Nonlinear static and dynamic responses of graphene platelets reinforced composite beam with dielectric permittivity

Chen, 2014, Poly(methyl methacrylate)-functionalized graphene/polyurethane dielectric elastomer composites with superior electric field induced strain, Mater. Lett., 128, 19, 10.1016/j.matlet.2014.04.075 Liu, 2015, High performance dielectric elastomers by partially reduced graphene oxide and disruption of hydrogen bonding of polyurethanes, Polymer, 56, 375, 10.1016/j.polymer.2014.11.012 Javey, 2002, High-kappa dielectrics for advanced carbon-nanotube transistors and logic gates, Nat. Mater., 1, 241, 10.1038/nmat769 Feng, 2011, Dynamic characteristics of a dielectric elastomer-based microbeam resonator with small vibration amplitude, J. Micromech. Microeng., 21, 1, 10.1088/0960-1317/21/9/095002 Jung, 2008, A self-sensing dielectric elastomer actuator, Sens. Actuat. A Phys., 143, 343, 10.1016/j.sna.2007.10.076 Wissler, 2005, Modeling and simulation of dielectric elastomer actuators, Smart Mater. Struct., 14, 1396, 10.1088/0964-1726/14/6/032 Feng, 2014, Dynamic analysis of a dielectric elastomer-based microbeam resonator with large vibration amplitude, Int. J. Nonlinear Mech., 65, 63, 10.1016/j.ijnonlinmec.2014.05.004 Selvi, 2014, Carbon black-polybenzoxazine nanocomposites for highKdielectric applications, Polym. Compos., 35, 2121, 10.1002/pc.22874 Calberg, 1999, Electrical and dielectric properties of carbon black filled co-continuous two-phase polymer blends, J. Phys. D Appl. Phys., 32, 1517, 10.1088/0022-3727/32/13/313 Gholami, 2017, Nonlinear resonant dynamics of geometrically imperfect higher-order shear deformable functionally graded carbon-nanotube reinforced composite beams, Compos. Struct., 174, 45, 10.1016/j.compstruct.2017.04.042 Wang, 2005, Carbon nanotube composites with high dielectric constant at low percolation threshold, Appl. Phys. Lett., 87 Gholami, 2018, Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading, Eur. Phys. J. Plus, 133 Ameli, 2014, Polypropylene/carbon nanotube nano/microcellular structures with high dielectric permittivity, low dielectric loss, and low percolation threshold, Carbon, 71, 206, 10.1016/j.carbon.2014.01.031 Gholami, 2018, Nonlinear bending of third-order shear deformable carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with different edge supports, Eur. Phys. J. Plus, 133, 56, 10.1140/epjp/i2018-11874-6 Ren, 2017, Nanocable-structured polymer/carbon nanotube composite with low dielectric loss and high impedance, Compos. Part A Appl. Sci. Manuf., 98, 66, 10.1016/j.compositesa.2017.03.014 Gholami, 2018, The effect of initial geometric imperfection on the nonlinear resonance of functionally graded carbon nanotube-reinforced composite rectangular plates, Appl. Math. Mech., 39, 1219, 10.1007/s10483-018-2367-9 Gholami, 2018, Vibration of FG-CNTRC annular sector plates resting on the Winkler-Pasternak elastic foundation under a periodic radial compressive load, Mater. Res. Express, 5 Gholami, 2018, Numerical study on the nonlinear resonant dynamics of carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with various boundary conditions, Aerosp. Sci. Technol., 78, 118, 10.1016/j.ast.2018.03.043 Tian, 2014, Graphene encapsulated rubber latex composites with high dielectric constant, low dielectric loss and low percolation threshold, J. Colloid Interface Sci., 430, 249, 10.1016/j.jcis.2014.05.034 Chen, 2013, Preparation of thermostable PBO/graphene nanocomposites with high dielectric constant, Nanotechnology, 24, 10.1088/0957-4484/24/24/245702 Fan, 2012, Graphene/poly(vinylidene fluoride) composites with high dielectric constant and low percolation threshold, Nanotechnology, 23, 10.1088/0957-4484/23/36/365702 Park, 2015, Epoxy toughening with low graphene loading, Adv. Funct. Mater., 25, 575, 10.1002/adfm.201402553 Rafiee, 2009, Buckling resistant graphene nanocomposites, Appl. Phys. Lett., 95, 10.1063/1.3269637 Zhao, 2010, Enhanced mechanical properties of graphene-based poly(vinyl alcohol) composites, Macromolecules, 43, 2357, 10.1021/ma902862u Rahman, 2013, Molecular modeling of crosslinked graphene–epoxy nanocomposites for characterization of elastic constants and interfacial properties, Compos. Part B Eng., 54, 353, 10.1016/j.compositesb.2013.05.034 Sun, 2018, Tensile behavior of polymer nanocomposite reinforced with graphene containing defects, Eur. Polym. J., 98, 475, 10.1016/j.eurpolymj.2017.11.050 Feng, 2018, Effects of reorientation of graphene platelets (GPLs) on Young's modulus of polymer composites under Bi-axial stretching, Nanomaterials, 8, 27, 10.3390/nano8010027 Ji, 2010, Micromechanics prediction of the effective elastic moduli of graphene sheet-reinforced polymer nanocomposites, Model. Simul. Mater. Sci. Eng., 18, 10.1088/0965-0393/18/4/045005 Spanos, 2015, Mechanical properties of graphene nanocomposites: a multiscale finite element prediction, Compos. Struct., 132, 536, 10.1016/j.compstruct.2015.05.078 Feng, 2017, Effects of reorientation of graphene platelets (GPLs) on Young's modulus of polymer nanocomposites under uni-axial stretching, Polymers, 9, 532, 10.3390/polym9100532 He, 2009, High dielectric permittivity and low percolation threshold in nanocomposites based on poly(vinylidene fluoride) and exfoliated graphite nanoplates, Adv. Mater., 21, 10.1002/adma.200801758 Xia, 2017, A frequency-dependent theory of electrical conductivity and dielectric permittivity for graphene-polymer nanocomposites, Carbon, 111, 221, 10.1016/j.carbon.2016.09.078 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 Kiani, 2018, Enhancement of non-linear thermal stability of temperature dependent laminated beams with graphene reinforcements, Compos. Struct., 186, 114, 10.1016/j.compstruct.2017.11.086 Wu, 2017, Dynamic instability of functionally graded multilayer graphene nanocomposite beams in thermal environment, Compos. Struct., 162, 244, 10.1016/j.compstruct.2016.12.001 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 Chen, 2017, Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams, Compos. Sci. Technol., 142, 235, 10.1016/j.compscitech.2017.02.008 Feng, 2017, Nonlinear bending of polymer nanocomposite beams reinforced with non -uniformly distributed graphene platelets (GPLs), Compos. Part B Eng., 110, 132, 10.1016/j.compositesb.2016.11.024 Gholami, 2017, Large deflection geometrically nonlinear analysis of functionally graded multilayer graphene platelet-reinforced polymer composite rectangular plates, Compos. Struct., 180, 760, 10.1016/j.compstruct.2017.08.053 Shen, 2017, Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments, Compos. Struct., 170, 80, 10.1016/j.compstruct.2017.03.001 Gholami, 2018, Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates, Eng. Struct., 156, 197, 10.1016/j.engstruct.2017.11.019 Zhao, 2017, Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs), Compos. Struct., 180, 799, 10.1016/j.compstruct.2017.08.044 Gholami, 2019, Nonlinear stability and vibration of pre/post-buckled multilayer FG-GPLRPC rectangular plates, Appl. Math. Model., 65, 627, 10.1016/j.apm.2018.08.038 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 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 Shen, 2017, Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments, Comput. Math. Appl. Mech. Eng., 319, 175, 10.1016/j.cma.2017.02.029 Wang, 2018, Buckling of graphene platelet reinforced composite cylindrical shell with cutout, Int. J. Struct. Stab. Dyn., 18, 10.1142/S0219455418500402 Wang, 2018, Eigenvalue buckling of functionally graded cylindrical shells reinforced with graphene platelets (GPL), Compos. Struct., 202, 38, 10.1016/j.compstruct.2017.10.005 Sahmani, 2017, A nonlocal strain gradient hyperbolic shear deformable shell model for radial postbuckling analysis of functionally graded multilayer GPLRC nanoshells, Compos. Struct., 178, 97, 10.1016/j.compstruct.2017.06.062 Wang, 2018, Torsional buckling of graphene platelets (GPLs) reinforced functionally graded cylindrical shell with cutout, Compos. Struct., 197, 72, 10.1016/j.compstruct.2018.05.056 Rafiee, 2009, Enhanced mechanical properties of nanocomposites at low graphene content, ACS Nano, 3, 3884, 10.1021/nn9010472 Weng, 2010, A dynamical theory for the Mori–Tanaka and Ponte Castañeda–Willis estimates, Mech. Mater., 42, 886, 10.1016/j.mechmat.2010.06.004 Liu, 2008, Reinforcing efficiency of nanoparticles: a simple comparison for polymer nanocomposites, Compos. Sci. Technol., 68, 1502, 10.1016/j.compscitech.2007.10.033 Taya, 2005 Seidel, 2009, A micromechanics model for the electrical conductivity of nanotube-polymer nanocomposites, J. Compos. Mater., 43, 917, 10.1177/0021998308105124 Feng, 2013, Micromechanics modeling of the electrical conductivity of carbon nanotube (CNT)–polymer nanocomposites, Compos. Part A Appl. Sci. Manuf., 47, 143, 10.1016/j.compositesa.2012.12.008 Wang, 2015, Percolation threshold and electrical conductivity of graphene-based nanocomposites with filler agglomeration and interfacial tunneling, J. Appl. Phys., 118 Wang, 2014, A continuum model with a percolation threshold and tunneling-assisted interfacial conductivity for carbon nanotube-based nanocomposites, J. Appl. Phys., 115, 10.1063/1.4878195 Hashemi, 2016, A theoretical treatment of graphene nanocomposites with percolation threshold, tunneling-assisted conductivity and microcapacitor effect in AC and DC electrical settings, Carbon, 96, 474, 10.1016/j.carbon.2015.09.103 Dyre, 1985, A simple-model of ac hopping conductivity in disordered solids, Phys. Lett. A, 108, 457, 10.1016/0375-9601(85)90039-8 Layek, 2010, Physical and mechanical properties of poly(methyl methacrylate) -functionalized graphene/poly(vinylidine fluoride) nanocomposites Piezoelectric beta polymorph formation, Polymer, 51, 5846, 10.1016/j.polymer.2010.09.067 Nayfeh, 2006, Dynamic pull-in phenomenon in MEMS resonators, Nonlinear Dyn., 48, 153, 10.1007/s11071-006-9079-z Wang, 2015 Ibrahim, 2009, Modified shooting approach to the non-linear periodic forced response of isotropic/composite curved beams, Int. J. Nonlinear Mech., 44, 1073, 10.1016/j.ijnonlinmec.2009.08.004 Reddy, 2014, Non-linear analysis of functionally graded microbeams using Eringen׳s non-local differential model, Int. J. Nonlinear Mech., 67, 308, 10.1016/j.ijnonlinmec.2014.09.014