[1] Shahverdi H, Barati MR (2017) Vibration analysis of porous functionally graded nanoplates. Int J Eng Sci 120: 82-99.
[2] Daneshmehr A, Rajabpoor A, 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.
[3] Lü CF, Lim CW, Chen W Q (2009) Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory. Int J Solids Struct 46: 1176-1185.
[4] Eringen AC (2002) Nonlocal continuum field theories. Springer, New York.
[5] Sobhy M, Radwan AF (2017) A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates. Int J Appl Mech 9(1):1750008.
[6] عزیزی ع، ستوده ع (1397) تحلیل خمش و ارتعاش آزاد نانوورق مدرج تابعی با استفاده از نظریه ورق مرتبه بالای مثلثاتی. نشریه مهندسی مکانیک امیرکبیر 1050-1039 :(5)50.
[7] Najafizadeh MM, Raki M, Yousefi P (2018) Vibration analysis of FG Nanoplate based on third-order shear deformation theory (TSDT) and nonlocal elasticity. J Solid Mech 10(3): 464-475.
[8] Senthilnathan NR, Lim SP, Lee KH, Chow ST (1987) Buckling of shear-deformable plates. AIAA J 25: 1268-1271.
[9] Zenkour AM (2013) A simple four-unknown refined theory for bending analysis of functionally graded plates. Appl Math Model 37: 9041-9051.
[10] Barati MR, 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.
[11] Fung CP, Chen CH (2006) Imperfection sensitivity in the nonlinear vibration of functionally graded plates. Eur J Mech A-Solid 25(3): 425-436.
[12] Jalali SK, Pugno NM, Jomehzadeh E (2016) Influence of out-of-plane defects on vibration analysis of graphene sheets: molecular and continuum approaches. Superlattice Microst 91: 331-344.
[13] Lusk MT, Carr LD (2008) Nanoengineering defect structures on graphene. Phys Rev Lett 100: 175503.
[14] Kitipornchai S, Yang J, Liew KM (2004) Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections. Int J Solids Struct 41: 2235-2257.
[15] Chen CH, Hsu C.Y (2007) Imperfection sensitivity in the nonlinear vibration oscillations of initially stressed plates. Appl Math Comput 190(1): 465-475.
[16] Yang J, Huang XL (2007) Nonlinear transient response of functionally graded plates with general imperfections in thermal environments. Comput Methods Appl Mech Eng 196: 2619-2630.
[17] Gupta A, Talha M (2016) An assessment of a non-polynomial based higher order shear and normal deformation theory for vibration response of gradient plates with initial geometric imperfections. Compos Part B-Eng 107: 141-161.
[18] Gupta A, Talha M (2017) Nonlinear flexural and vibration response of geometrically imperfect gradient plates using hyperbolic higher-order shear and normal deformation theory. Compos Part B-Eng 123: 241-261.
[19] Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194: 4135- 4195.
[20] Tran LV, Thai CH, Le HT, Gan BS, Lee J, Nguyen-Xuan H (2014) Isogeometric analysis of laminated composite plates based on a four-variable refined plate theory. Eng Anal Bound Elem 47: 68-81.
[21] Nguyen NT, Huic D, Lee J, Nguyen-Xuan H (2015) An efficient computational approach for size-dependent analysis of functionally graded nanoplates. Comput Methods Appl Mech Engrg 297: 191-218.
[22] Thai CH, Zenkour AM, Abdel Wahab M, Nguyen-Xuan H (2016) A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric Analysis. Compos Struct 139: 77-95.
[23] Farzam-Rad SA, Hassani B, Karamodin A (2017) Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface. Compos Part B-Eng 108: 174-189.
[24] Nguyen Hoang X, Nguyen Tuan N, Abdel Wahab M, Bordas SPA, Nguyen- Xuan H, Thuc PV (2017) A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory. Comput Meth Appl Mech Eng 313: 904-940.
[25] Phung-Van P, Lieu QX, Nguyen-Xuan H, Abdel-Wahab M (2017) Size-dependent isogeometric analysis of functionally graded carbon nanotube-reinforced composite nanoplates. Compos Struct 166: 120-135.
[26] Xue Y,
Jin G, Ding H, Chen M (2018) Free vibration analysis of in-plane functionally graded plates using a refined plate theory and isogeometric approach. Compos Struct 192:193-205.
[27] Liu Z, Wang C, Duan G, Tan J (2019) A new refined plate theory with isogeometric approach for the static and buckling analysis of functionally graded plates. Int J Mech Sci 161-162: 105036.
[28] Phung-Van P, Thai CH, Nguyen-Xuan H, Abdel-Wahab M (2019) An isogeometric approach of static and free vibration analyses for porous FG nanoplates. Eur J Mech A-Solid 78: 103851.
[29] Lieu QX, Lee S, Kang J, Lee J (2018) Bending and free vibration analyses of in-plane bi-directional functionally graded plates with variable thickness using isogeometric analysis. Compos Struct 192.
[30] Farzam A, Hassani B (2019) Isogeometric analysis of in-plane functionally graded porous microplates using modified couple stress theory. Aerosp Sci Technol 91: 508-524.
[31] Karamanli A (2020) Size-dependent behaviors of three directional functionally graded shear and normal deformable imperfect microplates. Compos Struct 113076.
[32] Li S, Zheng S, Chen D (2020) Porosity-dependent isogeometric analysis of bi-directional functionally graded plates. Thin Wall Struct 156: 106999.
[33] خورشیدی ک، بخششی ا، قدیریان ح (1395) بررسی تاثیرات محیط حرارتی بر ارتعاشات آزاد ورق مستطیلی از جنس مواد تابعی مدرج دوبعدی مستقر بر بستر پسترناک. نشریه علمی مکانیک سازهها و شارهها 147-137 :(3)6.
[34] هاشمی س، جعفری ع ا (1399) تحلیل ارتعاش آزاد غیرخطی ورقهای مستطیلی از جنس ماده مدرج تابعی دوجهته. نشریه علمی مکانیک سازهها و شارهها 52-31 :(1)10.
[35] Hashemi S, Jafari AA (2020) Nonlinear Free and Forced vibrations of in-plane bi-directional functionally graded rectangular plate with temperature-dependent properties. Int J Struct Stab Dy 20(8): 2050097
[36] Vel SS, Batra RC (2002) Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA J 40: 1421-1433
[37] Mori T,Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21: 571-574.
)
