[1] A.R . Setoodeh, P. Malekzadeh, A.R. Vosoughi, Nonlinear free vibration of orthotropic graphene sheets using nonlocal mindlin plate theory, Proc. Inst. Mech. Eng., Part C: J Mech. Eng. Sci., 226(7) (2011) 1896-1906.
[2] K.F. Wang, B.L. Wang, Effect of surface energy on the non-linear postbuckling behavior of nanoplates, International Journal of Non-Linear Mechanics, 55 (2013) 19-24.
[3] R. Maitra, S. Bose, Post Buckling Behaviour of a
[3] R. Maitra, S. Bose, Post Buckling Behaviour of a Nanobeam considering both the surface and nonlocal effects, International Journal of Advancements in Research & Technology, 1 (2012) 1-5.
[4] W.T. Koiter, Couple Stresses in the Theory of Elasticity, I and II, Prac. Royal Netherlands Academy of Sciences, Series B, LXVII, 1(67) (1964) 17–44.
[5] R.D. Mindlin, N.N. Eshel, On first strain-gradient theories in linear elasticity, Int. J. Sol. Struct., 4 (1968) 109–124.
[6] F. Yang, A. Chong, D. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, Int. J. Sol.Struct., 39 (2002) 2731–2743.
[7] A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., 54 (1983) 4703–4710.
[8] A.C. Eringen, Nonlocal Continuum Field Theories, New York, 2002.
[9] S.C. Pradhan, J.K. Phadikar, Nonlocal elasticity theory for vibration of nanoplates, J. Sound. Vib., 325 (2009) 206–223.
[10] G.A. Varzandian, S. Ziaee, Analytical Solution of Non-Linear Free Vibration of Thin Rectangular Nano Plates with Various Boundary Conditions Based on Non-Local Theory, Amirkabir Journal of Mechanical Engineering, 48(4) (2017) 331–346 (in Persian).
[11] N. Yamaki, M. Chiba, Nonlinear Vibrations of aClamped Rectangular Plate with Initial Deflection and Initial Edge Displacement Part I: Theory, Thin-Walled Structures, 1 (1983) 3-29.
[12] J.K. Paik, Large deflection orthotropic plate approach to develop ultimate strength formulations for stiffened panels under combined biaxial compression/tension and lateral pressure, Thin-Walled Structures, 39 (2001) 215-246.
[13] R. Ansari, R. Gholami, Size-dependent modeling of the free vibration characteristics of postbuckled third- order shear deformable rectangular nanoplates based on the surface stress elasticity theory, Composites Part B (at press), (2016).
[14] Chen Liu, Liao-Liang Ke, Jie Yang, Sritawat Kitipornchai, Yue-Sheng Wang, Buckling and post- buckling analyses of size-dependent piezoelectric nanoplates, Theoretical & Applied Mechanics Letters, 6 (2016) 253-267.
[15] Y.M. Yue, C.Q. Ru, K.Y. Xu, Modified von Kármán equations for elastic nanoplates with surface tension and surface elasticity, International Journal of Non– Linear Mechanics, 88 (2017) 67-73.
[16] R. Gholami, R. Ansari, Y. Gholami, Size-dependent bending, buckling and vibration of higher-order shear deformable magneto-electro-thermo-elastic rectangular nanoplates, Mater. Res. Express, (at press), (2017).
[17] C.-L. Zhang, H.-S. Shen, Temperature-dependent elastic properties of single-walled carbon nanotubes: prediction from molecular dynamics simulation, Appl. Phys. Lett. 89 081904, (2006).
[18] H.-S. Shen, Y.-M. Xu, C.-L. Zhang, Prediction of nonlinear vibration of bilayer graphene sheets in thermal environments via molecular dynamics simulations and nonlocal elasticity, Comput. Methods Appl. Mech. Engrg, 267 (2013) 458–470.
[19] H.-S. Shen, X.-Q. He, D.-Q. Yang, Vibration of thermally postbuckled carbon nanotube-reinforced composite beams resting on elastic foundations, International Journal of Non-Linear Mechanics, (2017).
[20] W. Lestari, S. Hanagud, Nonlinear vibration of buckled beams: some exact solutions, International Journal of Solids and Structures, 38 (2001) 4741— 4757.
[21] M. Karimi, A.R. Shahidi, A general comparison the surface layer degree on the out-of phase and in-phase vibration behavior of a skew double-layer magneto– electro–thermo-elastic nanoplate, Applied Physics A, 125(106) (2019) (in press).
[22] M. Karimi, A.R. Shahidi, Comparing magnitudes of surface energy stress in synchronous and asynchronous bending/buckling analysis of slanting double-layer METE nanoplates, Applied Physics A, 125(154) (2019) (in press).
[23] L. C., C.T. W., Elastic moduli of multi-walled carbon nanotubes and the effect of vanderWaals forces, Composites Science and Technology, 11 (2003) 1517– 1524.
[24] S. Kitipornchai, X.Q. He, K.M. Liew, Continuum model for the vibration of multilayered graphene sheets, Physical Review B, 72 (2005) 075443.
[25] J. Wang, X. He, S. Kitipornchai, H. Zhang, Geometrical nonlinear free vibration of multi-layered graphene sheets, J. Phys. D: Appl. Phys, 44 (2011) 135401 (135409pp).
[26] A. Farajpour, A. ArabSolghar, A. Shahidi, postbuckling analysis of multi-layered graphene sheets under non-uniform biaxial compression, Physica E, 47 (2013) 197-206.
[27] M.R. Barati, Magneto-hygro-thermal vibration behavior of elastically coupled nanoplate systems incorporating nonlocal and strain gradient effects, The Brazilian Society of Mechanical Sciences and Engineering, (TECHNICAL PAPER), (2017).
[28] M. Karimi, A.R. Shahidi, S. Ziaei-Rad, Surface layer and nonlocal parameter effects on the in-phase and out-of-phase natural frequencies of a double-layer piezoelectric nanoplate under thermo-electro- mechanical loadings, Microsystem Technologies, (TECHNICAL PAPER) (2017).
[29] E. Jomehzadeh, A.R. Saidi, A study on large amplitude vibration of multilayered graphene sheets, Computational Materials Science, 50 (2011) 1043– 1051.
[30] S. Arghavan, A.V. Singh, Effects of van der Waals interactions on the nonlinear vibration of multi- layered graphene sheets, J. Phys. D: Appl. Phys., 45 (2012) 455305 (455308pp).
[31] L. Shen, H. Shen, C. Zhang, Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments, Comput. Mater. Sci., 48:680 (2010).
[32] E. Ventsel, T. Krauthammer, Thin Plates and Shells: Theory, Analysis and Applications, Marcell Dekker Inc, 2001.
[33] J.N. Reddy, Theory and Analysis of Elastic plates and Shells: 2nd Edition, Taylor & Francis Group, 2007.
[34] I.S. Raju, G.V. Rao, K.K. Raju, Effect of longitudinal or inplane deformation and inertia on the large amplitude flexural vibrations of slender beams and thin plates, Journal of Sound and Vibration, 49(3) (1976) 415-422.
[35] A.H. Nayfeh, S.A. Emam, Exact solution and stability of postbuckling configurations of beams, Nonlinear Dynamics, 54 (2008) 395–408.
[36] K.-S. Na, J.-H. Kim, Thermal postbuckling investigations of functionally graded plates using 3-D finite element method, Finite Elements in Analysis and Design, 42 (2006) 749-756.
[37] M. Neek-Amal, F.M. Peeters, Graphene nanoribbons subjected to axial stress, PHYSICAL REVIEW B, 82, (2010) 085432.
[38] M. Terrones et.al, Graphene and graphite nanoribbons: Morphology, properties, synthesis, defects and Applications, nano today, 5, (2010) 351-372.
[39] Xiu-Xi Wang, Jiang Qian ,Mao-Kuang Huang, A boundary integral equation formulation for large amplitude nonlinear vibration of thin elastic plates, Computer Methods in Applied Mechanics and Engineering, 86 (1991) 73-86.
[40] S.R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, 11 (2014) 1541-1564.
[41] M. Karimi, A.R. Shahidi, Buckling analysis of skew magneto-electro-thermo-elastic nanoplates considering surface energy layers and utilizing the Galerkin method, Applied Physics A, (2018) 124:681.
[42] M. Karimi, A.R. Shahidi, H.R. Mirdamadi, Shear vibration and buckling of double‑layer orthotropic nanoplates based on RPT resting on elastic foundations by DQM including surface effects, Microsystem Technologies, (TECHNICAL PAPER) (2015).
)