Structural Engineering and Mechanics

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Investigating dynamic response of porous advanced composite plates resting on Winkler/Pasternak/Kerr foundations using a new quasi-3D HSDT

  • Rabhi, Mohamed (Department of Civil Engineering and Hydraulics, Faculty of Technology, University of Saida Dr Moulay Tahar) ;
  • Benrahou, Kouider Halim (Materials and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Yeghnem, Redha (Department of Civil Engineering and Hydraulics, Faculty of Technology, University of Saida Dr Moulay Tahar) ;
  • Guerroudj, Hicham Zakaria (Department of Civil Engineering and Hydraulics, Faculty of Technology, University of Saida Dr Moulay Tahar) ;
  • Kaci, Abdelhakim (Department of Civil Engineering and Hydraulics, Faculty of Technology, University of Saida Dr Moulay Tahar) ;
  • Tounsi, Abdelouahed (Materials and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad)
  • Received : 2022.01.02
  • Accepted : 2022.07.24
  • Published : 2022.09.25
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Abstract

This research investigates the free vibration of porous advanced composite plates resting on Winkler/Pasternak/ Kerr foundations by using a new hyperbolic quasi three dimensional (quasi-3D) shear deformation theory. The present theory, which does not require shear correction factor, accounts for shear deformation and thickness stretching effects by parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate. In this work, we consider imperfect FG plates with porosities embedded within elastic Winkler, Pasternak or Kerr foundations. Implementing an analytical approach, the obtained governing equations from Hamilton's principle according to FG plates are derived. The closed form solutions are obtained by using Navier technique, and natural frequencies of FG plates are found, for simply supported plates, by solving the results of eigenvalue problems. A comprehensive parametric study is presented to evaluate effects of the geometry of material, mode numbers, porosity volume fraction, Power-law index and stiffness of foundations parameters on free vibration characteristics of FG plates.

Keywords

References

  1. Abrate, S. (2008), "Functionally graded plates behave like homogeneous plates", Compos. B Eng., 39, 151-158. https://doi.org/10.1016/j.compositesb.2007.02.026.
  2. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi-3D HSDT", Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.
  3. Ahmed, R.A., Al-Maliki, A.F.H. and Faleh, N.M. (2020), "Dynamic characteristics of multi-phase crystalline porous shells with using strain gradient elasticity", Adv. Nano Res., 8(2), 157-167. https://doi.org/10.12989/anr.2020.8.2.157.
  4. Ait Atmane H., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mat. Des., 6(2), 113-121. https://doi.org/10.1007/s10999-010-9110-x.
  5. Akavci, S.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Stuct., 108, 667-676. https://doi.org/10.1016/j.compstruct.2013.10.019.
  6. Akavci, S.S. and Tanrikulu, A.H. (2015), "Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories", Compos. Part B: Eng., 83, 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043.
  7. Al Khateeb, S.A. and Zenkour, A.M. (2014), "A refined fourunknown plate theory for advanced plates resting on elastic foundations in hygrothermal environment", Compos. Struct., 111, 240-248. https://doi.org/10.1016/j.compstruct.2013.12.033.
  8. Allahkarami, F., Tohidi, H., Dimitri, R. and Tornabene, F. (2020), "Dynamic stability of bi-directional functionally graded porous cylindrical shells embedded in an elastic foundation", Appl. Sci., 10(4), 1345. https://doi.org/10.3390/app10041345.
  9. Ansari, I. Md, Kumar, A., Barnat-Hunek, D. Suchorab, Z. and Kwiatkowski, B. (2019), "Investigation of porosity effect on flexural analysis of doubly curved FGM conoids", Sci. Eng. Compos. Mater., 26(1), 435-448. https://doi.org/10.1515/secm2019-0026.
  10. Arshid, H., Khorasani, M., Soleimani-Javid, Z., Dimitri, R. and Tornabene, F. (2020), "Quasi-3D hyperbolic shear deformation theory for the free vibration study of honeycomb microplates with graphene nanoplatelets-reinforced epoxy skins", Molecul., 25(21), 5085. https://doi.org/10.3390/molecules25215085.
  11. Baferani, A.H., Saidi, A.R and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93, 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020.
  12. Baferani, A.H., Saidi, A.R and Jomehzadeh, E. (2011), "An exact solution for free vibration of thin functionally graded rectangular plates", Proc. Inst. Mech. Eng. Part C 225, 526-536. https://doi.org/10.1243/09544062JMES21.
  13. Bamdad, M., Mohammedimehr, M. and Alambeigi, K. (2020), "Buckling and bending analysis of sandwich Reddy beam considering shape memory alloy wires and porosity resting on Vlasov", Steel Compos. Struct., 36(6), 671-687. https://doi.org/10.12989/scs.2020.36.6.671.
  14. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B: Eng., 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057.
  15. Benahmed, A., Houari, S.M.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi- 3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundations", Geomech. Eng., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009.
  16. Bensaid, I., Bekhadda, A. and Kerboua, B. (2018), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., 6(3), 279-298. https://doi.org/10.12989/anr.2018.6.3.279.
  17. Bensaid, I., Cheikh, A., Mangouchi, A. and Kerboua, B. (2017), "Static deflection and dynamic behavior of higher-order hyperbolic shear deformable compositionally graded beams", Adv. Mater. Res., 6(1), 13-26. https://doi.org/10.12989/amr.2017.6.1.013.
  18. Bensattalah, T., Zidour, M., Tounsi, A. and Adda Bedia, E.A. (2016), "Investigation on thermal and chirality effects on vibration of single-walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories", Mech. Compos. Mater., 52(4), 1-14. https://doi.org/10.1007/s11029-016-9606-z.
  19. Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Adda Bedia, E.A. (2015), "Post-buckling analysis of nanobeams using trigonometric shear deformation theory", Appl. Sci. Report., 10(2), 112-121. https://doi.org/10.15192/PSCP.ASR.2015.10.2.112121.
  20. Chen, C.S., Chen, T.J. and Chien, R.D. (2006), "Nonlinear vibration of initially stressed functionally graded plates", Thin Wall. Struct., 44(8), 844-851. https://doi.org/10.1016/j.tws.2006.08.007.
  21. Daikh, A.A. and Zenkour, A.M. (2020), "Bending of functionally graded sandwich nanoplates resting on Pasternak foundation under different boundary conditions", J. Appl. Comput. Mech., 6, 1245-1249. https://doi.org/10.22055/JACM.2020.33136.2166.
  22. Daikh, A.A. Houari, M.S.A. and Tounsi, A. (2019), "Buckling of porous FGM sandwich nanoplates due to heat conduction via nonlocal strain gradient theory", Eng. Res. Exp., 1, 15-22.
  23. Dastjerdi, S., Malikan, M., Dimitri, R. and Tornabene, F. (2021), "Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment", Compos. Struct., 255, 112925. https://doi.org/10.1016/j.compstruct.2020.112925.
  24. Doan, T.L., Le, P.B., Tran, T.T., Trai, V.K. and Pham, Q.H. (2021), "Free vibration analysis of functionally graded porous nanoplates with different shapes resting on elastic foundation", J. Appl. Comput. Mech., 7(3), 1593-1605. https://doi.org/10.22055/JACM.2021.36181.2807.
  25. Ebrahimi, F. and Seyfi, A. (2020), "Studying propagation of wave in metal foam cylindrical shells with graded porosities resting on variable elastic substrate", Eng. Comput., 38, 379-395. https://doi.org/10.1007/s00366-020-01069-w.
  26. Ebrahimi, F., Jafari, A. and Selvamani, R. (2020), "Thermal buckling analysis of magneto-electro-elastic porous FG beam in thermal environment", Adv. Nano Res., 8(1), 83-94. https://doi.org/10.12989/anr.2020.8.1.083.
  27. Farzam-Rad, S.A., Hassani, B. and Karamodin, A. (2017), "Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface", Compos. Part B Eng., 108, 174-189. https://doi.org/10.1016/j.compositesb.2016.09.029.
  28. Feldman, E. and Aboudi, J. (1997), "Buckling analysis of functionally graded plates subjected to uniaxial loading", Compos. Struct., 38, 29-36. https://doi.org/10.1016/S0263-8223(97)00038-X.
  29. Fenjan, R.M., Faleh, N.M. and Ridha, A.A. (2020), "Strain gradient basic static stability analysis of composite crystalline shell structures having porosities", Steel Compos. Struct., 36(6), 631-642. https://doi.org/10.12989/scs.2020.36.6.631.
  30. Ghandourah, E.E. and Abdraboh, A.M. (2020), "Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models", Steel Compos. Struct., 36(3), 293-305. https://doi.org/10.12989/scs.2020.36.3.293.
  31. Gupta, A. and Talha, M. (2018), "Influence of porosity on the flexural and free vibration responses of functionally graded plates in thermal environment", Int. J. Struct. Stab. Dyn., 38(1), 1-31. https://doi.org/10.1142/S021945541850013X.
  32. Hassaine Daouadji, T. and Hadji, L. (2015), "Analytical solution of nonlinear cylindrical bending for functionally graded plates", Geomech. Eng., 9(5), 631-644. https://doi.org/10.12989/gae.2015.9.5.631.
  33. Hosseini-Hashemi, Sh., Fadaee, M., Rokni Damavandi Taher, H. (2011), "Exact solutions for free flexural vibration of Levy-type rectangular thick plates via third-order shear deformation plate theory", Appl. Math. Model., 35, 708-727. https://doi.org/10.1016/j.apm.2010.07.028.
  34. Javaheri, R. and Eslami, M. (2002), "Buckling of functionally graded plates under in-plane compressive loading", J. Appl. Math. Mech., 82, 277-283. https://doi.org/10.1002/1521-4001(200204)82:4<277::AID-ZAMM277>3.0.CO;2-Y.
  35. Jha, D.K., Kant, T. and Singh, T.K. (2013), "Free vibration response of functionally graded thick plates with shear and normal deformations effects", Compos. Struct., 96, 799-823. https://doi.org/10.1016/j.compstruct.2012.09.034.
  36. Jin, G., Su, Z., Shi, S., Ye, T. and Gao, S. (2014), "Threedimensional exact solution for the free vibration of arbitrarily thick functionally graded plates with general boundary conditions", Compos. Struct., 108, 565-577. https://doi.org/10.1016/j.compstruct.2013.09.051.
  37. Kar, V.R. (2015a), "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.
  38. Kar, V.R. (2015b), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661.
  39. Kar, V.R. and Panda, S.K. (2013), "Free vibration responses of functionally graded spherical shell panels using finite element method", ASME 2013 Gas Turbine India Conference, December.
  40. Kar, V.R. and Panda, S.K. (2014), "Nonlinear free vibration of functionally graded doubly curved shear deformable panels using finite element method", Vib. Control, 22(7), 1935-1945. https://doi.org/10.1177/1077546314545102.
  41. Kar, V.R. and Panda, S.K. (2015a), "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.
  42. Kar, V.R. and Panda, S.K. (2015b), "Thermoelastic analysis of functionally graded doubly curved shell panels using nonlinear finite element method", Compos. Struct., 129, 202-212. https://doi.org/10.1016/j.compstruct.2015.04.006.
  43. Kar, V.R. and Panda, S.K. (2015c), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Lat. Am. J. Solid. Struct., 12(11), 2006-2024. https://doi.org/10.1590/1679-78251691.
  44. Kar, V.R. and Panda, S.K. (2015d), "Effect of temperature on stability behaviour of functionally graded spherical panel", IOP Conf. Ser.: Mater. Sci. Eng., 75(1), 012014. https://doi.org/10.1088/1757-899X/75/1/012014
  45. Kar, V.R. and Panda, S.K. (2016a), "Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties", J. Therm. Stress., 39(8), 942-959. https://doi.org/10.1080/01495739.2016.1188623.
  46. Kar, V.R. and Panda, S.K. (2016b), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115, 318-324. https://doi.org/10.1016/j.ijmecsci.2016.07.014.
  47. Kar, V.R. and Panda, S.K. (2016c), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chin. J. Aeronaut., 29(1), 173-183. https://doi.org/10.1016/j.cja.2015.12.007.
  48. Kar, V.R. and Panda, S.K. (2016d), "Nonlinear thermomechanical behavior of functionally graded material cylindrical/hyperbolic/elliptical shell panel with temperaturedependent and temperature-independent properties", J. Press. Ves. Technol., 138(6), 061202. https://doi.org/10.1115/1.4033701.
  49. Kar, V.R. and Panda, S.K. (2017a), "Postbuckling analysis of shear deformable FG shallow spherical shell panel under nonuniform thermal environment", J. Therm. Stress., 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118.
  50. Kar, V.R. and Panda, S.K. (2017b), "Large-amplitude vibration of functionally graded doubly-curved panels under heat conduction", AIAA J., 55(12), 4376-4386. https://doi.org/10.2514/1.J055878.
  51. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2017), "Effect of different temperature load on thermal postbuckling behaviour of functionally graded shallow curved shell panels", Compos. Struct., 160(15), 1236-1247. https://doi.org/10.1016/j.compstruct.2016.10.125.
  52. Karama, M., Afaq, K.S. and Mistou, S. (2009), "A new theory for laminated composite plates", J. Mater. Des. Appl., 223(2), 53-62. https://doi.org/10.1243/14644207JMDA189.
  53. Karami, B., Jangorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/scs.2017.25.3.361.
  54. Karami, B., Jangorban, M., Shahsavari, D. and Tounsi, A. (2018), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099.
  55. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2020), "free vibration analysis of FG nanoplate with poriferous imperfection in hygrothermal environment", Struct. Eng. Mech., 73(2), 191-207. https://doi.org/10.12989/sem.2020.73.2.191.
  56. Keleshteri, M.M. and Jelovica, J. (2021), "Nonlinear vibration analysis of bidirectional porous beams", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-021-01553-x.
  57. Khaniki, H.B., Ghayesh, M.H., Hussain, S. and Amabili, M. (2020), "Porosity, mass and geometric imperfection sensitivity in coupled vibration characteristics of CNT-strengthened beams with different boundary conditions", Eng. Comput., 38, 2313-2339. https://doi.org/10.1007/s00366-020-01208-3.
  58. Khazaei, P. and Mohammedimehr, M. (2020), "Size dependent effect on deflection and buckling analyses of porous nanocomposite plate based on nonlocal strain gradient theory", Struct. Eng. Mech., 76(1), 27-56. https://doi.org/10.12989/sem.2020.76.1.027.
  59. Kiarasi, F., Babaei, M., Asemi, K., Dimitri, R. and Tornabene, F. (2021), "Three-dimensional buckling analysis of functionally graded saturated porous rectangular plates under combined loading conditions", Appl. Sci., 11(21), 10434. https://doi.org/10.3390/app112110434.
  60. Kneifati, M.C. (1985), "Analysis of Plates on a Kerr foundation model", J. Eng. Mech., 111(11), 1325-1342. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:11(1325).
  61. Koizumi, M. (1993), "The concept of FGM", Ceram. Trans,, 34, 3-10.
  62. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part. B Eng., 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.
  63. Li, J.F., Takagi, K., Ono, M., Pan, M., Watanabe, R., Almajid, A. and Taya, M. (2003), "Fabrication and evaluation of porous piezoelectric ceramics and porosity-graded piezoelectric actuators", J. Am. Ceram. Soc., 86, 1094-1098. https://doi.org/10.1111/j.1151-2916.2003.tb03430.x.
  64. Liang, D., Wu, Q., Lu, X. and Tahouneh, V. (2020), "Vibration behavior of trapezoidal sandwich plate with functionally graded-porous core and graphene platelet-reinforced layers", Steel Compos. Struct., 36(1), 47-62. https://doi.org/10.12989/scs.2020.36.1.47.
  65. Lu, C., Lim, C.W. and Chen, (2009), "Exact solutions for free vibrations of functionally graded thick plates on elastic foundations", Mech. Adv. Mat. Struct., 16, 576-584. https://doi.org/10.1080/15376490903138888.
  66. Madenci, E. (2021), "Free vibration analysis of carbone nanotube RC nanobeams with variational approaches", Adv. Nano Res., 11(2), 157-171. https://doi.org/10.12989/anr.2021.11.2.157.
  67. Madenci, E. and Ozkili, 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.
  68. Mahdavian, M. (2009), "Buckling analysis of simply-supported functionally graded rectangular plates under non-uniform inplane compressive loading", J. Solid. Mech., 1, 213-225.
  69. Mantari, J.L. (2015), "A refined theory with stretching effect for the dynamic analysis of advanced composites on elastic foundation", Mech. Mater., 86, 31-43. https://doi.org/10.1016/j.mechmat.2015.02.010.
  70. Mantari, J.L. (2015), "Refined and generalized hybrid type quasi3D shear deformation theory for the bending analysis of functionally graded shells", Compos. B. Eng., 83, 142-152. https://doi.org/10.1016/j.compositesb.2015.08.048.
  71. Mantari, J.L. and Granados, E.V. (2015), "Free vibration of single and sandwich laminated composite plates by using a simplified FSDT", Compos. Struct., 132, 952-959. https://doi.org/10.1016/j.compstruct.2015.06.035.
  72. Mantari, J.L., Granados, E.V., Hinostroza, M. and Soares, C.G. (2014), "Modelling advanced composite plates resting on elastic foundation by using a quasi-3D hybrid type HSDT", Compos. Struct., 118, 455-471. https://doi.org/10.1016/j.compstruct.2014.07.039.
  73. Mantari, J.L., Oktem, A.S. and Soares, C.G. (2012), "A new Higher order shear deformation theory for sandwich and composite laminated plates", Compos. Part B., 43, 1489-1499. https://doi.org/10.1016/j.compositesb.2011.07.017.
  74. Mehar, K., Panda, S.K., Mahapatra, T.R. (2018), "Nonlinear frequency responses of functionally graded carbon nanotubereinforced sandwich curved panel under uniform temperature field", Int. J. Appl. Mech., 10(3), 1850028. https://doi.org/10.1142/S175882511850028X.
  75. Meksi, A., Benyoucef, S., Houari, M.S.A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215.
  76. Menaa, R., Tounsi, A., Mouaci, F., Mechab, I., Zidi, M. and Adda Bedia, E.A. (2012), "Analytical solutions for static shear correction factor for beams", Mech. Adv. Mater. Struct., 19(8), 641-652. https://doi.org/10.1080/15376494.2011.581409.
  77. Merdaci, S., Mostefa Adda, H., Belghoul, H., Dimitri, R. and Tornabene, F. (2021), "Higher-order free vibration analysis of porous functionally graded plates", J. Compos. Sci., 5(11), 305. https://doi.org/10.3390/jcs5110305.
  78. Mirjavadi, S.S., Forsat, M., Barati, M.R. and Hamouda, A.M.S. (2020), "Post-buckling of higher-order stiffened metal foam curved shells with porosity distributions and geometrical imperfection", Steel Compos. Struct., 35(4), 567-578. https://doi.org/10.12989/scs.2020.35.4.567.
  79. Mirjavadi, S.S., Forsat, M., Nia, A.F., Badvana, 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. https://doi.org/10.12989/anr.2020.8.2.149.
  80. Miyamoto, Y., Kaysser, W.A., Rabin, B.H. and Ford, R.G. (1999), Functionally Graded Materials: Design, Processing and Applications, Kluwer Academic Publishers, London.
  81. Mohammedi, M., Saidi, A.R. and Jomehzadeh, E. (2010), "Levy solution for buckling analysis of functionally graded rectangular plates", Appl. Compos. Mater., 17, 81-93. https://doi.org/10.1007/s10443-009-9100-z.
  82. Mohammedimehr, M. and Meskini, M. (2020), "Analysis of porous micro sandwich plate: free and forced vibration under magneto-electro-elastic loadings", Adv. Nano Res., 8(1), 69-82. https://doi.org/10.12989/anr.2020.8.1.069.
  83. Naveen Kumar, H.S. and Kattimani, S. (2022a), "Effect of different geometrical non-uniformities on nonlinear vibration of porous functionally graded skew plates: A finite element study", Defence Tech., 18(6), 918-936. https://doi.org/10.1016/j.dt.2021.05.002.
  84. Naveen Kumar, H.S. and Kattimani, S. (2022b), "Nonlinear analysis of two-directional functionally graded doubly curved panels with porosities", Struct. Eng. Mech., 82(4), 477-490. https://doi.org/10.12989/sem.2022.82.4.477.
  85. Naveen Kumar, H.S., Kattimani, S. and Nguyen-Thoi, T., (2021), "Influence of porosity distribution on non-linear free vibration and transient responses of porous functionally graded skew plates", Defence Tech., 17(6), 1918-1935. https://doi.org/10.1016/j.dt.2021.02.003.
  86. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N., Mota Soares, C.M. and Araujo, A.L. (2017), "Influence of zig-zag and warping effects on buckling of functionally graded sandwich plates according to sinusoidal shear deformation theories", Mech. Adv. Mater. Struct., 24(5), 360-376. https://doi.org/10.1080/15376494.2016.1191095.
  87. Nguyen, P.C., Pham, Q.H., Tran, T.T. and Nguyen-Thoi, T. (2022), "Effects of partially supported elastic foundation on free vibration of FGP plates using ES-MITC3 elements", Ain Shams Eng. J., 13(3), 101615. https://doi.org/10.1016/j.asej.2021.10.010.
  88. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719.
  89. Reddy, J.N. (2002), Energy Pprinciples and Variational Methods in Applied Mechanics, John Wiley & Sons.
  90. Sahmani, S., Fettahi, A.M. and Amed, N.A. (2020), "Analytical treatment on the local strain gradient vibrational response of postbuckled functionally graded porous micro- nanoplates reinforced with GPL", Eng. Comput., 36, 1559-1578. https://doi.org/10.1007/s00366-019-00782-5.
  91. Shahraki, H, Riahi, H.T., Izadinia, M. and Talaeitaba, S.B. (2019), "Buckling and vibration analysis of FG-CNT-reinforced composite rectangular thick nanoplates resting on Kerr foundation based on nonlocal strain gradient theory", J. Vib. Control, 26(5-6), 277-305. https://doi.org/10.1177/1077546319878976.
  92. Shahsavari, D, Shahsavari, M, Li, L. and Karami, B. (2018), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004.
  93. 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.
  94. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.
  95. Thai, H.T. and Choi, D.H. (2011), "A refined plate theory for functionally graded plates resting on elastic foundation", Compos. Sci. Technol., 71(16), 1850-1858. https://doi.org/10.1016/j.compscitech.2011.08.016.
  96. Tornabene, F., Viscoti, M. and Dimitri, R. (2022), "Generalized higher order layerwise theory for the dynamic study of anisotropic doubly-curved shells with a mapped geometry", Eng. Anal. Bound. Elem., 134, 147-183. https://doi.org/10.1016/j.enganabound.2021.09.017.
  97. Tornabene, F., Viscoti, M., Dimitri, R. and Aiello, M.A. (2021), "Higher order formulations for doubly-curved shell structures with a honeycomb core", Thin Wall. Struct., 164, 107789. https://doi.org/10.1016/j.tws.2021.107789.
  98. Tornabene, F., Viscoti, M., Dimitri, R. and Reddy, J.N. (2021), "Higher order theories for the vibration study of doubly-curved anisotropic shells with a variable thickness and isogeometric mapped geometry", Compos. Struct., 267, 113829. https://doi.org/10.1016/j.compstruct.2021.113829.
  99. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci, 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.
  100. Wang, Y., Tham, L. and Cheung, Y. (2005), "Beams and plates on elastic foundations, A review", Prog. Struct. Eng. Mater., 7, 174-182. https://doi.org/10.1002/pse.202.
  101. Wang, Y.Q. and Zu, J.W. (2017), "Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment", Aerosp. Sci. Technol., 69, 550-562. https://doi.org/10.1016/j.ast.2017.07.023.
  102. Wattanasakulpong, N. (2012), "Free vibration analysis of functionally graded beams with general elastically end constraints by DTM", World J. Mech., 2(6), 297-310. https://doi.org/10.4236/wjm.2012.26036.
  103. Xu, T.F. and Xing, Y.F. (2016), "Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation", Acta Mechanica Sinica, 32(6), 1088-1103. https://doi.org/10.1007/s10409-016-0600-4.
  104. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48(8), 2019-2039. https://doi.org/10.1007/s11012-013-9720-0.
  105. Yan, K., Zhang, Y., Cai, H. and Tahouneh, V. (2020), "Vibrational characteristic of FG porous conical shells using Donnell's shell theory", Steel Compos. Struct., 35(2), 249-260. https://doi.org/10.12989/scs.2020.35.2.249.
  106. Zhang, D.G. and Zhou, Y.H. (2008), "A theoretical analysis of FGM thin plates based on physical neutral surface", Comput. Mater. Sci., 44, 716-720. https://doi.org/10.1016/j.commatsci.2008.05.016.
  107. Zhou, D., Cheung, Y.K., Au, F.T.K. and Lo, S.H. (2002), "Threedimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method", Int. J. Solid. Stuct., 39, 6339-6353. https://doi.org/10.1016/S0020-7683(02)00460-2.
  108. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68, 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2.