Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Eigenfrequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory

  • Guerroudj, Hicham Zakaria (University of SAIDA Dr MOULAY TAHAR, Faculty of Technology, Department of Civil Engineering and Hydraulics) ;
  • Yeghnem, Redha (University of SAIDA Dr MOULAY TAHAR, Faculty of Technology, Department of Civil Engineering and Hydraulics) ;
  • Kaci, Abdelhakim (University of SAIDA Dr MOULAY TAHAR, Faculty of Technology, Department of Civil Engineering and Hydraulics) ;
  • Zaoui, Fatima Zohra (Department of Mechanical Engineering, Faculty of Science and Technology, University of MOSTAGANEM) ;
  • Benyoucef, Samir (Material and Hydrology Laboratory, University of SIDI BEL ABBES) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of SIDI BEL ABBES)
  • Received : 2018.01.14
  • Accepted : 2018.05.10
  • Published : 2018.07.25
⟨ Previous Next ⟩

Abstract

This research investigates the free vibration analysis of advanced composite plates such as functionally graded plates (FGPs) resting on a two-parameter elastic foundations using a hybrid quasi-3D (trigonometric as well as polynomial) higher-order shear deformation theory (HSDT). This present theory, which does not require shear correction factor, accounts for shear deformation and thickness stretching effects by a sinusoidal and parabolic variation of all displacements across the thickness. Governing equations of motion for FGM plates are derived from Hamilton's principle. The closed form solutions are obtained by using Navier technique, and natural frequencies are found, for simply supported plates, by solving the results of eigenvalue problems. The accuracy of the present method is verified by comparing the obtained results with First-order shear deformation theory, and other predicted by quasi-3D higher-order shear deformation theories. It can be concluded that the proposed theory is efficient and simple in predicting the natural frequencies of functionally graded plates on elastic foundations.

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. Abualnour, M., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047
  3. Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined 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
  4. Ait Atmane H. and Tounsi, A. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mat., 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x
  5. 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
  6. Attia, A., Tounsi, A., Adda 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
  7. 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/10.1243/09544062JMES2171
  8. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Brazil. Soc. Mech. Sci. Eng., 38 (1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  9. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "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
  10. 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
  11. 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/s11029-016-9553-8
  12. 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.
  13. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of Functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  14. Boukhari, A., Ait Atmane, H., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  15. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  16. Chen, C.S., Chen, T.J. and Chien, R.D. (2006), "Nonlinear vibration of initially stressed functionally graded plates", Thin-Walled Struct., 44(8), 844-851. https://doi.org/10.1016/j.tws.2006.08.007
  17. 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
  18. 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
  19. Hosseini-Hashemi, Sh., Fadaee, M. and Rokni Damavandi Taher, H. (2011), "Exact solutions for free flexural vibration of Levytype 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
  20. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  21. Javaheri, R. and Eslami, M. (2002), "Buckling of functionally graded plates under in-plane compressive loading", J. Appl. Math. Mech., 82, 277-283.
  22. 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
  23. 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
  24. 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.
  25. 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.
  26. 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
  27. 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
  28. Kar, V.R. and Panda, S.K. (2015c), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment ", Latin Am. J. Solids Struct., 12(11), 2006-2024. https://doi.org/10.1590/1679-78251691
  29. Kar, V.R. and Panda, S.K. (2015d), "Effect of temperature on stability behaviour of functionally graded spherical panel", IOP Conference Series: Materials Science and Engineering, 75(1), 012014. https://doi.org/10.1088/1757-899X/75/1/012014
  30. 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. Stresses, 39(8), 942-959. https://doi.org/10.1080/01495739.2016.1188623
  31. 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.
  32. Kar, V.R. and Panda, S.K. (2016c), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chinese J. Aeronaut., 29(1), 173-183. https://doi.org/10.1016/j.cja.2015.12.007
  33. 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. Pressure Vessel Technol., 138(6), 061202-061202-13.
  34. Kar, V.R. and Panda, S.K. (2017a), "Postbuckling analysis of shear deformable FG shallow spherical shell panel under nonuniform thermal environment", J. Therm. Stresses, 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118
  35. 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
  36. 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
  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. Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Modern Phys. Lett. B, 30(36).
  40. Karami, B., Janghorban, M. and Li, L. (2018), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astraunautica, 143, 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011
  41. Karami, B., Shahsavari, D. and Janghorban, M. (2017), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 1-11.
  42. Karami, B., Shahsavari, D. and Janghorban, M. (2018), "Wave dispersion of mounted graphene with initial stress". Thin-Wall. Struct., 122, 102-111. https://doi.org/10.1016/j.tws.2017.10.004
  43. Khdeir, A.A. and Reddy, J.N. (1999), "Free vibrations of laminated composite plates using second-order shear deformation theory". Compos. Struct., 71, 617-626. https://doi.org/10.1016/S0045-7949(98)00301-0
  44. Koizumi, M. (1993), "The concept of FGM", Ceram. Trans. Func. Grad. Mater., 34, 3-10.
  45. 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
  46. 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
  47. 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
  48. Mahapatra, T.R., Kar, V.R., Panda, S.K. and Mehar, K. (2017), " Nonlinear thermoelastic deflection of temperature-dependent FGM curved shallow shell under nonlinear thermal loading", J. Therm. Stresses, 40(9), 1184-1199. https://doi.org/10.1080/01495739.2017.1302788
  49. Mahdavian, M. (2009), "Buckling analysis of simply-supported functionally graded rectangular plates under non-uniform inplane compressive loading", J. Solid. Mech., 1, 213-225.
  50. 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
  51. 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
  52. 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
  53. Mantari, J.L. (2015), "Refined and generalized hybrid type quasi-3D 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
  54. 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. B. Eng., 43(3), 1489-1499. https://doi.org/10.1016/j.compositesb.2011.07.017
  55. Meftah, A., Bakora, A., Zaoui, F.Z., Tounsi, A. and Adda Bedia, E., (2017), "A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundations", Steel Compos. Struct., 23(3), 317-330. https://doi.org/10.12989/scs.2017.23.3.317
  56. 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
  57. Miyamoto, Y., Kaysser, W.A., Rabin, B.H. and Ford, R.G. (1999), Functionally graded materials: design, processing and applications , London: Kluwer Academic publishers.
  58. 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
  59. Nagino, H., Mikami, T. and Mizusawa, T. (2008), "Threedimensional free vibration analysis of isotropic rectangular plates using using the B-spline Ritz method", J. Sound Vib., 317, 329-353. https://doi.org/10.1016/j.jsv.2008.03.021
  60. Nami, M.R., Janghorban, M. and Damadam, M. (2015), "Thermal buckling analysis of functionally graded rectangular nanoplates based on nonlocal third-order shear deformation theory", Aerosp. Sci. Techno., 41, 7-15. https://doi.org/10.1016/j.ast.2014.12.001
  61. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, CM.M. (2012), "Buckling analysis of sandwich plates with functionally graded skins using a new quasi-3D hyperbolic sine shear deformation theory and collocation with radial basis functions", J. Appl. Math. Mech., 92(9), 749-766.
  62. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N., Mota Soares, C.M., et al. (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
  63. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N., et al. (2012),"A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94(5), 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005
  64. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N., et al. (2012),"A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. B. Eng., 43(2), 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009
  65. Nguyen, K., Thai, H.T. and Vo, T. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., 18 (1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  66. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Method. Eng., 47, 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  67. Reddy, J.N. (2002), "Energy principles and variational methods in applied mechanics", John Wiley & Sons.
  68. Saidi, A.R. and Sahraee, S. (2006), "Axisymmetric solutions of functionally graded circular and annular plates using secondorder shear deformation plate theory", ESDA2006-95699, Proceedings of the 8th Biennial ASME Conference on Engineering Systems Design and Analysis, Torino, Italy.
  69. Shahrjerdi, A. and Mustapha, F. (2011), "Second Order Shear Deformation Theory (SSDT) for Free Vibration Analysis on a Functionally Graded Quadrangle Plate", Recent Advances in Vibrations Analysis, (Ed., Natalie Baddour).
  70. Shahsavari, D., Karami, B. and Mansouri, S. (2018), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech. A-Solid., 67, 200-214. https://doi.org/10.1016/j.euromechsol.2017.09.004
  71. 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
  72. Shimpi, R. and Patel, H. (2006), "Free vibrations of plate using two variable refined plate theory", J. Sound Vib., 296, 979-999. https://doi.org/10.1016/j.jsv.2006.03.030
  73. Shufrin, I. and Eisenberger, M., (2005),"Stability and vibration of shear deformable plates-first order and higher order analyses", Int. J. Solids Struct., 42, 1225-1251. https://doi.org/10.1016/j.ijsolstr.2004.06.067
  74. 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
  75. Xu, T.F. and Xing, Y.F. (2016), "Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation", Acta Mech. Sin., 32(6), 1088-1103. https://doi.org/10.1007/s10409-016-0600-4
  76. 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
  77. 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
  78. 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. Solids Struct., 39, 6339-6353. https://doi.org/10.1016/S0020-7683(02)00460-2