Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model

Davood Shahsavari; Behrouz Karami; Li Li

doi:10.1016/j.crme.2018.08.011

Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model

Davood Shahsavari ¹ ; Behrouz Karami ¹ ; Li Li ²

¹ Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
² State Key Lab of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Comptes Rendus. Mécanique, Volume 346 (2018) no. 12, pp. 1216-1232.

Résumé

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.

Reçu le : 2018-05-22
Accepté le : 2018-08-24
Publié le : 2018-09-05

DOI : 10.1016/j.crme.2018.08.011

Mots clés : Damped vibration, Bi-Helmholtz nonlocal strain gradient theory, Environmental effects, Graphene, Visco-Pasternak foundation

Affiliations des auteurs :

Davood Shahsavari ¹ ; Behrouz Karami ¹ ; Li Li ²

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     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},
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     language = {en},
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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/

Bibliographie
Cité par

[1] C. Chen; J. Hone 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] K. Duan et al. Pillared graphene as an ultra-high sensitivity mass sensor, Sci. Rep., Volume 7 (2017) no. 1

[4] J. Liang et al. Electromechanical actuators based on graphene and graphene/Fe₃O₄ hybrid paper, Adv. Funct. Mater., Volume 21 (2011) no. 19, pp. 3778-3784

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

[6] E. Andrews 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] G.-L. She et al. Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory, Compos. Struct. (2018)

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

[9] D. Shahsavari; B. Karami; L. Li A high-order gradient model for wave propagation analysis of porous FG nanoplates, Steel Compos. Struct. (2018) (just-accepted)

[10] G.-L. She; F.-G. Yuan; Y.-R. Ren 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] B. Karami; D. Shahsavari; M. Janghorban 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] A.C. Eringen; D. Edelen On nonlocal elasticity, Int. J. Eng. Sci., Volume 10 (1972) no. 3, pp. 233-248

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

[14] M. Aydogdu 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] L. Shen; H.-S. Shen; C.-L. Zhang 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] B. Arash; Q. Wang 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] F.M. de Sciarra; M. Canadija; R. Barretta A gradient model for torsion of nanobeams, C. R. Mecanique, Volume 343 (2015) no. 4, pp. 289-300

[18] D. Shahsavari 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] D. Shahsavari; M. Janghorban 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] B. Karami; M. Janghorban; L. Li On guided wave propagation in fully clamped porous functionally graded nanoplates, Acta Astronaut., Volume 143 (2018), pp. 380-390

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

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

[23] G.-L. She; F.-G. Yuan; Y.-R. Ren On wave propagation of porous nanotubes, Int. J. Eng. Sci., Volume 130 (2018), pp. 62-74

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

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

[26] B. Karami 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] D. Shahsavari 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] M. Lazar; G.A. Maugin; E.C. Aifantis 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] C.C. Koutsoumaris 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] M. Shaat; A. Abdelkefi New insights on the applicability of Eringen's nonlocal theory, Int. J. Mech. Sci., Volume 121 (2017), pp. 67-75

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

[32] C. Lim; G. Zhang; J. Reddy 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] Q.-Y. Lin et al. Stretch-induced stiffness enhancement of graphene grown by chemical vapor deposition, ACS Nano, Volume 7 (2013) no. 2, pp. 1171-1177

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

[35] B. Karami; D. Shahsavari; L. Li 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] E.C. Aifantis Update on a class of gradient theories, Mech. Mater., Volume 35 (2003) no. 3–6, pp. 259-280

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

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

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

[40] F. Ebrahimi; M.R. Barati; A. Dabbagh 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] B. Karami; M. Janghorban; A. Tounsi Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles, Steel Compos. Struct., Volume 27 (2018) no. 2, pp. 201-216

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

[43] B. Karami; M. Janghorban; A. Tounsi 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] H.B. Khaniki; S. Hosseini-Hashemi 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] L. Li; H. Tang; Y. Hu The effect of thickness on the mechanics of nanobeams, Int. J. Eng. Sci., Volume 123 (2018), pp. 81-91

[46] M.R. Nami; M. Janghorban 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] B. Karami et al. Wave dispersion of mounted graphene with initial stress, Thin-Walled Struct., Volume 122 (2018), pp. 102-111

[48] D. Shahsavari; B. Karami; S. Mansouri 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] B. Karami 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] B. Karami; M. Janghorban; A. Tounsi Effects of triaxial magnetic field on the anisotropic nanoplates, Steel Compos. Struct., Volume 25 (2017) no. 3, pp. 361-374

[51] B. Karami; D. Shahsavari; L. Li 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] M.R. Barati On wave propagation in nanoporous materials, Int. J. Eng. Sci., Volume 116 (2017), pp. 1-11

[53] M.R. Barati; A. Zenkour 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] A. Farajpour 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] B. Karami 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] H.-S. Shen; L. Shen; C.-L. Zhang 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] D.D. Han et al. Moisture-responsive graphene paper prepared by self-controlled photoreduction, Adv. Mater., Volume 27 (2015) no. 2, pp. 332-338

[58] E.O. Alzahrani; A.M. Zenkour; M. Sobhy Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium, Compos. Struct., Volume 105 (2013), pp. 163-172

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

[60] D. Shahsavari 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] R. Kolahchi; M. Safari; M. Esmailpour 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] S. Pouresmaeeli; E. Ghavanloo; S. Fazelzadeh Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium, Compos. Struct., Volume 96 (2013), pp. 405-410

[63] H.F. Brinson; L.C. Brinson Polymer Engineering Science and Viscoelasticity, Springer, 2008

[64] A.G. Arani 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] B. Karami; M. Janghorban 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] P. Malekzadeh; A. Setoodeh; A.A. Beni 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] J.E. Lagnese Boundary Stabilization of Thin Plates, SIAM, 1989

[68] A.D. Drozdov Viscoelastic Structures: Mechanics of Growth and Aging, Academic Press, 1998

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

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

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

[72] M. Sobhy 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] H. Ma; X.-L. Gao; J. Reddy 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] W. Xiao; L. Li; M. Wang 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] M. Mohr et al. Phonon dispersion of graphite by inelastic X-ray scattering, Phys. Rev. B, Volume 76 (2007) no. 3

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