Advances in materials Research

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Effect of porosity on the free vibration analysis of various functionally graded sandwich plates

  • Saad, Mohamed (Department of Mechanical Engineering, University of Tiaret) ;
  • Hadji, Lazreg (Department of Mechanical Engineering, University of Tiaret) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • Received : 2020.11.24
  • Accepted : 2021.09.19
  • Published : 2021.12.25
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Abstract

In this paper, a simple refined shear deformation theory which eliminates the use of a shear correction factor was presented for free vibration analysis of FG sandwich plates composed of FG porous face sheets and an isotropic homogeneous core. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. Material properties of FGM layers are assumed to vary continuously across the plate thickness according to either power-law function in terms of the volume fractions of the constituents. The face layers are considered to be FG porous across each face thickness while the core is made of a ceramic homogeneous layer. Four models of porosity distribution are proposed. Governing equations and boundary conditions are derived from Hamilton's principle. Analytical solutions were obtained for free vibration analysis of square sandwich plates with FG porous layers under various boundary conditions. Numerical results are presented to show the effect of the porosity volume fraction, type of porosity distribution model, side to thickness ratio, lay-up scheme, and boundary conditions on the free vibration of FG sandwich plates. The validity of the present theory is investigated by comparing some of the present results with other published results.

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References

  1. Ahmadi, I. (2017), "A Galerkin layerwise formulation for three-dimensional stress analysis in long sandwich plates", Steel Compos. Struct., Int. J., 24(5), 523-536. https://doi.org/10.12989/scs.2017.24.5.523
  2. Akbas, S.D. (2017), "Vibration and static analysis of functionally graded porous plates", J. Appl. Computat. Mech., 3(3),199-207. https://doi.org/10.22055/JACM.2017.21540.1107
  3. Ashoori, A.R., Vanini, S.A.S. and Salari, E. (2017), "Size-dependent axisymmetric vibration of functionally graded circular plates in bifurcation/limit point instability", Appl. Phys. A, 123, 226. https://doi.org/10.1007/s00339-017-0825-5
  4. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  5. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2021), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216
  6. Daikh, A.A. and Zenkour, A.M. (2019), "Effect of porosity on the bending analysis of various functionally graded sandwich plates", Mater. Res. Express, 6(6), 065703. https://doi.org/10.1088/2053-1591/ab0971
  7. Delale, F. and Erdogan, F. (1983), "The crack problem for a nonhomogeneous plane", J. Appl. Mech., 50(6), 609-614. https://doi.org/10.1115/1.3167098
  8. Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng., 2016. https://doi.org/10.1155/2016/9561504
  9. Ebrahimi, F. and Salari, E. (2016), "Thermal loading effects on electro-mechanical vibration behavior of piezoelectrically actuated inhomogeneous size-dependent Timoshenko nanobeams", Adv. Nano Res., Int. J., 4(3), 197-228. https://doi.org/10.12989/anr.2016.4.3.197
  10. Ebrahimi, F. and Salari, E. (2017), "Semi-analytical vibration analysis of functionally graded size-dependent nanobeams with various boundary conditions", Smart Struct. Syst., Int. J., 19(3), 243-257. https://doi.org/10.12989/sss.2017.19.3.243
  11. 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., 18, 1850013. https://doi.org/10.1142/S021945541850013X
  12. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311(1-2), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018
  13. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443
  14. Salari, E. and Vanini, S.A.S. (2021), "Investigation of thermal preloading and porosity effects on the nonlocal nonlinear instability of FG nanobeams with geometrical imperfection", Eur. J. Mech.-A/Solids, 86, 104183. https://doi.org/10.1016/j.euromechsol.2020.104183
  15. Salari, E., Ashoori, A. and Vanini, S.A.S. (2019), "Porosity-dependent asymmetric thermal buckling of inhomogeneous annular nanoplates resting on elastic substrate", Adv. Nano Res., Int. J., 7(1), 25-38. https://doi.org/10.12989/anr.2019.7.1.025
  16. Salari, E., Vanini, S.A.S., Ashoori, A.R. and Akbarzadeh, A.H. (2020), "Nonlinear thermal behavior of shear deformable FG porous nanobeams with geometrical imperfection: Snap-through and postbuckling analysis", Int. J. Mech. Sci., 178, 105615. https://doi.org/10.1016/j.ijmecsci.2020.105615
  17. 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
  18. 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
  19. Taati, E. and Fallah, F. (2019), "Exact solution for frequency response of sandwich microbeams with functionally graded cores", J. Vib. Control, 25(19-20), 2641-2655. https://doi.org/10.1177/1077546319864645
  20. Wang, Z., Ruiken, A., Jacobs, F. and Ziegler, M. (2014), "A new suggestion for determining 2D porosities in DEM studies", Geomech. Eng., Int. J., 7(6), 665-678. https://doi.org/10.12989/gae.2014.7.6.665
  21. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  22. Wu, D., Liu, A., Huang, Y., Huang, Y., Pi, Y. and Gao, W. (2018), "Dynamic analysis of functionally graded porous structures through finite element analysis", Eng. Struct., 165, 287-301. https://doi.org/10.1016/j.engstruct.2018.03.023
  23. 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", Composite Structures, 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090
  24. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. J. Solids Struct., 42, 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016
  25. Zouatnia, N., Hadji, L. and Kassoul, A. (2017), "An analytical solution for bending and vibration responses of functionally graded beams with porosities", Wind Struct., Int. J., 25(4), 329-342. https://doi.org/10.12989/was.2017.25.4.329