Earthquakes and Structures

  • 제10권5호
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  • Pages.1033-1048
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  • 2016
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  • 2092-7614(pISSN)
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  • 2092-7622(eISSN)
테크노프레스 (Techno-Press)
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Free vibration analysis of FG plates resting on the elastic foundation and based on the neutral surface concept using higher order shear deformation theory

  • 투고 : 2015.10.28
  • 심사 : 2015.12.02
  • 발행 : 2016.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

An analytical solution based on the neutral surface concept is developed to study the free vibration behavior of simply supported functionally graded plate reposed on the elastic foundation by taking into account the effect of transverse shear deformations. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain obtained by using a new refined shear deformation theory. The foundation is described by the Winkler-Pasternak model. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power law formulation, and the Poisson ratio is held constant. The equation of motion for FG rectangular plates resting on elastic foundation is obtained through Hamilton's principle. Numerical examples are provided to show the effect of foundation stiffness parameters presented for thick to thin plates and for various values of the gradient index, aspect and side to thickness ratio. It was found that the proposed theory predicts the fundamental frequencies very well with the ones available in literature.

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참고문헌

  1. Ait Amar Meziane, M., 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. Sandwich Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  2. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  3. Akavci, S.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676. https://doi.org/10.1016/j.compstruct.2013.10.019
  4. Akhavan, H., Hosseini-Hashemi, S.H., Rokni, Damavandi, Taher, H., Alibeigloo, A. and Vahabi, S.H. (2009), "Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation", Part II Freq. Anal. Comput. Mater. Sci., 44(3), 951-961. https://doi.org/10.1016/j.commatsci.2008.07.001
  5. 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
  6. 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", Composites: Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  7. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  8. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2014), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  9. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  10. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  11. Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810. https://doi.org/10.1007/s11012-013-9827-3
  12. Ferreira, A.J.M., Batra, R.C., Roque, C.M.C., Qian, L.F. and Martins, P.A.L.S. (2005), "Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method", Compos. Struct., 69(4), 449-457. https://doi.org/10.1016/j.compstruct.2004.08.003
  13. Hadji, L., Daouadji, T.H., Tounsi, A. and Adda Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519. https://doi.org/10.12989/scs.2014.16.5.507
  14. 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
  15. Hassen, A., Abdelouahed, T., Ismail, M. and El Abbas, A.B. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mater. Des., 6(2), 113-121. https://doi.org/10.1007/s10999-010-9110-x
  16. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., ASCE, 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  17. Hien, T.D., Thuan, N.V. and Hyuk, C.N. (2014), "Eigen analysis of functionally graded beams with variable cross-section resting on elastic supports and elastic foundation", Struct. Eng. Mech., 52(5), 1033-1049. https://doi.org/10.12989/sem.2014.52.5.1033
  18. Hosseini-Hashemi, S.H., Rokni, H., Damavandi, Taher., Akhavan, H. and Omidi, M. (2010), "Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory", Appl. Math. Model., 34(5), 1276-1291. https://doi.org/10.1016/j.apm.2009.08.008
  19. Hosseini-Hashemi, Sh., Fadaee, M., Rokni, Damavandi and 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(2), 708-727. https://doi.org/10.1016/j.apm.2010.07.028
  20. Joodaky, A., Iman, J., Mohammad, H., Reza, M. and Ehsan, B.F. (2013), "Deflection and stress analysis of thin FGM skew plates on Winkler foundation with various boundary conditions using extended Kantorovich method", Composites Part B, 51, 191-196. https://doi.org/10.1016/j.compositesb.2013.03.010
  21. Kamran, A., Manouchehr, S. and Mojtaba, S. (2014), "Three dimensional static and dynamic analysis of two dimensional functionally graded annular sector plates", Struct. Eng. Mech., 51(6), 1067-1089. https://doi.org/10.12989/sem.2014.51.6.1067
  22. Kerr, A.D. (1964), "Elastic and viscoelastic foundation models", J. Appl. Mech., ASME, 31(3), 491-498. https://doi.org/10.1115/1.3629667
  23. Koizumi, M. (1997), "FGM activities in Japan", Composites Part B, 28(1), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9
  24. Leissa, A.W. (1973), "The Free vibration of rectangular plates", J. Sound Vib., 31(3), 257-293. https://doi.org/10.1016/S0022-460X(73)80371-2
  25. Liu, F.L. and Liew, K.M. (1999), "Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method", J. Sound Vib., 225(5), 915-934. https://doi.org/10.1006/jsvi.1999.2262
  26. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  27. Mantari, J.L. and Guedes Soares, C. (2012), "Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory", Compos. Struct., 94(6), 1991-2000. https://doi.org/10.1016/j.compstruct.2012.01.005
  28. Matsunaga, H. (2000), "Vibration and stability of thick plates on elastic foundations", J. Eng. Mech., 126(1), 27-34. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(27)
  29. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higherorder deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  30. Nagino, H., Mikami, T. and Mizusawa, T. (2008), "Three-dimensional free vibration analysis of isotropic rectangular plates using the B-spline Ritz method", J. Sound Vib., 317(1), 329-353. https://doi.org/10.1016/j.jsv.2008.03.021
  31. Park, Jae-Sang and Ji-Hwan, Kim (2006), "Thermal postbuckling and vibration analyses of functionally graded plates", J. Sound Vib., 289(1), 77-93. https://doi.org/10.1016/j.jsv.2005.01.031
  32. Pasternak, P.L. (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants", Cosudarstrennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture Moscow USSR, 1-56. (in Russian)
  33. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramicmetal plates", Int. J. Solid. Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  34. Ramirez, F., Paul, R.H. and Ernian, P. (2006), "Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach", Composite Part B, 37(1), 10-20. https://doi.org/10.1016/j.compositesb.2005.05.009
  35. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J Numer. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  36. Senthil, S.V. and Batra, R.C. (2002), "Exact solution for thermoelastic deformations of functionally graded thick rectangular plates", AIAA J., 40(7), 1421-1433. https://doi.org/10.2514/2.1805
  37. Shufrin, I. and Eisenberger, M. (2005), "Stability and vibration of shear deformable plates-first order and higher order analyses", Int. J. Solid. Struct., 42(3), 1225-1251. https://doi.org/10.1016/j.ijsolstr.2004.06.067
  38. Talha, Mohammad and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034
  39. Thai, H.T. and Dong-Ho, C. (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
  40. Thai, H.T. and Choi, D.H. (2012), "A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation", Composites Part B, 43(5), 2335-2347. https://doi.org/10.1016/j.compositesb.2011.11.062
  41. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aero. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  42. Xiang, Y., Wang, C.M. and Kitipornchai S. (1994), "Exact vibration solution for initially stressed Mindlin plates on Pasternak foundation", Int. J. Mech. Sci., 36(4), 311-316. https://doi.org/10.1016/0020-7403(94)90037-X
  43. Zhang, D.G. and Zhou, Y.H. (2008), "A theoretical analysis of FGM thin plates based on physical neutral surface", Comput. Mater. Sci., 44(2), 716-720. https://doi.org/10.1016/j.commatsci.2008.05.016
  44. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method", J. Sound Vib., 319(3), 918-939. https://doi.org/10.1016/j.jsv.2008.06.025
  45. Zhou, D., Cheung, Y.K., Au, F.T.K. and Lo, S.H. (2002), "Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method", Int. J. Solid. Struct., 39(26), 6339-6353. https://doi.org/10.1016/S0020-7683(02)00460-2
  46. Zhou, D., Cheung, Y.K., Lo, S.H. and Au, F.T.K. (2004), "Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundations", Int. J. Numer. Meth. Eng., 59(10), 1313-1334. https://doi.org/10.1002/nme.915
  47. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aero. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

피인용 문헌

  1. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575