Geomechanics and Engineering

  • 제16권1호
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  • Pages.1-9
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  • 2018
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  • 2005-307X(pISSN)
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  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

An efficient and simple refined theory for free vibration of functionally graded plates under various boundary conditions

  • Zouatnia, Nafissa (Department of Civil Engineering, Laboratory of Structures, Geotechnics and Risks (LSGR), Hassiba Benbouali University of Chlef) ;
  • Hadji, Lazreg (Department of Civil Engineering, Ibn Khaldoun University) ;
  • Kassoul, Amar (Department of Civil Engineering, Laboratory of Structures, Geotechnics and Risks (LSGR), Hassiba Benbouali University of Chlef)
  • 투고 : 2017.06.01
  • 심사 : 2018.03.06
  • 발행 : 2018.09.20
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper an efficient and simple refined shear deformation theory is presented for the free vibration of Functionally Graded Plates Under Various Boundary Conditions. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. The plates are considered of the type having two opposite sides simply-supported, and the two other sides having combinations of simply-supported, clamped, and free boundary conditions. The mechanical properties of functionally graded material are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived using Hamilton's principle. The results of this theory are compared with those of other shear deformation theories. Various numerical results including the effect of boundary conditions, power-law index, plate aspect ratio, and side-to-thickness ratio on the free vibration of FGM plates are presented.

키워드

참고문헌

  1. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  2. Arani, A.G., Haghparast, E. and Zarei, H.B. (2017), "Vibration analysis of functionally graded nanocomposite plate moving in two directions", Compos. Struct., 23(5), 529-541. https://doi.org/10.12989/scs.2017.23.5.529
  3. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Beg, O.A (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  4. Benahmed, A., Houari, M.S.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 foundation", Geomech. Eng., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009
  5. Benbakhti, A., Bouiadjra, M.B., Retiel, N. and Tounsi, A. (2016), "A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates", Steel Compos. Struct., 22(5), 975-999. https://doi.org/10.12989/scs.2016.22.5.975
  6. Benferhat, R., Hassaine, D., Hadji, L. and Said, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123
  7. Deng, H.Q., Li, T.J., Xue, B.J. and Wang, Z.W. (2015), "Analysis of thermally induced vibration of cable-beam structures", Struct. Eng. Mech., 53(3), 443-453. https://doi.org/10.12989/sem.2015.53.3.443
  8. Farahani, H. and Barati, F. (2015), "Vibration of sumberged functionally graded cylindrical shell based on first order shear deformation theory using wave propagation method", Struct. Eng. Mech., 53(3), 575-587. https://doi.org/10.12989/sem.2015.53.3.575
  9. Gao, Y., Yu, L.Y., Yang, L.Z. and Zhang, L.L. (2015), "The refined theory of 2D quasicrystal deep beams based on elasticity of quasicrystals", Struct. Eng. Mech., 53(3), 411-427. https://doi.org/10.12989/sem.2015.53.3.411
  10. Hadji, L., Zouatnia, N. and Kassoul, A. (2017), "Wave propagation in functionally graded beams using various higher-order shear deformation beams theories", Struct. Eng. Mech., 62(2), 143-149. https://doi.org/10.12989/sem.2017.62.2.143
  11. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  12. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  13. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011b), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure", Compos. Struct., 93(2), 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007
  14. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011a), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", J. Mech. Sci., 53(1), 11-22. https://doi.org/10.1016/j.ijmecsci.2010.10.002
  15. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  16. Merazi, M., Hadji, L., Daouadji, T.H., Tounsi, A. and Adda, B. (2015), "A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position", Geomech. Eng., 8(3), 305-321. https://doi.org/10.12989/gae.2015.8.3.305
  17. Meziane, M.A.A., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  18. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higherorder finite element formulation", J. Sound Vib., 318(1-2), 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  19. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, Florida, U.S.A.
  20. 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
  21. Tahouneh, V. (2014), "Free vibration analysis of bidirectional functionally graded annular plates resting on elastic foundations using differential quadrature method", Struct. Eng. Mech., 52(4), 663-686. https://doi.org/10.12989/sem.2014.52.4.663
  22. Tai, H.T. and Choi, D.H. (2014), "Levy solution for free vibration analysis of functionally graded plates based on a refined plate theory, KSCE J. Civ. Eng., 18(6),1813-1824. https://doi.org/10.1007/s12205-014-0409-2
  23. Tai, H.T. and Kim, S.E. (2011), "Levy-type solution for buckling analysis of orthotropic plates based on two variable refined plate theory", Compos. Struct., 93(7), 1738-1746. https://doi.org/10.1016/j.compstruct.2011.01.012
  24. Tai, H.T. and Kim, S.E. (2012), "Levy-type solution for free vibration analysis of orthotropic plates based on two variable refined plate theory", Appl. Math. Modell., 36(8), 3870-3882. https://doi.org/10.1016/j.apm.2011.11.003
  25. Vel, S.S. and Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272(3-5), 703-730. https://doi.org/10.1016/S0022-460X(03)00412-7

피인용 문헌

  1. Forced vibration of a functionally graded porous beam resting on viscoelastic foundation vol.24, pp.1, 2018, https://doi.org/10.12989/gae.2021.24.1.091