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Free vibration characteristics of three-phases functionally graded sandwich plates using novel nth-order shear deformation theory

  • Pham Van Vinh (Department of Solid Mechanics, Le Quy Don Technical University) ;
  • Le Quang Huy (Institute of Techniques for Special Engineering, Le Quy Don Technical University) ;
  • Abdelouahed Tounsi (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • 투고 : 2023.05.26
  • 심사 : 2023.07.24
  • 발행 : 2024.01.25

초록

In this study, the authors investigate the free vibration behavior of three-phases functionally graded sandwich plates using a novel nth-order shear deformation theory. These plates are composed of a homogeneous core and two face-sheet layers made of different functionally graded materials. This is the novel type of the sandwich structures that can be applied in many fields of mechanical engineering and industrial. The proposed theory only requires four unknown displacement functions, and the transverse displacement does not need to be separated into bending and shear parts, simplifying the theory. One noteworthy feature of the proposed theory is its ability to capture the parabolic distribution of transverse shear strains and stresses throughout the plate's thickness while ensuring zero values on the two free surfaces. By eliminating the need for shear correction factors, the theory further enhances computational efficiency. Equations of motion are established using Hamilton's principle and solved via Navier's solution. The accuracy and efficiency of the proposed theory are verified by comparing results with available solutions. The authors then use the proposed theory to investigate the free vibration characteristics of three-phases functionally graded sandwich plates, considering the effects of parameters such as aspect ratio, side-to-thickness ratio, skin-core-skin thicknesses, and power-law indexes. Through careful analysis of the free vibration behavior of three-phases functionally graded sandwich plates, the work highlighted the significant roles played by individual material ingredients in influencing their frequencies.

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참고문헌

  1. Abdelaziz, H.H., Atmane, H.A., Mechab, I., Boumia, L., Tounsi, A. and El Abbas, A.B. (2011), "Static analysis of functionally graded sandwich plates using an efficient and simple refined theory", Chin. J. Aeronaut., 24(4), 434-448. https://doi.org/10.1016/S1000-9361(11)60051-4. 
  2. Abdelhaffez, G.S., Daikh, A.A., Saleem, H.A. and Eltaher, M.A. (2023), "Buckling of coated functionally graded spherical nanoshells rested on orthotropic elastic medium", Math., 11(2), 11020409. https://doi.org/10.3390/math11020409. 
  3. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197. 
  4. Adiyaman, G., Oner, E., Yaylaci, M. and Birinci, A. (2023), "A study on the contact problem of a layer consisting of functionally graded material (FGM) in the presence of body force", J. Mech. Mater. Struct., 18(1), 125-141. https://doi.org/10.2140/jomms.2023.18.125. 
  5. Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B: Eng., 96, 136-152. https://doi.org/10.1016/j.compositesb.2016.04.035. 
  6. Alibeigloo, A. and Alizadeh, M. (2015), "Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method", Eur. J. Mech. A/Solids, 54, 252-266. https://doi.org/10.1016/j.euromechsol.2015.06.011. 
  7. AlSaid-Alwan, H.H.S. and Avcar, M. (2020), "Analytical solution of free vibration of FG beam utilizing different types of beam theories: A comparative study", Comput. Concrete, 26(3), 285-292. https://doi.org/10.12989/cac.2020.26.3.285. 
  8. Belarbi, M.O., Daikh, A.A., Garg, A., Hirane, H., Houari, M.S.A., Civalek, O . and Chalak, H.D. (2023), "Bending and free vibration analysis of porous functionally graded sandwich plate with various porosity distributions using an extended layerwise theory", Arch. Civil Mech. Eng., 23(1), 15. https://doi.org/10.1007/s43452-022-00551-0. 
  9. Benguediab, S., Kebir, T., Kettaf, F.Z., Daikh, A.A., Tounsi, A., Benguediab, M. and Eltaher, M.A. (2023), "Thermomechanical behavior of macro and nano fgm sandwich plates", Adv. Aircr. Spacecr. Sci., 10(1), 83-106. https://doi.org/10.12989/aas.2023.10.1.083. 
  10. Bessaim, A., Houari, M.S., Tounsi, A., Mahmoud, S.R. and Bedia, E.A.A. (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15(6), 671-703. https://doi.org/10.1177/1099636213498888. 
  11. Civalek, O ., Dastjerdi, S., Akbas, S.D. and Akgoz, B. (2021), "Vibration analysis of carbon nanotube-reinforced composite microbeams", Math. Method. Appl. Sci., 2021, 1. https://doi.org/10.1002/mma.7069. 
  12. Daikh, A.A. and Megueni, A. (2018), "Thermal buckling analysis of functionally graded sandwich plates", J. Therm. Stress., 41(2), 139-159. https://doi.org/10.1080/01495739.2017.1393644. 
  13. Daikh, A.A. and Zenkour, A.M. (2019), "Effect of porosity on the bending analysis of various functionally graded sandwich plates", Mater. Res. Exp., 6(6), 65703. https://doi.org/10.1088/2053-1591/ab0971. 
  14. Daikh, A.A., Belarbi, M.O., Ahmed, D., Houari, M.S.A., Avcar, M., Tounsi, A. and Eltaher, M.A. (2023a), "Static analysis of functionally graded plate structures resting on variable elastic foundation under various boundary conditions", Acta Mech., 234(2), 775-806. https://doi.org/10.1007/s00707-022-03405-1. 
  15. Daikh, A.A., Belarbi, M.O., Khechai, A., Li, L., Ahmed, H.M. and Eltaher, M.A. (2023b), "Buckling of bi-coated functionally graded porous nanoplates via a nonlocal strain gradient quasi3D theory", Acta Mech., 2023, 1-24. https://doi.org/10.1007/s00707-023-03548-9. 
  16. Do, V.T., Pham, V.V. and Nguyen, H.N. (2020), "On the development of refined plate theory for static bending behavior of functionally graded plates", Math. Probl. Eng., 2020, 1-13. https://doi.org/10.1155/2020/2836763. 
  17. Van Do, V.N., & Lee, C.H. (2019), "Mesh-free thermal buckling analysis of multilayered composite plates based on an nth-order shear deformation theory", Compos. Struct., 224, 111042. https://doi.org/10.1016/j.compstruct.2019.111042. 
  18. Dorduncu, M. (2020), "Stress analysis of sandwich plates with functionally graded cores using peridynamic differential operator and refined zigzag theory", Thin Wall. Struct., 146, 106468. https://doi.org/10.1016/j.tws.2019.106468. 
  19. 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", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004. 
  20. Fu, T., Chen, Z., Yu, H., Wang, Z. and Liu, X. (2018), "Free vibration of functionally graded sandwich plates based on nth-order shear deformation theory via differential quadrature method", J. Sandw. Struct. Mater., 22(5), 1660-1680. https://doi.org/10.1177/1099636218809451. 
  21. Ghandourah, E.E., Daikh, A.A., Khatir, S., Alhawsawi, A.M., Banoqitah, E.M. and Eltaher, M.A. (2023), "A dynamic analysis of porous coated functionally graded nanoshells rested on viscoelastic medium", Math., 11(10), 11102407. https://doi.org/10.3390/math11102407. 
  22. Hoa, L.K., Vinh, P.V., Duc, N.D., Trung, N.T., Son, L.T. and Thom, D.V. (2021), "Bending and free vibration analyses of functionally graded material nanoplates via a novel nonlocal single variable shear deformation plate theory", Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci., 235(18), 3641-3653. https://doi.org/10.1177/0954406220964522. 
  23. Hosseini-Hashemi, S., Taher, H.R.D., Akhavan, H. and Omidi, M. (2010), "Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory", Appl. Math. Modell., 34(5), 1276-1291. https://doi.org/10.1016/j.apm.2009.08.008. 
  24. Iurlaro, L., Gherlone, M. and Di Sciuva, M. (2014), "Bending and free vibration analysis of functionally graded sandwich plates using the refined zigzag theory", J. Sandw. Struct. Mater., 16(6), 669-699. https://doi.org/10.1177/1099636214548618. 
  25. Khazaei, P. and Mohammadimehr, M. (2020), "Vibration analysis of porous nanocomposite viscoelastic plate reinforced by FGSWCNTs based on a nonlocal strain gradient theory", Comput. Concrete, 26(1), 31-52. https://doi.org/10.12989/cac.2020.26.1.031. 
  26. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B: Eng., 28(1), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9. 
  27. 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. 
  28. Liu, N. and Jeffers, A.E. (2017), "Isogeometric analysis of laminated composite and functionally graded sandwich plates based on a layerwise displacement theory", Compos. Struct., 176, 143-153. https://doi.org/10.1016/j.compstruct.2017.05.037, 
  29. Mantari, J.L. and Granados, E.V. (2015), "A refined FSDT for the static analysis of functionally graded sandwich plates", Thin Wall. Struct., 90, 150-158. https://doi.org/10.1016/j.tws.2015.01.015. 
  30. Mantari, J.L. and Soares, C.G. (2013), "A novel higher-order shear deformation theory with stretching effect for functionally graded plates", Compos. Part B: Eng., 45(1), 268-281. https://doi.org/10.1016/j.compositesb.2012.05.036. 
  31. 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. 
  32. Nam, V.H., Nam, N.H., Vinh, P.V., Khoa, D.N., Thom, D.V. and Minh, P.V. (2019), "A new efficient modified first-order shear model for static bending and vibration behaviors of two-layer composite plate", Adv. Civil Eng., 2019, 6814367. https://doi.org/10.1155/2019/6814367. 
  33. Nam, V.H., Vinh, P.V., Chinh, N.V., Thom, D.V. and Hong, T.T. (2019), "A new beam model for simulation of the mechanical behaviour of variable thickness functionally graded material beams based on modified first order shear deformation theory", Mater., 12(3), https://doi.org/10.3390/ma12030404. 
  34. Natarajan, S. and Manickam, G. (2012), "Bending and vibration of functionally graded material sandwich plates using an accurate theory", Finite Elem. Anal. Des., 57, 32-42. https://doi.org/10.1016/j.finel.2012.03.006. 
  35. Neves, A.M.A, Ferreira, A.J.M.E., Carrera, M., Cinefra, Jorge, R.M.N., Mota Soares, C.M. and Araujo, A.L. (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. 
  36. Neves, A.M.A., Ferreira, A.J., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012a), "Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering zig-zag and warping effects", Adv. Eng. Softw., 52, 30-43. https://doi.org/10.1016/j.advengsoft.2012.05.005. 
  37. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012b), "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", ZAMM J. Appl. Math. Mech., 92(9), 749-766. https://doi.org/10.1002/zamm.201100186. 
  38. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2012), "A quasi3D 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. 
  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, H.N., Hong, T.T., Vinh, P.V., Quang, N.D. and Thom, D.V. (2019), "A refined simple first-order shear deformation theory for static bending and free vibration analysis of advanced composite plates", Mater., 12(15), 2385. https://doi.org/10.3390/ma12152385. 
  41. Nguyen, H.N., Hong, T.T., Vinh, P.V. and Thom, D.V. (2019), "An efficient beam element based on quasi-3D theory for static bending analysis of functionally graded beams", Mater., 12(13), 2198. https://doi.org/10.3390/ma12132198. 
  42. Nguyen, T.K., Vo, T.P. and Thai, H.T. (2013), "Vibration and buckling analysis of functionally graded sandwich plates with improved transverse shear stiffness based on the first-order shear deformation theory", Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci., 228(12), 2110-2131. https://doi.org/10.1177/0954406213516088. 
  43. Nguyen, V.H., Nguyen, T.K., Thai, H.T. and Vo, T.P. (2014), "A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates", Compos. Part B: Eng., 66, 233-246. https://doi.org/10.1016/j.compositesb.2014.05.012. 
  44. Oner, E., Sengul Sabano, B., Uzun Yaylaci, E., Adiyaman, G., Yaylaci, M. and Birinci, A. (2022), "On the plane receding contact between two functionally graded layers using computational, finite element and artificial neural network methods", ZAMM J. Appl. Math. Mech., 102(2), 202100287. https://doi.org/10.1002/zamm.202100287. 
  45. Pandey, S. and Pradyumna, S. (2015), "Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory", Eur. J. Mech. A/Solids, 51, 55-66. https://doi.org/10.1016/j.euromechsol.2014.12.001. 
  46. Pandya, B.N. and Kant, T. (1988), "Higher-order shear deformable theories for flexure of sandwich plates-Finite element evaluations", Int. J. Solid. Struct., 24(12), 1267-1286. https://doi.org/10.1016/0020-7683(88)90090-X. 
  47. Reddy, J.N, (2011), "A general nonlinear third-order theory of functionally graded plates", Int. J. Aerosp. Lightweight Struct., 1(1), 1-21. https://doi.org/10.3850/s201042861100002x. 
  48. Reddy, J.N, (2000), "Analysis of functionally graded plates", Int. J. Numer. Method. 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. 
  49. 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. 
  50. Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M. amd Carrera, E. (2015), "Stress, vibration and buckling analyses of FGM plates-A state-of-the-art review", Compos. Struct., 120, 10-31. https://doi.org/10.1016/j.compstruct.2014.09.070. 
  51. Talha, M. and Singh, B. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Modell., 34(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034. 
  52. Thai, H.T. and Kim, S.E. (2013), "A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates", Compos. Struct., 96, 165-173. https://doi.org/10.1016/j.compstruct.2012.08.025. 
  53. Thai, H.T., Nguyen, T.K., Vo, T.P. and Lee, J. (2014), "Analysis of functionally graded sandwich plates using a new first-order shear deformation theory", Eur. J. Mech. A/Solids, 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008. 
  54. Timesli, A. (2020), "Prediction of the critical buckling load of swcnt reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, 26(2), 53-62. https://doi.org/10.12989/cac.2020.26.2.151. 
  55. Turan, M., Uzun Yaylaci, E. and Yaylaci, M. (2022), "Free vibration and buckling of functionally graded porous beams using analytical, finite element, and artificial neural network methods", Arch. Appl. Mech., 93, 1351-1372. https://doi.org/10.1007/s00419-022-02332-w. 
  56. Van Vinh, P. (2021), "Deflections, stresses and free vibration analysis of bi-functionally graded sandwich plates resting on Pasternak'S elastic foundations via a hybrid quasi-3D theory", Mech. Based Des. Struct. Mach., 51(4), 2323-2354. https://doi.org/10.1080/15397734.2021.1894948. 
  57. Vinh, P.V. and Huy, L.Q. (2022), "Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory", Defence Technol., 18(3), 490-508. https://doi.org/10.1016/j.dt.2021.03.006. 
  58. Van Vinh, P. (2021), "Formulation of a new mixed four-node quadrilateral element for static bending analysis of variable thickness functionally graded material plates", Math. Probl. Eng., 2021, 1-23. https://doi.org/10.1155/2021/6653350. 
  59. Van Vinh, P., Dung, N.T. and Tho, N.C. (2021), "Modified single variable shear deformation plate theory for free vibration analysis of rectangular FGM plates", Struct., 29, 1435-1444. https://doi.org/10.1016/j.istruc.2020.12.027. 
  60. Xiang, S., Jin, Y.X., Bi, Z.Y., Jiang, S.X. and Yang, M.S. (2011), "A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates", Compos. Struct., 93(11), 2826-2832. https://doi.org/10.1016/j.compstruct.2011.05.022. 
  61. Xiang, S. and Kang, G.W. (2013), "A nth-order shear deformation theory for the bending analysis on the functionally graded plates", Eur. J. Mech. A/Solids, 37, 336-343. https://doi.org/10.1016/j.euromechsol.2012.08.005. 
  62. Xiang, S. and Liu, Y.Q. (2016), "An nth-order shear deformation theory for static analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 18(5), 579-596. https://doi.org/10.1177/1099636216647928. 
  63. Yaghoobi, H. and Fereidoon, A. (2014), "Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: An assessment of a simple refined nth-order shear deformation theory", Compos. Part B: Eng., 62, 54-64. https://doi.org/10.1016/j.compositesb.2014.02.014. 
  64. Yaylaci, M., ADIYAMAN, G., Oner, E. and Birinci, A. (2021), "Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM", Comput. Concrete, 27(3), 199-210. https://doi.org/10.12989/cac.2021.27.3.199. 
  65. Yaylaci, M., Sabano, B.S., O zdemir, M.E. and Birinci, A. (2022a), "Solving the contact problem of functionally graded layers resting on a HP and pressed with a uniformly distributed load by analytical and numerical methods", Struct. Eng. Mech., 82(3), 401-416. https://doi.org/10.12989/sem.2022.82.3.401. 
  66. Yaylaci, M., Uzun Yaylaci, E., Ozdemir, M.E., Ay, S. and Ozturk, S. (2022b), "Implementation of finite element and artificial neural network methods to analyze the contact problem of a functionally graded layer containing crack", Steel Compos. Struct., 45(4), 501-511. https://doi.org/10.12989/scs.2022.45.4.501. 
  67. Yaylaci, M., Yaylaci, E.U., Ozdemir, M.E., Ozturk, S. and Sesli, H. (2023), "Vibration and buckling analyses of FGM beam with edge crack: Finite element and multilayer perceptron methods", Steel Compos. Struct., 46(4), 565-575. https://doi.org/10.12989/scs.2023.46.4.565. 
  68. Yaylaci, M., Yayli, M., Yaylaci, E.U., Olmez, H. and Birinci, A. (2021), "Analyzing the contact problem of a functionally graded layer resting on an elastic half plane with theory of elasticity, finite element method and multilayer perceptron", Struct. Eng. Mech., 78(5), 585-597. https://doi.org/10.12989/sem.2021.78.5.585. 
  69. Zenkour, A.M, (2005a), "A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses", Int. J. Solid. Struct., 42(18-19), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015. 
  70. Zenkour, A.M, (2005b), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. J. Solid. Struct., 42(18), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016. 
  71. Zenkour, A.M, (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Modell., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009. 
  72. Zenkour, A.M, (2013a), "A simple four-unknown refined theory for bending analysis of functionally graded plates", Appl. Math. Modell., 37(20), 9041-9051. https://doi.org/10.1016/j.apm.2013.04.022. 
  73. Zenkour, A.M, (2013b), "Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory", J. Sandw. Struct. Mater., 15(6), 629-656. https://doi.org/10.1177/1099636213498886.