Structural Engineering and Mechanics

  • 제68권1호
  • /
  • Pages.131-157
  • /
  • 2018
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Vibration characteristics of advanced nanoplates in humid-thermal environment incorporating surface elasticity effects via differential quadrature method

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Heidari, Ebrahim (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • 투고 : 2018.05.05
  • 심사 : 2018.06.25
  • 발행 : 2018.10.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, Eringen nonlocal elasticity theory in conjunction with surface elasticity theory is employed to study nonlinear free vibration behavior of FG nano-plate lying on elastic foundation, on the base of Reddy's plate theory. The material distribution is assumed as a power-law function and effective material properties are modeled using Mori-Tanaka homogenization scheme. Hamilton's principle is implemented to derive the governing equations which solved using DQ method. Finally, the effects of different factors on natural frequencies of the nano-plate under hygrothermal situation and various boundary conditions are studied.

키워드

참고문헌

  1. Ahn, S.J. (2004), Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space, Springer Science & Business Media.
  2. Ansari, R. and Gholami, R. (2016), "Surface effect on the large amplitude periodic forced vibration of first-order shear deformable rectangular nanoplates with various edge supports", Acta Astronaut., 118, 72-89. https://doi.org/10.1016/j.actaastro.2015.09.020
  3. Ansari, R., Ashrafi, M.A., Pourashraf, S. and Sahmani, S. (2015), "Vibration and buckling characteristics of functionally graded nanoplates subjected to thermal loading based on surface elasticity theory", Acta Astronaut., 109, 42-51. https://doi.org/10.1016/j.actaastro.2014.12.015
  4. Ansari, R., Faghih Shojaei, M., Mohammadi, V., Gholami, R. and Darabi, M.A. (2014), "Nonlinear vibrations of functionally graded Mindlin microplates based on the modified couple stress theory", Compos. Struct., 114, 124-134.
  5. Ansari, R., Shojaei, M.F., Shahabodini, A. and Vahdati, M.B. (2015), "Three-dimensional bending and vibration analysis of functionally graded nanoplates by a novel differential quadrature-based approach", Compos. Struct., 131, 753-764.
  6. Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707
  7. Barati, M.R. and Shahverdi, H. (2017), "An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position", Mech. Adv. Mater. Struct., 24(10), 840-853. https://doi.org/10.1080/15376494.2016.1196788
  8. Barati, M.R., Zenkour, A.M. and Shahverdi, H. (2016), "Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory", Compos. Struct., 141, 203-212. https://doi.org/10.1016/j.compstruct.2016.01.056
  9. Berthelot, J.M. (2012), Composite Materials: Mechanical Behavior and Structural Analysis, Springer Science & Business Media.
  10. Bloom, F. and Coffin, D.W. (2000), "Modelling the hygroscopic buckling of layered paper sheets", Math. Comput. Modell., 31(8-9), 43-60. https://doi.org/10.1016/S0895-7177(00)00059-5
  11. Chen, W.J. and Li, X.P. (2013), "Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modified couple stress theory", Arch. Appl. Mech., 83(3), 431-444. https://doi.org/10.1007/s00419-012-0689-2
  12. Daneshmehr, A., Rauabpoor, A. and Hadi, A. (2015), "Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories", Int. J. Eng. Sci., 95, 23-35. https://doi.org/10.1016/j.ijengsci.2015.05.011
  13. Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., 11(5), 671-690. https://doi.org/10.12989/GAE.2016.11.5.671
  14. Duffy, D.G. (2015), Green's Functions with Applications, CRC Press.
  15. Ebrahimi, F. and Barati, M.R. (2016a), "Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory", Smart Mater. Struct., 25(10), 105014. https://doi.org/10.1088/0964-1726/25/10/105014
  16. Ebrahimi, F. and Barati, M.R. (2016b), "Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments", Appl. Phys. A, 122(10), 910.
  17. Ebrahimi, F. and Barati, M.R. (2016c), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", Int. J. Nano Mater., 7(3), 119-143. https://doi.org/10.1080/19475411.2016.1223203
  18. Ebrahimi, F. and Barati, M.R. (2017a), "Investigating physical field effects on the size-dependent dynamic behavior of inhomogeneous nanoscale plates", Eur. Phys. J. Plus, 132(2).
  19. Ebrahimi, F. and Barati, M.R. (2017b), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intellig. Mater. Syst. Struct., 28(11), 1472-1490. https://doi.org/10.1177/1045389X16672569
  20. Ebrahimi, F. and Barati, M.R. (2017c), "Magnetic field effects on dynamic behavior of inhomogeneous thermo-piezo-electrically actuated nanoplates", J. Brazil. Soc. Mech. Sci. Eng., 39(6), 2203-2223. https://doi.org/10.1007/s40430-016-0646-z
  21. Ebrahimi, F. and Barati, M.R. (2017d), "Damping vibration analysis of smart piezoelectric polymeric nanoplates on viscoelastic substrate based on nonlocal strain gradient theory", Smart Mater. Struct., 26(6), 065018. https://doi.org/10.1088/0964-1726/26/6/065018
  22. Ebrahimi, F. and Barati, M.R. (2018a), "Damping vibration analysis of graphene sheets on viscoelastic medium incorporating hygro-thermal effects employing nonlocal strain gradient theory", Compos. Struct., 185, 241-253. https://doi.org/10.1016/j.compstruct.2017.10.021
  23. Ebrahimi, F. and Barati, M.R. (2018b), "Vibration analysis of size-dependent flexoelectric nanoplates incorporating surface and thermal effects", Mech. Adv. Mater. Struct., 25(7), 611-621.
  24. Ebrahimi, F. and Heidari, E. (2017), "Surface effects on nonlinear vibration of embedded functionally graded nanoplates via higher order shear deformation plate theory", Mech. Adv. Mater. Struct., 1-29.
  25. Ebrahimi, F. and Hosseini, S. (2016a), "Double nanoplate-based NEMS under hydrostatic and electrostatic actuations", Eur. Phys. J. Plus, 131(5), 160. https://doi.org/10.1140/epjp/i2016-16160-1
  26. Ebrahimi, F. and Hosseini, S. (2016b), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Therm. Stress., 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684
  27. Ebrahimi, F. and Salari, E. (2015), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380. https://doi.org/10.1016/j.compstruct.2015.03.023
  28. Ebrahimi, F. and Shafiei, N. (2017), "Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy's higher-order shear deformation plate theory", Adv. Mater. Struct., 24(9), 761-772.
  29. Ebrahimi, F., Hamed, S. and Hosseini, S. (2016), "Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates", Appl. Phys. A, 122(10), 922. https://doi.org/10.1007/s00339-016-0452-6
  30. Ebrahimi, F., Barati, M.R. and Haghi, P. (2017), "Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams", J. Therm. Stress., 40(5), 535-547. https://doi.org/10.1080/01495739.2016.1230483
  31. Ebrahimi, F. and Barati, M.R. (2016g), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vibr. Contr., 1077546316646239.
  32. Ebrahimi, F. and Barati, M.R. (2016h), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 1-16.
  33. Ebrahimi, F. and Barati, M.R. (2016i), "Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., Just Accepted.
  34. Ebrahimi, F. and Barati, M.R. (2016j), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  35. Ebrahimi, F. and Barati, M.R. (2016k), "Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  36. Ebrahimi, F. and Barati, M.R. (2016l), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279.
  37. Ebrahimi, F. and Barati, M.R. (2016m), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", Int. J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001
  38. Ebrahimi, F. and Barati, M.R. (2016n), "Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 1-13.
  39. Ebrahimi, F. and Barati, M.R. (2016o), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A, 122(9), 792. https://doi.org/10.1007/s00339-016-0322-2
  40. Ebrahimi, F. and Barati, M.R. (2016p), "Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment", Int. J. Smart Nano Mater., 7(2), 69-90. https://doi.org/10.1080/19475411.2016.1191556
  41. Ebrahimi, F. and Barati, M.R. (2016q), "Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory", Appl. Phys. A, 122(9), 843. https://doi.org/10.1007/s00339-016-0368-1
  42. Ebrahimi, F. and Barati, M.R. (2016r), "Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory", Arab. J. Sci. Eng., 1-12.
  43. Ebrahimi, F. and Barati, M.R. (2016s), "On nonlocal characteristics of curved inhomogeneous Euler-Bernoulli nanobeams under different temperature distributions", Appl. Phys. A, 122(10), 880. https://doi.org/10.1007/s00339-016-0399-7
  44. Ebrahimi, F. and Barati, M.R. (2016t), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intellig. Mater. Syst. Struct., 1045389X16672569.
  45. Ebrahimi, F. and Barati, M.R. (2016u), "Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments", Appl. Phys. A, 122(10), 910. https://doi.org/10.1007/s00339-016-0441-9
  46. Ebrahimi, F. and Barati, M.R. (2016v), "Magnetic field effects on dynamic behavior of inhomogeneous thermo-piezo-electrically actuated nanoplates", J. Brazil. Soc. Mech. Sci. Eng., 1-21.
  47. Ebrahimi, F. and Barati, M.R. (2017a), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092
  48. Ebrahimi, F. and Barati, M.R. (2017b), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182.
  49. Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S.A.H. and Shaghaghi, G.R. (2015), "Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams", J. Mech. Sci. Technol., 29, 1207-1215. https://doi.org/10.1007/s12206-015-0234-7
  50. Ebrahimi, F., Ehyaei, J. and Babaei, R. (2016), "Thermal buckling of FGM nanoplates subjected to linear and nonlinear varying loads on Pasternak foundation", Adv. Mater. Res., 5(4), 245-261. https://doi.org/10.12989/amr.2016.5.4.245
  51. Ebrahimi, F. and Jafari, A. (2016), "Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory", Adv. Mater. Res., 5(4), 261-276.
  52. Ebrahimi, F. and Barati, M.R. (2016), "An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams", Adv. Nano Res., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  53. Ebrahimi, F. and Salari, E. (2015), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Compos. B, 79, 156-169. https://doi.org/10.1016/j.compositesb.2015.04.010
  54. Ebrahimi, F. and Salari, E. (2015), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380.
  55. Ebrahimi, F. and Salari, E. (2015), "Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions", Compos. B, 78, 272-290.
  56. Ebrahimi F. and Mohsen, D. (2016), "Dynamic modeling of embedded curved nanobeams incorporating surface effects", Coupled Syst. Mech., 5(3).
  57. El-Haina, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/SEM.2017.63.5.585
  58. Eringen, A.C. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  59. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803
  60. Fourn, H., Atmane, H.A., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/SCS.2018.27.1.109
  61. Ghassabi, A., Alipour, A., Dag, S. and Cigeroglu, E. (2017), "Free vibration analysis of functionally graded rectangular nanoplates considering spatial variation of the nonlocal parameter", Arch. Mech., 69(2).
  62. Gurses, M., Civalek, Ö., Korkmaz, A.K. and Ersoy, H. (2009), "Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first‐order shear deformation theory", Int. J. Numer. Meth. Eng., 79(3), 290-313. https://doi.org/10.1002/nme.2553
  63. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Rat. Mech. Analy., 57(4), 291-323. https://doi.org/10.1007/BF00261375
  64. Gurtin, M.E. and Murdoch, A.I. (1978), "Surface stress in solids", Int. J. Sol. Struct., 14(6), 431-440. https://doi.org/10.1016/0020-7683(78)90008-2
  65. Hosseini, M., Jamalpoor, A. and Fath, A. (2017), "Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation", Meccan., 52(6), 1381-1396. https://doi.org/10.1007/s11012-016-0469-0
  66. Hull, R. (1999), Properties of Crystalline Silicon, IET.
  67. Ibach, H. (1997), "The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structures", Surf. Sci. Rep., 29(5-6), 195-263. https://doi.org/10.1016/S0167-5729(97)00010-1
  68. Javaheri, R. and Eslami, M.R. (2002), "Thermal buckling of functionally graded plates", AIAA J., 40(1), 162-169. https://doi.org/10.2514/2.1626
  69. Jung, W.Y., Park, W.T. and Han, S.C. (2014), "Bending and vibration analysis of S-FGM microplates embedded in Pasternak elastic medium using the modified couple stress theory", Int. J. Mech. Sci., 87, 150-162. https://doi.org/10.1016/j.ijmecsci.2014.05.025
  70. Karimi, M., Mirdamadi, H.R. and Shahidi, A.R. (2017), "Positive and negative surface effects on the buckling and vibration of rectangular nanoplates under biaxial and shear in-plane loadings based on nonlocal elasticity theory", J. Brazil. Soc. Mech. Sci. Eng., 39(4), 1391-1404. https://doi.org/10.1007/s40430-016-0595-6
  71. Kim, Y.W. (2005), "Temperature dependent vibration analysis of functionally graded rectangular plates", J. Sound Vibr., 284(3), 531-549. https://doi.org/10.1016/j.jsv.2004.06.043
  72. Lee, W.H., Han, S.C. and Park, W.T. (2015), "A refined higher order shear and normal deformation theory for E-, P-, and S-FGM plates on Pasternak elastic foundation", Compos. Struct., 122, 330-342. https://doi.org/10.1016/j.compstruct.2014.11.047
  73. Liew, K.M., Zhang, Y. and Zhang, L.W. (2017), "Nonlocal elasticity theory for graphene modeling and simulation: Prospects and challenges", J. Model. Mech. Mater., 1(1).
  74. Lu, P., He, L.H., Lee, H.P. and Lu, C. (2006), "Thin plate theory including surface effects", Int. J. Sol. Struct., 43(16), 4631-4647. https://doi.org/10.1016/j.ijsolstr.2005.07.036
  75. Malekzadeh, P. (2007), "A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates", Thin-Wall. Struct., 45(2), 237-250. https://doi.org/10.1016/j.tws.2007.01.011
  76. Malekzadeh, P. and Shojaee, M. (2015), "A two-variable first-order shear deformation theory coupled with surface and nonlocal effects for free vibration of nanoplates", J. Vibr. Contr., 21(14), 2755-2772. https://doi.org/10.1177/1077546313516667
  77. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/SCS.2017.25.2.157
  78. Mondolfo, L.F. (2013), Aluminum Alloys: Structure and Properties, Elsevier.
  79. Nami, M.R. and Janghorban, M. (2015), "Free vibration of functionally graded size dependent nanoplates based on second order shear deformation theory using nonlocal elasticity theory", Iran. J. Sci. Technol. Trans. Mech. Eng., 39, 15-28.
  80. Nguyen, N.T., Hui, D., Lee, J. and Xuan, H.N. (2015), "An efficient computational approach for size-dependent analysis of functionally graded nanoplates", Comput. Meth. Appl. Mech. Eng., 297, 191-218. https://doi.org/10.1016/j.cma.2015.07.021
  81. Panyatong, M., Chinnaboon, B. and Chucheepsakul, S. (2015), "Nonlocal second-order shear deformation plate theory for free vibration of nanoplates", Suranar. J. Sci. Technol., 22(4), 339-348.
  82. Panyatong, M., Chinnaboon, B. and Chucheepsakul, S. (2016), "Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity", Compos. Struct., 153, 428-441. https://doi.org/10.1016/j.compstruct.2016.06.045
  83. Poirier, D.R. and Geiger, G.H. (2016), Transport Phenomena in Materials Processing, Springer.
  84. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Sol. Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  85. Qian, L.F., Batra, R.C. and Chen, L.M. (2004), "Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method", Compos. Part B: Eng., 35(6), 685-697. https://doi.org/10.1016/j.compositesb.2004.02.004
  86. Reddy, J.N. (1984), "A refined nonlinear theory of plates with transverse shear deformation", Int. J. Sol. Struct., 20(9), 881-896. https://doi.org/10.1016/0020-7683(84)90056-8
  87. Reddy, J.N. (2006), Theory and Analysis of Elastic Plates and Shells, CRC press.
  88. Reddy, J.N. (2010), "Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates", Int. J. Eng. Sci., 48(11), 1507-1518. https://doi.org/10.1016/j.ijengsci.2010.09.020
  89. Reddy, J.N. (2011), "A general nonlinear third-order theory of functionally graded plates", Int. J. Aerosp. Lightw. Struct., 1(1), 1-21. https://doi.org/10.3850/S201042861100002X
  90. Salehipour, H., Nahvi, H. and Shahidi, A.R. (2015), "Exact analytical solution for free vibration of functionally graded micro/nanoplates via three-dimensional nonlocal elasticity", Phys. E: Low-Dimens. Syst. Nanostruct., 66, 350-358.
  91. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., 64(6), 737-749. https://doi.org/10.12989/SEM.2017.64.6.737
  92. Shaat, M., Mahmoud, F.F., Alshorbagy, A.E. and Alieldin, S.S. (2013), "Bending analysis of ultra-thin functionally graded Mindlin plates incorporating surface energy effects", Int. J. Mech. Sci., 75, 223-232. https://doi.org/10.1016/j.ijmecsci.2013.07.001
  93. Shen, H.S. (2016), Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press.
  94. Shu, C. (2012), Differential Quadrature and Its Application in Engineering, Springer Science & Business Media, Singapore.
  95. Sobhy, M. (2015), "A comprehensive study on FGM nanoplates embedded in an elastic medium", Compos. Struct., 134, 966-980.
  96. Sobhy, M. and Radwan, A.F. (2017), "A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates", Int. J. Appl. Mech., 9(1), 1750008. https://doi.org/10.1142/S1758825117500089
  97. Swarnakar, A.K., Biest, O.V. and Vanhellemont, J. (2014), "Determination of the Si Young's modulus between room and melt temperature using the impulse excitation technique", Phys. Stat. Sol., 11(1), 150-155. https://doi.org/10.1002/pssc.201300101
  98. Thai, H.T. and Kim, S.E. (2013), "A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates", Compos. Struct., 99, 172-180. https://doi.org/10.1016/j.compstruct.2012.11.030
  99. Vasiliev, V.V. and Morozov, E.V. (2013), Advanced Mechanics of Composite Materials and Structural Elements, Newnes.
  100. Yahia, S.A., Atmane, H.A., Houari, M.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
  101. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., 21(1), 15-25. https://doi.org/10.12989/SSS.2018.21.1.015
  102. Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., 21(1), 65-74. https://doi.org/10.12989/SSS.2018.21.1.065
  103. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/GAE.2018.14.6.519
  104. Zare, M., Nazemnezhad, R. and Hashemi, S.H. (2015), "Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method", Meccan., 50(9), 2391-2408. https://doi.org/10.1007/s11012-015-0161-9
  105. Zidi, M., Tounsi, A., Houari, M.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

피인용 문헌

  1. Influence of shear preload on wave propagation in small-scale plates with nanofibers vol.70, pp.4, 2018, https://doi.org/10.12989/sem.2019.70.4.407
  2. Fluid-conveying piezoelectric nanosensor: Nonclassical effects on vibration-stability analysis vol.76, pp.5, 2018, https://doi.org/10.12989/sem.2020.76.5.619
  3. Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method vol.10, pp.1, 2018, https://doi.org/10.12989/anr.2021.10.1.025
  4. Damage detection using both energy and displacement damage index on the ASCE benchmark problem vol.77, pp.2, 2018, https://doi.org/10.12989/sem.2021.77.2.151