Free vibrations of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets

Rafiee, 2009, Enhanced mechanical properties of nanocomposites at low graphene content, ACS Nano, 3, 3884, 10.1021/nn9010472 Liang, 2008, Electromagnetic interference shielding of graphene/epoxy composites, Carbon N.Y., 47, 922, 10.1016/j.carbon.2008.12.038 Castellano, 2014, Ultrasonic immersion tests for mechanical characterization of multilayered anisotropic materials, 1 Castellano, 2018, Quantitative analysis of QSI and LVI damage in GFRP unidirectional composite laminates by a new ultrasonic approach, Composites, Part B, Eng., 151, 106, 10.1016/j.compositesb.2018.06.003 Yue, 2014, Epoxy composites with carbon nanotubes and graphene nanoplatelets – dispersion and synergy effects, Carbon N.Y., 78, 268, 10.1016/j.carbon.2014.07.003 Chandrasekaran, 2013, Preparation and characterization of graphite nano-platelet (GNP)/epoxy nano-composite: mechanical, electrical and thermal properties, Eur. Polym. J., 49, 3878, 10.1016/j.eurpolymj.2013.10.008 Wu, 2014, Dynamic instability of functionally graded multilayer graphene nanocomposite beams in thermal environment, Compos. Struct., 162, 244, 10.1016/j.compstruct.2016.12.001 Song, 2017, Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Compos. Struct., 159, 579, 10.1016/j.compstruct.2016.09.070 Song, 2018, Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Composites, Part B, Eng., 134, 106, 10.1016/j.compositesb.2017.09.043 Wang, 2018, Buckling of graphene platelet reinforced composite cylindrical shell with cutout, Int. J. Struct. Stab. Dyn., 18, 10.1142/S0219455418500402 Sahmani, 2017, Nonlocal strain gradient beam model for nonlinear vibration of prebuckled and postbuckled multilayer functionally graded GPLRC nanobeams, Compos. Struct., 179, 77, 10.1016/j.compstruct.2017.07.064 Yang, 2017, 3D thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates, Appl. Math. Model., 49, 69, 10.1016/j.apm.2017.04.044 Arefi, 2017, Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory, J. Sandw. Struct. Mater. Arefi, 2018, Size-dependent electro-elastic analysis of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory, J. Intell. Mater. Syst. Struct., 29, 1394, 10.1177/1045389X17733333 Shaat, 2014, Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects, Int. J. Mech. Sci., 79, 31, 10.1016/j.ijmecsci.2013.11.022 Arefi, 2017, Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak's foundation, J. Intell. Mater. Syst. Struct., 29, 774, 10.1177/1045389X17721039 Natarajan, 2012, Size-dependent free flexural vibration behavior of functionally graded nanoplates, Comput. Mater. Sci., 65, 74, 10.1016/j.commatsci.2012.06.031 Arefi, 2017, Effect of thermo-mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear-deformation plate theory, J. Sandw. Struct. Mater. Kamarian, 2016, Free vibration analysis of conical shells reinforced with agglomerated carbon nanotubes, Int. J. Mech. Sci., 108–109, 157, 10.1016/j.ijmecsci.2016.02.006 Tornabene, 2014, Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories, Composites, Part B, Eng., 67, 490, 10.1016/j.compositesb.2014.08.012 Tornabene, 2016, Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells, Composites, Part B, Eng., 89, 187, 10.1016/j.compositesb.2015.11.016 Banić, 2017, Influence of Winkler–Pasternak foundation on the vibrational behavior of plates and shells reinforced by agglomerated carbon nanotubes, Appl. Sci., 7, 10.3390/app7121228 Fantuzzi, 2017, Free vibration analysis of arbitrarily shaped functionally graded carbon nanotube-reinforced plates, Composites, Part B, Eng., 115, 384, 10.1016/j.compositesb.2016.09.021 Nejati, 2017, Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes, Int. J. Mech. Sci., 130, 383, 10.1016/j.ijmecsci.2017.06.024 Nejati, 2017, Thermal buckling of nanocomposite stiffened cylindrical shells reinforced by functionally graded wavy carbon nano-tubes with temperature-dependent properties, Appl. Sci., 7, 10.3390/app7121223 Tornabene, 2017, Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes, Composites, Part B, Eng., 115, 449, 10.1016/j.compositesb.2016.07.011 Tornabene, 2017, Multiscale approach for three-phase CNT/polymer/fiber laminated nanocomposite structures, Polym. Compos. Arefi, 2017, Transient sinusoidal shear deformation formulation of a size-dependent three-layer piezo-magnetic curved nanobeam, Acta Mech., 228, 3657, 10.1007/s00707-017-1892-6 Liu, 2013, Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory, Compos. Struct., 106, 167, 10.1016/j.compstruct.2013.05.031 Yang, 2017, Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams, Compos. Struct., 161, 111, 10.1016/j.compstruct.2016.11.048 Yang, 2018, Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev–Ritz method, Compos. Struct., 193, 281, 10.1016/j.compstruct.2018.03.090 Feng, 2017, Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs), Composites, Part B, Eng., 110, 132, 10.1016/j.compositesb.2016.11.024 Feng, 2017, Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs), Eng. Struct., 140, 110, 10.1016/j.engstruct.2017.02.052 Kitipornchai, 2017, Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets, Mater. Des., 116, 656, 10.1016/j.matdes.2016.12.061 Halpin, 1976, The Halpin–Tsai equations: a review, Polym. Eng. Sci., 16, 344, 10.1002/pen.760160512 Hull, 1996 Song, 2017, Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates, Int. J. Mech. Sci., 131–132, 345, 10.1016/j.ijmecsci.2017.07.017 Zenkour, 2009, The effect of transverse shear and normal deformations on the thermomechanical bending of functionally graded sandwich plates, Int. J. Appl. Mech., 1, 667, 10.1142/S1758825109000368 Arefi, 2016, Employing sinusoidal shear deformation plate theory for transient analysis of three layers sandwich nanoplate integrated with piezo-magnetic face-sheets, Smart Mater. Struct., 25, 10.1088/0964-1726/25/11/115040 Zenkour, 2017, Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation, J. Therm. Stresses, 40, 167, 10.1080/01495739.2016.1229146 Arefi, 2017, Vibration and bending analysis of a sandwich microbeam with two integrated piezo-magnetic face sheets, Compos. Struct., 159, 479, 10.1016/j.compstruct.2016.09.088 Aghababaei, 2009, Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, J. Sound Vib., 326, 277, 10.1016/j.jsv.2009.04.044