A higher-order nonlocal strain-gradient model is presented for the damped vibration analysis of single-layer graphene sheets (SLGSs) in hygrothermal environment. Based on Kirchhoff plate theory in conjunction with a higher-order (bi-Helmholtz) nonlocal strain gradient theory, the equations of motion are obtained using Hamilton's principle. The higher-order nonlocal strain gradient theory has lower- and higher-order nonlocal parameters and a material characteristic parameter. The presented model can reasonably interpret the softening effects of the SLGS, and indicates a reasonably good match with the experimental flexural frequencies. Finally, the roles of viscous and structural damping coefficients, small-scale parameters, hygrothermal environment and elastic foundation on the vibrational responses of SLGSs are studied in detail.

Accepted:

Published online:

Davood Shahsavari ^{1};
Behrouz Karami ^{1};
Li Li ^{2}

@article{CRMECA_2018__346_12_1216_0, author = {Davood Shahsavari and Behrouz Karami and Li Li}, title = {Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient {Kirchhoff} plate model}, journal = {Comptes Rendus. M\'ecanique}, pages = {1216--1232}, publisher = {Elsevier}, volume = {346}, number = {12}, year = {2018}, doi = {10.1016/j.crme.2018.08.011}, language = {en}, }

TY - JOUR AU - Davood Shahsavari AU - Behrouz Karami AU - Li Li TI - Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model JO - Comptes Rendus. Mécanique PY - 2018 SP - 1216 EP - 1232 VL - 346 IS - 12 PB - Elsevier DO - 10.1016/j.crme.2018.08.011 LA - en ID - CRMECA_2018__346_12_1216_0 ER -

%0 Journal Article %A Davood Shahsavari %A Behrouz Karami %A Li Li %T Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model %J Comptes Rendus. Mécanique %D 2018 %P 1216-1232 %V 346 %N 12 %I Elsevier %R 10.1016/j.crme.2018.08.011 %G en %F CRMECA_2018__346_12_1216_0

Davood Shahsavari; Behrouz Karami; Li Li. Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model. Comptes Rendus. Mécanique, Volume 346 (2018) no. 12, pp. 1216-1232. doi : 10.1016/j.crme.2018.08.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.08.011/

[1] Graphene nanoelectromechanical systems, Proc. IEEE, Volume 101 (2013) no. 7, pp. 1766-1779

[2] J. Schroeder, F.P. Cammisa, Carbon nanotubes and graphene patches and implants for biological tissue, 2014, Google Patents.

[3] et al. Pillared graphene as an ultra-high sensitivity mass sensor, Sci. Rep., Volume 7 (2017) no. 1

[4] et al. Electromechanical actuators based on graphene and graphene/Fe_{3}O_{4} hybrid paper, Adv. Funct. Mater., Volume 21 (2011) no. 19, pp. 3778-3784

[5] et al. Experiments and theory in strain gradient elasticity, J. Mech. Phys. Solids, Volume 51 (2003) no. 8, pp. 1477-1508

[6] et al. Size effects in ductile cellular solids, part II: experimental results, Int. J. Mech. Sci., Volume 43 (2001) no. 3, pp. 701-713

[7] et al. Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory, Compos. Struct. (2018)

[8] et al. On buckling and postbuckling behavior of nanotubes, Int. J. Eng. Sci., Volume 121 (2017), pp. 130-142

[9] A high-order gradient model for wave propagation analysis of porous FG nanoplates, Steel Compos. Struct. (2018) (just-accepted)

[10] Nonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory, Compos. Struct., Volume 165 (2017), pp. 74-82

[11] Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory, Mech. Adv. Mat. Struct., Volume 25 (2018) no. 12, pp. 1047-1057

[12] On nonlocal elasticity, Int. J. Eng. Sci., Volume 10 (1972) no. 3, pp. 233-248

[13] Nonlocal theories for bending, buckling and vibration of beams, Int. J. Eng. Sci., Volume 45 (2007) no. 2–8, pp. 288-307

[14] A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration, Physica E, Low-Dimens. Syst. Nanostruct., Volume 41 (2009) no. 9, pp. 1651-1655

[15] Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments, Comput. Mater. Sci., Volume 48 (2010) no. 3, pp. 680-685

[16] A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes, Comput. Mater. Sci., Volume 51 (2012) no. 1, pp. 303-313

[17] A gradient model for torsion of nanobeams, C. R. Mecanique, Volume 343 (2015) no. 4, pp. 289-300

[18] et al. Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment, Mater. Res. Express, Volume 4 (2017) no. 8

[19] Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load, J. Braz. Soc. Mech. Sci. Eng., Volume 39 (2017) no. 10, pp. 3849-3861

[20] On guided wave propagation in fully clamped porous functionally graded nanoplates, Acta Astronaut., Volume 143 (2018), pp. 380-390

[21] Modelling vibrating nano-strings by lattice, finite difference and Eringen's nonlocal models, J. Sound Vib., Volume 425 (2018), pp. 41-52

[22] et al. On vibrations of porous nanotubes, Int. J. Eng. Sci., Volume 125 (2018), pp. 23-35

[23] On wave propagation of porous nanotubes, Int. J. Eng. Sci., Volume 130 (2018), pp. 62-74

[24] Torsional vibration of bi-directional functionally graded nanotubes based on nonlocal elasticity theory, Compos. Struct., Volume 172 (2017), pp. 242-250

[25] Twisting statics of functionally graded nanotubes using Eringen's nonlocal integral model, Compos. Struct., Volume 178 (2017), pp. 87-96

[26] et al. Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory, Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci. (2018)

[27] et al. On the shear buckling of porous nanoplates using a new size-dependent quasi-3D shear deformation theory, Acta Mech. (2018) (article in press)

[28] On a theory of nonlocal elasticity of bi-Helmholtz type and some applications, Int. J. Solids Struct., Volume 43 (2006) no. 6, pp. 1404-1421

[29] et al. Application of bi-Helmholtz nonlocal elasticity and molecular simulations to the dynamical response of carbon nanotubes, AIP Conference Proceedings, AIP Publishing, 2015

[30] New insights on the applicability of Eringen's nonlocal theory, Int. J. Mech. Sci., Volume 121 (2017), pp. 67-75

[31] et al. Functionally graded Timoshenko nanobeams: a novel nonlocal gradient formulation, Composites, Part B, Eng., Volume 100 (2016), pp. 208-219

[32] A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, J. Mech. Phys. Solids, Volume 78 (2015), pp. 298-313

[33] et al. Stretch-induced stiffness enhancement of graphene grown by chemical vapor deposition, ACS Nano, Volume 7 (2013) no. 2, pp. 1171-1177

[34] On longitudinal dynamics of nanorods, Int. J. Eng. Sci., Volume 120 (2017), pp. 129-145

[35] Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory, Physica E, Low-Dimens. Syst. Nanostruct., Volume 97 (2018), pp. 317-327

[36] Update on a class of gradient theories, Mech. Mater., Volume 35 (2003) no. 3–6, pp. 259-280

[37] The small length scale effect for a non-local cantilever beam: a paradox solved, Nanotechnology, Volume 19 (2008) no. 34

[38] Bending, buckling, and vibration of micro/nanobeams by hybrid nonlocal beam model, J. Eng. Mech., Volume 136 (2009) no. 5, pp. 562-574

[39] Size dependency in vibration analysis of nano plates; one problem, different answers, Eur. J. Mech. A, Solids, Volume 59 (2016), pp. 124-139

[40] A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates, Int. J. Eng. Sci., Volume 107 (2016), pp. 169-182

[41] Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles, Steel Compos. Struct., Volume 27 (2018) no. 2, pp. 201-216

[42] Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory, Int. J. Mech. Sci., Volume 115–116 (2016), pp. 135-144

[43] Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory, Thin-Walled Struct., Volume 129 (2018), pp. 251-264

[44] Buckling analysis of tapered nanobeams using nonlocal strain gradient theory and a generalized differential quadrature method, Mater. Res. Express, Volume 4 (2017) no. 6

[45] The effect of thickness on the mechanics of nanobeams, Int. J. Eng. Sci., Volume 123 (2018), pp. 81-91

[46] Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant, Compos. Struct., Volume 111 (2014), pp. 349-353

[47] et al. Wave dispersion of mounted graphene with initial stress, Thin-Walled Struct., Volume 122 (2018), pp. 102-111

[48] Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories, Eur. J. Mech. A, Solids, Volume 67 (2018), pp. 200-214

[49] et al. Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field, Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci. (2018)

[50] Effects of triaxial magnetic field on the anisotropic nanoplates, Steel Compos. Struct., Volume 25 (2017) no. 3, pp. 361-374

[51] Temperature-dependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field, J. Therm. Stresses, Volume 41 (2018) no. 4, pp. 483-499

[52] On wave propagation in nanoporous materials, Int. J. Eng. Sci., Volume 116 (2017), pp. 1-11

[53] A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate, Compos. Struct., Volume 168 (2017), pp. 885-892

[54] et al. A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment, Acta Mech., Volume 227 (2016) no. 7, pp. 1849-1867

[55] et al. A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates, Steel Compos. Struct., Volume 28 (2018) no. 1, pp. 99-110

[56] Nonlocal plate model for nonlinear bending of single-layer graphene sheets subjected to transverse loads in thermal environments, Appl. Phys. A, Mater. Sci. Process., Volume 103 (2011) no. 1, pp. 103-112

[57] et al. Moisture-responsive graphene paper prepared by self-controlled photoreduction, Adv. Mater., Volume 27 (2015) no. 2, pp. 332-338

[58] Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium, Compos. Struct., Volume 105 (2013), pp. 163-172

[59] Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory, Compos. Struct., Volume 159 (2017), pp. 433-444

[60] et al. A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation, Aerosp. Sci. Technol., Volume 72 (2018), pp. 134-149

[61] Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium, Compos. Struct., Volume 150 (2016), pp. 255-265

[62] Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium, Compos. Struct., Volume 96 (2013), pp. 405-410

[63] Polymer Engineering Science and Viscoelasticity, Springer, 2008

[64] et al. Nonlocal vibration of coupled DLGS systems embedded on visco-Pasternak foundation, Physica B, Condens. Matter, Volume 407 (2012) no. 21, pp. 4123-4131

[65] Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory, Mod. Phys. Lett. B, Volume 30 (2016) no. 36

[66] Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium, Compos. Struct., Volume 93 (2011) no. 8, pp. 2083-2089

[67] Boundary Stabilization of Thin Plates, SIAM, 1989

[68] Viscoelastic Structures: Mechanics of Growth and Aging, Academic Press, 1998

[69] et al. Dynamics of structural systems with various frequency-dependent damping models, Front. Mech. Eng., Volume 10 (2015) no. 1, pp. 48-63

[70] Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory, Comput. Mater. Sci., Volume 112 (2016), pp. 282-288

[71] Hygrothermal deformation of orthotropic nanoplates based on the state-space concept, Composites, Part B, Eng., Volume 79 (2015), pp. 224-235

[72] Hygrothermal vibration of orthotropic double-layered graphene sheets embedded in an elastic medium using the two-variable plate theory, Appl. Math. Model., Volume 40 (2016) no. 1, pp. 85-99

[73] A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, J. Mech. Phys. Solids, Volume 56 (2008) no. 12, pp. 3379-3391

[74] Propagation of in-plane wave in viscoelastic monolayer graphene via nonlocal strain gradient theory, Appl. Phys. A, Volume 123 (2017) no. 6, p. 388

[75] et al. Phonon dispersion of graphite by inelastic X-ray scattering, Phys. Rev. B, Volume 76 (2007) no. 3

*Cited by Sources: *

Comments - Policy