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A novel hyperbolic plate theory including stretching effect for free vibration analysis of advanced composite plates in thermal environments

  • Elmascri, Setti (Department of Civil Engineering, University Abdelhamid Ibn Badis of Mostaganem) ;
  • Bessaim, Aicha (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Taleb, Ouahiba (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Houari, Mohammed Sid Ahmed (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Mohamed, Sekkal (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bernard, Fabrice (Universite Europeenne de Bretagne) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2019.09.26
  • Accepted : 2020.02.17
  • Published : 2020.07.25

Abstract

This paper presents a new hyperbolic shear deformation plate theory including the stretching effect for free vibration of the simply supported functionally graded plates in thermal environments. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The present one has a new displacement field which introduces undetermined integral variables. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equation of motion of the vibrated plate obtained via the classical Hamilton's principle and solved using Navier's steps. The accuracy of the proposed solution is checked by comparing the present results with those available in existing literature. The effects of the temperature field, volume fraction index of functionally graded material, side-to-thickness ratio on free vibration responses of the functionally graded plates are investigated. It can be concluded that the present theory is not only accurate but also simple in predicting the natural frequencies of functionally graded plates with stretching effect in thermal environments.

Keywords

References

  1. Adhikari, B., and Singh, B. N. (2019), "Dynamic response of functionally graded plates resting on two-parameter-based elastic foundation model using a quasi-3D theory", Mech. Based Design Struct. Machines, 1-31. https://doi.org/10.1080/15397734.2018.1555965.
  2. Akbas, S.D. (2017), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207. https://doi.org/10.22055/JACM.2017.21540.1107.
  3. Alibeigloo, A., and Alizadeh, M. (2015), "Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method", J. Mech. Solids, 54, 252-266. https://doi.org/10.1016/j.euromechsol.2015.06.011.
  4. Attia, A., Tounsi, A., Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187.
  5. Berghouti, H., Adda Bedia, E.A. Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  6. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A., Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  7. Carrera, E., Brischetto, S., Cinefra, M., and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B Eng., 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005.
  8. Chakraverty, S., and Pradhan, K. K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Technol., 36, 132-156. https://doi.org/10.1016/j.ast.2014.04.005.
  9. Cui, D. and Hu, H. (2016), "Thermal buckling and natural vibration of a rectangular thin plate with in-plane stick-slip-stop boundaries", J. Vib. Control., 22(7), 1950-1966. https://doi.org/10.1177/1077546314546394.
  10. Daikh, A. A. (2019), "Temperature dependent vibration analysis of functionally graded sandwich plates resting on Winkler/Pasternak/Kerr foundation", Mater. Res. Express, 6(6), 065702. https://doi.org/10.1088/2053-1591/ab097b.
  11. Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., Int. J., 18(2), 395-408. https://doi.org/10.12989/scs.2015.18.2.395.
  12. Darilmaz, K., Aksoylu, M.G. and Durgun, Y. (2015), "Buckling analysis of functionally graded material grid systems", Struct. Eng. Mech., Int. J., 54(5), 877-890. https://doi.org/10.12989/sem.2015.54.5.87.
  13. Draiche, K., Bousahla, A. A., Tounsi, A., Alwabli, A. S., Tounsi, A., and Mahmoud, S. R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.36.
  14. Ebrahimi, F. (2013), "Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment", Mech. Adv. Mater. Struct., 20(10), 854-870. https://doi.org/10.1080/15376494.2012.677098.
  15. Ebrahimi, F., Jafari, A. (2016), "Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., 59(2), 343-371. https://doi.org/10.12989/sem.2016.59.2.34.
  16. El Meiche, N., Tounsi, A., Ziane, N., and Mechab, I. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004.
  17. Fazzolari, F. A. (2016), "Modal characteristics of P-and S-FGM plates with temperature-dependent materials in thermal environment", J. Thermal Stress., 39(7), 854-873. https://doi.org/10.1080/01495739.2016.1189772.
  18. Huang, X. L., Shen, H. S. (2004), "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments". International Journal of Solids and Structures., 41(9), 2403-2427. https://doi.org/10.1016/j.ijsolstr.2003.11.012.
  19. Joshi, P. V., Jain, N. K., Ramtekkar, G. D., and Virdi, G. S. (2016), "Vibration and buckling analysis of partially cracked thin orthotropic rectangular plates in thermal environment", Thin Wall. Struct., 109, 143-158. https://doi.org/10.1016/j.tws.2016.09.020.
  20. Kant, T. (1993), "A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches", Compos. Struct., 23(4), 293-312. https://doi.org/10.1016/0263-8223(93)90230-N.
  21. Kant, T., and Swaminathan, K. (2001), "Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories", Journal of Sound and Vibration., 241(2), 319-327. https://doi.org/10.1006/jsvi.2000.3232.
  22. Kar, V.R., Panda, S.K. (2014), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., Int. J., 53(4), 661 - 679. https://doi.org/10.12989/sem.2015.53.4.661.
  23. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693.
  24. Karami, B., Janghorban, M., Shahsavari, D., and Tounsi, A. (2018), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel and Compos. Struct, 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099.
  25. Karami, B., Janghorban, M., Tounsi, A. (2018b), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct, 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.20.
  26. Karami, B., Janghorban, M. and Tounsi, A. (2019a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  27. Karami, B., Shahsavari, D., Janghorban, M., and Tounsi, A. (2019b), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets", J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.
  28. Karami, B., Janghorban, M., and Tounsi, A. (2019c), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 70(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
  29. Karami, B., Janghorban, M. and Tounsi, A. (2019d), "On exact wave propagation analysis of triclinic material using three-dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487.
  30. Khalili, S. M. R., and Mohammadi, Y. (2012), "Free vibration analysis of sandwich plates with functionally graded face sheets and temperature-dependent material properties: A new approach", European J. Mech.-A/Solids, 35, 61-74. https://doi.org/10.1016/j.euromechsol.2012.01.003.
  31. Khiloun, M., Bousahla, A. A., Kaci, A., Bessaim, A., Tounsi, A., and Mahmoud, S. R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput, 1-15. https://doi.org/10.1007/s00366-019-00732-1.
  32. Kim, Y. W. (2005), "Temperature dependent vibration analysis of functionally graded rectangular plates", J. Sound Vib., 284(3-5), 531-549. https://doi.org/10.1016/j.jsv.2004.06.043.
  33. Kolahchi, R., Bidgoli, A.M.M. and Heydari, M.M. (2015), "Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., Int. J., 55(5), 1001-1014. https://doi.org/10.12989/sem.2015.55.5.1001.
  34. Lashkari, M. J. and Rahmani, O. (2016), "Bending analysis of sandwich plates with composite face sheets and compliance functionally graded syntactic foam core", Proceedings of the Institution of Mechanical Engineers, Part C J. Mechanical Engineering Science, 230(20), 3606-3630. https://doi.org/10.1177/0954406215616417.
  35. 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), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018.
  36. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A., Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandwich Struct. Mater., 21(6), 1906-1926. https://doi.org/10.1177/1099636217727577.
  37. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel and Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  38. Mehar, K., and Kumar Panda, S. (2018), "Thermal free vibration behavior of FG-CNT reinforced sandwich curved panel using finite element method", Polymer Compos., 39(8), 2751-2764. https://doi.org/10.1002/pc.24266.
  39. Neves, A. M. A., Ferreira, A. J. M., Carrera, E., Cinefra, M., Roque, C. M. C., Jorge, R. M. N. and Soares, C. M. (2013), "Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos. Part B Eng., 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  40. Nguyen, T.K. (2015), "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", Int.J.Mech.Mater.Des., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3.
  41. Pandey, S., and Pradyumna, S. (2015), "Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory", Europ. J. Mech. A Solids, 51, 55-66. https://doi.org/10.1016/j.euromechsol.2014.12.001.
  42. Parida, S., and Mohanty, S. C. (2018), "Free Vibration Analysis of Functionally Graded Skew Plate in Thermal Environment Using Higher Order Theory", International Journal of Applied Mechanics, 10(01), 1850007. https://doi.org/10.1142/S1758825118500072.
  43. Shahrjerdi, A., Mustapha, F., Bayat, M. and Majid, D.L.A. (2011), "Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory", J. Mech. Sci. Techol., 25(9), 2195-2209. https://doi.org/10.1007/s12206-011-0610-x.
  44. Taleb, O., Houari, M.S.A ., Bessaim, A., Tounsi, A and Mahmoud, S.R. (2018), "A new plate model for vibration response of advanced composite plates in thermal environment", Struct. Eng. Mech.., Int. J., 18(3), 693-709. https://doi.org/10.12989/sem.2018.67.4.369.
  45. Thai, H. T., and Choi, D. H. (2013), "A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates", Compos. Struct, 101, 332-340. https://doi.org/10.1016/j.compstruct.2013.02.019.
  46. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Methods Appl. Mech. Eng., 198(37-40), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011
  47. Tu, T. M., Quoc, T. H., and Van Long, N. (2019), "Vibration analysis of functionally graded plates using the eight-unknown higher order shear deformation theory in thermal environments", Aerosp. Sci. Technol., 84, 698-711. https://doi.org/10.1016/j.ast.2018.11.010.
  48. Van Long, N., Quoc, T. H., and Tu, T. M. (2016), "Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite-element method", J. Adv. Struct. Eng., 8(4), 391-399. https://doi.org/10.1007/s40091-016-0140-y.
  49. 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.
  50. Wattanasakulpong, N., Prusty, G. B., and Kelly, D. W. (2013), "Free and forced vibration analysis using improved third-order shear deformation theory for functionally graded plates under high temperature loading", J. Sandwich Struct. Mater., 15(5), 583-606. https://doi.org/10.1177/1099636213495751.
  51. 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), 2019-2035. https://doi.org/10.1007/s11012-013-9720-0.
  52. Yang, J., Kitipornchai, S., and Liew, K. M. (2003), "Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates", Comput. Methods Appl. Mech. Eng., 192(35-36), 3861-3885. https://doi.org/10.1016/S0045-7825(03)00387-6.
  53. Youzera, H., Meftah, S.A., and Daya, E.M. (2017), "Superharmonic resonance of cross-ply laminates by the method of multiple scales", J. Comput. Nonlinear Dynam., 12(5). https://doi.org/10.1115/1.4036914.
  54. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F., Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389
  55. Zaoui, F. Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations" Compos. Part B Eng., 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.
  56. Zenkour, A. M., and Sobhy, M. (2010), "Thermal buckling of various types of FGM sandwich plates", Compos. Struct, 93(1), 93-102. https://doi.org/10.1016/j.compstruct.2010.06.012.

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