami, R. and Ansari, R. (2021), "Analytical solution approach for nonlinear vibration of shear deformable imperfect FG-GPLR porous nanocomposite cylindrical shells", Mech. Based Des. Struct., 1-23. https://doi.org/10.1080/15397734.2021.1891096
  54. She, G.L., Liu, H.B. and Karami, B. (2020), "On resonance behavior of porous FG curved nanobeams", Steel Compos. Struct., 36(2), 179-186. https://doi.org/10.12989/scs.2020.36.2.179
  55. Su, Z., Jin, G., Shi, S. and Ye, T. (2014), "A unified accurate solution for vibration analysis of arbitrary functionally graded spherical shell segments with general end restraints", Compos. Struct., 111, 271-284. https://doi.org/10.1016/j.compstruct.2014.01.006
  56. Susmith, A.V. and Ram, K.S. (2019), "Free vibration of functionally graded carbon nanotube reinforced composite spherical shell cap", AIP Conf Proc., 2200(1), 020040. https://doi.org/10.1063/1.5141210
  57. Tao, C. and Dai, T. (2021), "Isogeometric analysis for postbuckling of sandwich cylindrical shell panels with graphene platelet reinforced functionally graded porous core", Compos. Struct., 260, 113258. https://doi.org/10.1016/j.compstruct.2020.113258
  58. Thi Phuong, N., Hoai Nam, V. and Thuy Dong, D. (2020), "Nonlinear vibration of functionally graded sandwich shallow spherical caps resting on elastic foundations by using first-order shear deformation theory in thermal environment", J. Sandw. Struct. Mater., 22(4), 1157-1183. https://doi.org/10.1177/109963621878264
  59. Ton-That, H.L., Nguyen-Van, H. and Chau-Dinh, T. (2021), "A novel quadrilateral element for analysis of functionally graded porous plates/shells reinforced by graphene platelets", Arch. Appl. Mech., 91(6), 2435-2466. https://doi.org/10.1007/s00419-021-01893-6
  60. Van Vinh, P. and Tounsi, A. (2022a), "The role of spatial variation of the nonlocal parameter on the free vibration of functionally graded sandwich nanoplates", Eng. Comput., 38(Suppl 5), 4301-4319. https://doi.org/10.1007/s00366-021-01475-8
  61. Van Vinh, P. and Tounsi, A. (2022b), "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. https://doi.org/10.1016/j.tws.2022.109084
  62. Van Vinh, P., Van Chinh, N. and Tounsi, A. (2022), "Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM", Eur. J. Mech A Solids, 96, 104743. https://doi.org/10.1016/j.euromechsol.2022.104743
  63. Wang, Y.Q., Ye, C. and Zu, J.W. (2019), "Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets", Aerosp. Sci. Technol., 85, 359-370. https://doi.org/10.1016/j.ast.2018.12.022
  64. Yaghoobi, H. and Taheri, F. (2020), "Analytical solution and statistical analysis of buckling capacity of sandwich plates with uniform and non-uniform porous core reinforced with graphene nanoplatelets", Composite Structures., 252, 112700. https://doi.org/10.1016/j.compstruct.2020.112700
  65. Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090
  66. Ye, C. and Wang, Y.Q. (2021), "Nonlinear forced vibration of functionally graded graphene platelet-reinforced metal foam cylindrical shells: Internal resonances", Nonlinear Dyn., 104(3), 2051-2069. https://doi.org/10.1007/s11071-021-06401-7
  67. Ye, T., Jin, G. and Su, Z. (2014), "Three-dimensional vibration analysis of laminated functionally graded spherical shells with general boundary conditions", Compos. Struct., 116, 571-588. https://doi.org/10.1016/j.compstruct.2014.05.046
  68. Zannon, M., Abu-Rqayiq, A. and Al-bdour, A. (2020), "Free vibration frequency of thick FGM spherical shells based on a third-order shear deformation theory", Eur. J. Pure Appl. Math., 13(4), 766-778. https://doi.org/10.29020/nybg.ejpam.v13i4.3826
  69. Zhou, X., Wang, Y. and Zhang, W. (2021), "Vibration and flutter characteristics of GPL-reinforced functionally graded porous cylindrical panels subjected to supersonic flow", Acta Astronautica., 183, 89-100. https://doi.org/10.1016/j.actaastro.2021.03.003
  70. Zhou, Z., Ni, Y., Tong, Z., Zhu, S., Sun, J. and Xu, X. (2019), "Accurate nonlinear buckling analysis of functionally graded porous graphene platelet reinforced composite cylindrical shells", Int. J. Mech. Sci., 151, 537-550. https://doi.org/10.1016/j.ijmecsci.2018.12.012