Effect of nonlocal parameters and Kerr foundation on nonlinear static and dynamic stability of micro/nano plate with graphene platelet reinforcement

Eringen, 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., 54, 4703, 10.1063/1.332803 Eringen, 1972, Nonlocal polar elastic continua, Internat. J. Engrg. Sci., 10, 1, 10.1016/0020-7225(72)90070-5 Aksencer, 2011, Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E, 43, 954, 10.1016/j.physe.2010.11.024 Zhao, 2000, Influence of couple-stresses on stress concentrations around the cavity, Appl. Math. Mech., 21, 893, 10.1007/BF02428358 Akgöz, 2011, Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified couple stress theories, J. Comput. Theor. Nanosci., 8, 1821, 10.1166/jctn.2011.1888 Akgöz, 2014, Shear deformation beam models for functionally graded microbeams with new shear correction factors, Compos. Struct., 112, 214, 10.1016/j.compstruct.2014.02.022 Mindlin, 1965, Second gradient of strain and surface-tension in linear elasticity, Int. J. Solids Struct., 1, 417, 10.1016/0020-7683(65)90006-5 Akgöz, 2012, Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory, Arch. Appl. Mech., 82, 423, 10.1007/s00419-011-0565-5 Dingreville, 2005, Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films, J. Mech. Phys. Solids, 53, 1827, 10.1016/j.jmps.2005.02.012 Keivani, 2016, A nonlinear model for incorporating the coupled effects of surface energy and microstructure on the electromechanical stability of NEMS, Arab. J. Sci. Eng., 41, 4397, 10.1007/s13369-016-2135-1 Mercan, 2017, Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix, Arch. Appl. Mech., 87, 1797, 10.1007/s00419-017-1288-z Reddy, 2007, Nonlocal theories for bending, buckling and vibration of beams, Internat. J. Engrg. Sci., 45, 288, 10.1016/j.ijengsci.2007.04.004 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 Reza, 2014, Nonlocal nonlinear free vibration of functionally graded nanobeams, Compos. Struct., 110, 192, 10.1016/j.compstruct.2013.12.006 Sahmani, 2018, Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory, Compos. Struct., 186, 68, 10.1016/j.compstruct.2017.11.082 Sahmani, 2018, Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs, Compos. Struct., 198, 51, 10.1016/j.compstruct.2018.05.031 Shariyat, 2019, Nonlinear semi-analytical nonlocal strain-gradient dynamic response investigation of phase-transition-induced transversely graded hierarchical viscoelastic nano/microplates, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., 233, 5388, 10.1177/0954406219846145 Sobhy, 2017, A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates mohammed, Int. J. Appl. Mech., 9, 10.1142/S1758825117500089 Aria, 2019, A nonlocal finite element model for buckling and vibration of functionally graded nanobeams, Composites B, 166, 233, 10.1016/j.compositesb.2018.11.071 Li, 2015, Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory, Int. J. Eng. Sci., 97, 84, 10.1016/j.ijengsci.2015.08.013 Arefi, 2019, A nonlocal higher order shear deformation theory for electro-elastic analysis of a piezoelectric doubly curved nano shell, Composites B, 168, 496, 10.1016/j.compositesb.2019.03.065 Anjomshoa, 2016, Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal mindlin plate theory and using Galerkin method, J. Mech. Sci. Technol., 30, 2463, 10.1007/s12206-016-0506-x Fan, 2021, Buckling and postbuckling response of nonlocal strain gradient porous functionally graded micro/ nano-plates via NURBS-based isogeometric analysis, Thin-Walled Struct., 159, 10.1016/j.tws.2020.107231 Yuan, 2020, Size-dependent shear buckling response of FGM skew nanoplates, Appl. Math. Mech., 41, 587, 10.1007/s10483-020-2600-6 Khorshidi, 2016, Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory, Int. J. Mech. Sci., 113, 94, 10.1016/j.ijmecsci.2016.04.014 Kolahchi, 2017, A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods, Aerosp. Sci. Technol., 66, 235, 10.1016/j.ast.2017.03.016 Motezaker, 2020, Application of differential cubature method for nonlocal vibration, buckling and bending response of annular nanoplates integrated by piezoelectric layers based on surface-higher order nonlocal-piezoelasticity theory, J. Comput. Appl. Math., 369, 10.1016/j.cam.2019.112625 Arefi, 2019, Nonlocal bending analysis of curved nanobeams reinforced by graphene nanoplatelets, Composites B, 166, 1, 10.1016/j.compositesb.2018.11.092 Sahmani, 2013, On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory, Compos. Struct., 95, 430, 10.1016/j.compstruct.2012.07.025 Akgöz, 2015, A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory, Acta Mech., 226, 2277, 10.1007/s00707-015-1308-4 Dastjerdi, 2020, On the effect of viscoelasticity on behavior of gyroscopes, Internat. J. Engrg. Sci., 149, 10.1016/j.ijengsci.2020.103236 Numanoğlu, 2021, A new eigenvalue problem solver for thermo-mechanical vibration of Timoshenko nanobeams by an innovative nonlocal finite element method, Math. Methods Appl. Sci., 45, 2592, 10.1002/mma.7942 Farahmand, 2020, Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory, J. Braz. Soc. Mech. Sci. Eng., 42, 1, 10.1007/s40430-020-02341-2 Yu, 2020, Wavelet-based homotopy method for analysis of nonlinear bending of variable-thickness plate on elastic foundations, Thin-Walled Struct., 157, 10.1016/j.tws.2020.107105 Yang, 2011, Higher-order continuum theory applied to fracture simulation of nanoscale intergranular glassy film, J. Nanomech. Micromech., 1, 60, 10.1061/(ASCE)NM.2153-5477.0000030 Awrejcewicz, 2022, Analysing regular nonlinear vibrations of nano/micro plates based on the nonlocal theory and combination of reduced order modelling and multiple scale method, Mech. Syst. Signal Process., 163, 10.1016/j.ymssp.2021.108132 Awrejcewicz, 2021, Parametric vibrations of graphene sheets based on the double mode model and the nonlocal elasticity theory, Nonlinear Dynam., 105, 2173, 10.1007/s11071-021-06765-w Thang, 2021, Size-dependent analysis of functionally graded carbon nanotube-reinforced composite nanoshells with double curvature based on nonlocal strain gradient theory, Eng. Comput., 10.1007/s00366-021-01517-1 Vinh, 2022, Free vibration analysis offunctionally graded doubly curved nanoshells using nonlocal first-order shear deformation theory with variable nonlocal parameters, Thin-Walled Struct., 174 Vinh, 2021, The role of spatial variation of the nonlocal parameter on the free vibration of functionally graded sandwich nanoplates, Eng. Comput. Vinh, 2022, Nonlocal free vibration characteristics of power-law and sigmoid functionally graded nanoplates considering variable nonlocal parameter, Physica E, 135 Kneifati, 1985, Analysis of plates on a Kerr foundation model, J. Eng. Mech., 111, 1325, 10.1061/(ASCE)0733-9399(1985)111:11(1325) Addou, 2019, Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT, Comput. Concr., 24, 347 Li, 2021, Free vibration analysis of FGM plates on Winkler/Pasternak/Kerr foundation by using a simple quasi-3D HSDT, Compos. Struct., 264, 10.1016/j.compstruct.2021.113643 Keshtegar, 2020, Wave propagation and vibration responses in porous smart nanocomposite sandwich beam resting on Kerr foundation considering structural damping, Thin-Walled Struct., 154, 10.1016/j.tws.2020.106820 Shahsavari, 2018, A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation, Aerosp. Sci. Technol., 72, 134, 10.1016/j.ast.2017.11.004 Kumar, 2022, Vibration analysis of the rectangular FG materials plate with variable thickness on Winkler-Pasternak-Kerr elastic foundation, Mater. Today Proc. 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 Yang, 2020, Nonlinear flexural behavior of temperature-dependent FG-CNTRC laminated beams with negative Poisson’s ratio resting on the Pasternak foundation, Eng. Struct., 207, 10.1016/j.engstruct.2020.110250 Cong, 2018, New approach to investigate the nonlinear dynamic response and vibration of a functionally graded multilayer graphene nanocomposite plate on a viscoelastic Pasternak medium in a thermal environment, Acta Mech., 229, 3651, 10.1007/s00707-018-2178-3 Fan, 2020, Manufacture and characterization of graphene membranes with suspended silicon proof masses for MEMS and NEMS applications, Microsyst. Nanoeng., 6, 10.1038/s41378-019-0128-4 Khan, 2017, Mechanical and electromechanical properties of graphene and their potential application in MEMS, J. Phys. D. Appl. Phys., 50, 0, 10.1088/1361-6463/50/5/053003 Young, 2007, MEMS/NEMS devices and applications, 415 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 Kiani, 2022, Influence of graphene platelets on the response of composite plates subjected to a moving load, Mech. Based Des. Struct. Mach., 50, 1123, 10.1080/15397734.2020.1744006 Jafari, 2021, Free vibration of functionally graded graphene platelet reinforced plates: A quasi 3D shear and normal deformable plate model, Compos. Struct., 275, 10.1016/j.compstruct.2021.114409 Gholami, 2019, On the nonlinear vibrations of polymer nanocomposite rectangular plates reinforced by graphene nanoplatelets: A unified higher-order shear deformable model, Iran. J. Sci. Technol. Trans. Mech. Eng., 43, 603, 10.1007/s40997-018-0182-9 Teng, 2021, Nonlinear forced vibration of simply supported functionally graded porous nanocomposite thin plates reinforced with graphene platelets, Thin-Walled Struct., 164, 10.1016/j.tws.2021.107799 Civalek, 2022, Buckling and free vibrations of CNT-reinforced cross-ply laminated composite plates, Mech. Based Des. Struct. Mach., 50, 1914, 10.1080/15397734.2020.1766494 Duc, 2021 Duc, 2014 Duc, 2018, Nonlinear thermo-mechanical dynamic analysis and vibration of higher order shear deformable piezoelectric functionally graded material sandwich plates resting on elastic foundations, J. Sandw. Struct. Mater., 20 Cong, 2022, Nonlinear thermo-mechanical analysis of ES double curved shallow auxetic honeycomb sandwich shells with temperature-dependent properties, Compos. Struct., 279, 10.1016/j.compstruct.2021.114739 Cong, 2021, Nonlinear dynamic analysis of porous eccentrically stiffened double curved shallow auxetic shells in thermal environments, Thin-Walled Struct., 163, 10.1016/j.tws.2021.107748 Guzmań de Villoria, 2007, Mechanical model to evaluate the effect of the dispersion in nanocomposites, Acta Mater., 55, 3025, 10.1016/j.actamat.2007.01.007 Reddy, 2004 Renani, 2005, Buckling of imperfect functionally graded plates under in-plane compressive loading, Thin – Wall Struct., 43, 1020, 10.1016/j.tws.2005.01.002 Volmir, 1972 Dawe, 1980, Rayleigh-ritz vibration analysis of mindlin plates, J. Sound Vib., 69, 345, 10.1016/0022-460X(80)90477-0 Shen, 2005, Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings, Int. J. Solids Struct., 42, 6101, 10.1016/j.ijsolstr.2005.03.042