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Original Articles

Wave dispersion of nanobeams incorporating stretching effect

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Pages 639-659 | Received 16 Sep 2018, Accepted 09 Apr 2019, Published online: 22 Apr 2019

References

  • Arash B, Ansari R. Evaluation of nonlocal parameter in the vibrations of single-walled carbon nanotubes with initial strain. Physica E Low Dimens Syst Nanostruct. 2010;42:2058–2064. doi: 10.1016/j.physe.2010.03.028
  • Ghavanloo E, Fazelzadeh SA. Radial vibration of free anisotropic nanoparticles based on nonlocal continuum mechanics. Nanotechnology. 2013;24:075702. doi: 10.1088/0957-4484/24/7/075702
  • Lin Q-Y, Jing G, Zhou Y-B, et al. Stretch-induced stiffness enhancement of graphene grown by chemical vapor deposition. ACS Nano. 2013;7:1171–1177. doi: 10.1021/nn3053999
  • Eringen AC, Edelen D. On nonlocal elasticity. Int J Eng Sci. 1972;10:233–248. doi: 10.1016/0020-7225(72)90039-0
  • Lam DC, Yang F, Chong A, et al. Experiments and theory in strain gradient elasticity. J Mech Phys Solids. 2003;51:1477–1508. doi: 10.1016/S0022-5096(03)00053-X
  • Bounouara F, Benrahou KH, Belkorissat I, et al. A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation. Steel Compos Struct. 2016;20:227–249. doi: 10.12989/scs.2016.20.2.227
  • Belkorissat I, Houari MSA, Tounsi A, et al. On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model. Steel Compos Struct. 2015;18:1063–1081. doi: 10.12989/scs.2015.18.4.1063
  • Ebrahimi F, Salari E. Semi-analytical vibration analysis of functionally graded size-dependent nanobeams with various boundary conditions. Smart Struct Syst. 2017;19:243–257. doi: 10.12989/sss.2017.19.3.243
  • Shahsavari D, Karami B, Janghorban M, et al. Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment. Mater Res Express. 2017;4:085013. doi: 10.1088/2053-1591/aa7d89
  • Karami B, Janghorban M, Li L. On guided wave propagation in fully clamped porous functionally graded nanoplates. Acta Astronaut. 2018;143:380–390. doi: 10.1016/j.actaastro.2017.12.011
  • Karami B, Janghorban M. 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. 2016;30:1650421. doi: 10.1142/S0217984916504212
  • Karami B, Shahsavari D, Li L, 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 Pt C J Mechan Eng Sci. 2019;233:287–301. doi: 10.1177/0954406218756451
  • Karami B, Shahsavari D, Janghorban M. A comprehensive analytical study on functionally graded carbon nanotube-reinforced composite plates. Aerosp Sci Technol. 2018;82:499–512. doi: 10.1016/j.ast.2018.10.001
  • Yazid M, Heireche H, Tounsi A, et al. A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium. Smart Struct Syst. 2018;21:15–25.
  • Zemri A, Houari MSA, Bousahla AA, et al. A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory. Struct Eng Mech. 2015;54:693–710. doi: 10.12989/sem.2015.54.4.693
  • Bouadi A, Bousahla AA, Houari MSA, et al. A new nonlocal HSDT for analysis of stability of single layer graphene sheet. Adv Nano Res. 2018;6:147–162.
  • Hamza-Cherif R, Meradjah M, Zidour M, et al. Vibration analysis of nano beam using differential transform method including thermal effect. J Nano Res. 2018;54:1–14. doi: 10.4028/www.scientific.net/JNanoR.54.1
  • Mokhtar Y, Heireche H, Bousahla AA, et al. A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory. Smart Struct Syst. 2018;21:397–405.
  • Kadari B, Bessaim A, Tounsi A, et al. Buckling analysis of orthotropic nanoscale plates resting on elastic foundations. J Nano Res. 2018;55:42–56. doi: 10.4028/www.scientific.net/JNanoR.55.42
  • Khetir H, Bouiadjra MB, Houari MSA, et al. A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates. Struct Eng Mech. 2017;64:391–402.
  • Bakhadda B, Bouiadjra MB, Bourada F, et al. Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation. Wind Struct. 2018;27:311–324.
  • Sobhy M. Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory. Struct Eng Mech. 2017;63:401–415.
  • Pradhan S, Phadikar J. Nonlocal elasticity theory for vibration of nanoplates. J Sound Vib. 2009;325:206–223. doi: 10.1016/j.jsv.2009.03.007
  • Askes H, Aifantis EC. Gradient elasticity and flexural wave dispersion in carbon nanotubes. Phys Rev B. 2009;80:195412. doi: 10.1103/PhysRevB.80.195412
  • Lim C, Zhang G, Reddy J. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J Mech Phys Solids. 2015;78:298–313. doi: 10.1016/j.jmps.2015.02.001
  • Li L, Hu Y, Ling L. Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Compos Struct. 2015;133:1079–1092. doi: 10.1016/j.compstruct.2015.08.014
  • Nami MR, Janghorban M. Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant. Compos Struct. 2014;111:349–353. doi: 10.1016/j.compstruct.2014.01.012
  • Zhu X, Li L. Closed form solution for a nonlocal strain gradient rod in tension. Int J Eng Sci. 2017;119:16–28. doi: 10.1016/j.ijengsci.2017.06.019
  • Karami B, Janghorban M, Tounsi A. Effects of triaxial magnetic field on the anisotropic nanoplates. Steel Compos Struct. 2017;25:361–374.
  • Shahsavari D, Karami B, Mansouri S. 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. 2018;67:200–214. doi: 10.1016/j.euromechsol.2017.09.004
  • Li L, Li X, Hu Y. Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. Int J Eng Sci. 2016;102:77–92. doi: 10.1016/j.ijengsci.2016.02.010
  • Li L, Hu Y. Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. Int J Eng Sci. 2015;97:84–94. doi: 10.1016/j.ijengsci.2015.08.013
  • Li L, Hu Y. Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects. Int J Mech Sci. 2017;120:159–170. doi: 10.1016/j.ijmecsci.2016.11.025
  • Karami B, Janghorban M, Tounsi A. Galerkin’s approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions. Eng Comput. 2018. doi: 10.1007/s00366-018-0664-9
  • She G-L, Yuan F-G, Karami B, et al. On nonlinear bending behavior of FG porous curved nanotubes. Int J Eng Sci. 2019;135:58–74. doi: 10.1016/j.ijengsci.2018.11.005
  • She G-L, Yuan F-G, Ren Y-R, et al. Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory. Compos Struct. 2018;203:614–623. doi: 10.1016/j.compstruct.2018.07.063
  • Farajpour A, Yazdi MH, Rastgoo A, et al. A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment. Acta Mech. 2016;227:1849–1867. doi: 10.1007/s00707-016-1605-6
  • Sahmani S, Aghdam M. Nonlinear instability of axially loaded functionally graded multilayer graphene platelet-reinforced nanoshells based on nonlocal strain gradient elasticity theory. Int J Mech Sci. 2017;131:95–106. doi: 10.1016/j.ijmecsci.2017.06.052
  • She G-L, Yuan F-G, Ren Y-R, et al. On buckling and postbuckling behavior of nanotubes. Int J Eng Sci. 2017;121:130–142. doi: 10.1016/j.ijengsci.2017.09.005
  • Karami B, Karami S. Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials. Adv Nano Res. 2019;7:51–61.
  • She G-L, Ren Y-R, Xiao W-S, et al. Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations. Struct Eng Mech. 2018;66:729–736.
  • Zhu X, Li L. Longitudinal and torsional vibrations of size-dependent rods via nonlocal integral elasticity. Int J Mech Sci. 2017;133:639–650. doi: 10.1016/j.ijmecsci.2017.09.030
  • Sahmani S, Aghdam M. Nonlocal strain gradient beam model for nonlinear vibration of prebuckled and postbuckled multilayer functionally graded GPLRC nanobeams. Compos Struct. 2017;179:77–88. doi: 10.1016/j.compstruct.2017.07.064
  • Shafiei N, She G-L. On vibration of functionally graded nano-tubes in the thermal environment. Int J Eng Sci. 2018;133:84–98. doi: 10.1016/j.ijengsci.2018.08.004
  • Karami B, Janghorban M, Tounsi A. Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles. Steel Compos Struct. 2018;27:201–216.
  • Karami B, Janghorban M. On the dynamics of porous nanotubes with variable material properties and variable thickness. Int J Eng Sci. 2019;136:53–66. doi: 10.1016/j.ijengsci.2019.01.002
  • Farajpour A, Ghayesh MH, Farokhi H. Large-amplitude coupled scale-dependent behaviour of geometrically imperfect NSGT nanotubes. Int J Mech Sci. 2018;150:510–525. doi: 10.1016/j.ijmecsci.2018.09.043
  • Li L, Hu Y, Li X. Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory. Int J Mech Sci. 2016;115:135–144. doi: 10.1016/j.ijmecsci.2016.06.011
  • Li L, Hu Y. Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory. Comput Mater Sci. 2016;112:282–288. doi: 10.1016/j.commatsci.2015.10.044
  • Karami B, Janghorban M, Tounsi A. Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory. Thin-Walled Struct. 2018;129:251–264. doi: 10.1016/j.tws.2018.02.025
  • Karami B, Shahsavari D, Janghorban M. 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 Mater Struct. 2018;25:1047–1057. doi: 10.1080/15376494.2017.1323143
  • Karami B, Shahsavari D, Li L. Temperature-dependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field. J Therm Stresses. 2018;41:483–499. doi: 10.1080/01495739.2017.1393781
  • Karami B, Shahsavari D, Karami M, et al. Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field. Proc Inst Mech Eng Pt C J Mechan Eng Sci. 2019;233:2149–2169. doi: 10.1177/0954406218781680
  • Shahsavari D, Karami B, Li L. A high-order gradient model for wave propagation analysis of porous FG nanoplates. Steel Compos Struct. 2018;29:53–66.
  • She G-L, Yan K-M, Zhang Y-L, et al. Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory. Eur Phys J Plus. 2018;133:368. doi: 10.1140/epjp/i2018-12196-5
  • Karami B, janghorban M, Tounsi A. On exact wave propagation analysis of triclinic material using three-dimensional bi-Helmholtz gradient plate model. Struct Eng Mech. 2019;69:487–497.
  • Barati MR, Zenkour A. A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate. Compos Struct. 2017;168:885–892. doi: 10.1016/j.compstruct.2017.02.090
  • Xiao W, Li L, Wang M. Propagation of in-plane wave in viscoelastic monolayer graphene via nonlocal strain gradient theory. Appl Phys A. 2017;123:388. doi: 10.1007/s00339-017-1007-1
  • Karami B, Shahsavari D, Li L. Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory. Physica E Low Dimens Syst Nanostruct. 2018;97:317–327. doi: 10.1016/j.physe.2017.11.020
  • Shahsavari D, Karami B, Li L. Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model. Comptes Rendus Mécanique. 2018;346:1216–1232. doi: 10.1016/j.crme.2018.08.011
  • Karami B, Shahsavari D, Janghorban M, et al. Wave dispersion of mounted graphene with initial stress. Thin-Walled Struct. 2018;122:102–111. doi: 10.1016/j.tws.2017.10.004
  • Ghayesh MH. Functionally graded microbeams: simultaneous presence of imperfection and viscoelasticity. Int J Mech Sci. 2018;140:339–350. doi: 10.1016/j.ijmecsci.2018.02.037
  • Ghayesh MH. Dynamics of functionally graded viscoelastic microbeams. Int J Eng Sci. 2018;124:115–131. doi: 10.1016/j.ijengsci.2017.11.004
  • Ghayesh MH, Amabili M, Farokhi H. Three-dimensional nonlinear size-dependent behaviour of Timoshenko microbeams. Int J Eng Sci. 2013;71:1–14. doi: 10.1016/j.ijengsci.2013.04.003
  • Farokhi H, Ghayesh MH, Amabili M. Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory. Int J Eng Sci. 2013;68:11–23. doi: 10.1016/j.ijengsci.2013.03.001
  • Ghayesh MH, Farokhi H. Nonlinear dynamics of microplates. Int J Eng Sci. 2015;86:60–73. doi: 10.1016/j.ijengsci.2014.10.004
  • Farokhi H, Ghayesh MH. Size-dependent parametric dynamics of imperfect microbeams. Int J Eng Sci. 2016;99:39–55. doi: 10.1016/j.ijengsci.2015.10.014
  • Wang K, Kitamura T, Wang B. Nonlinear pull-in instability and free vibration of micro/nanoscale plates with surface energy – a modified couple stress theory model. Int J Mech Sci. 2015;99:288–296. doi: 10.1016/j.ijmecsci.2015.05.006
  • Ghugal Y, Shimpi R. A review of refined shear deformation theories for isotropic and anisotropic laminated beams. J Reinf Plast Compos. 2001;20:255–272. doi: 10.1177/073168401772678283
  • Bellifa H, Benrahou KH, Bousahla AA, et al. A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams. Struct Eng Mech. 2017;62:695–702.
  • Ebrahimi F, Barati MR. Vibration analysis of embedded size dependent FG nanobeams based on third-order shear deformation beam theory. Struct Eng Mech. 2017;61:721–736. doi: 10.12989/sem.2017.61.6.721
  • Karami B, Shahsavari D, Nazemosadat SMR, et al. Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation. Steel and Composite Structures. 2018;29:349–362.
  • Ebrahimi F, Daman M. Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment. Struct Eng Mech. 2017;64:121–133.
  • Karami B, shahsavari D, janghorban M, et al. Influence of homogenization schemes on vibration of functionally graded curved microbeams. Compos Struct. 2019;216:67–79. doi: 10.1016/j.compstruct.2019.02.089
  • Ghayesh MH, Farokhi H, Gholipour A. Oscillations of functionally graded microbeams. Int J Eng Sci. 2017;110:35–53. doi: 10.1016/j.ijengsci.2016.09.011
  • Ghayesh MH, Farokhi H, Gholipour A, et al. Resonance responses of geometrically imperfect functionally graded extensible microbeams. J Comput Nonlinear Dyn. 2017;12:051002. doi: 10.1115/1.4035214
  • Ghayesh MH, Farokhi H, Gholipour A, et al. Nonlinear oscillations of functionally graded microplates. Int J Eng Sci. 2018;122:56–72. doi: 10.1016/j.ijengsci.2017.03.014
  • Ghayesh MH, Farokhi H, Gholipour A, et al. Nonlinear bending and forced vibrations of axially functionally graded tapered microbeams. Int J Eng Sci. 2017;120:51–62. doi: 10.1016/j.ijengsci.2017.03.010
  • Gholipour A, Farokhi H, Ghayesh MH. In-plane and out-of-plane nonlinear size-dependent dynamics of microplates. Nonlinear Dyn. 2015;79:1771–1785. doi: 10.1007/s11071-014-1773-7
  • Farokhi H, Ghayesh MH. Nonlinear dynamical behaviour of geometrically imperfect microplates based on modified couple stress theory. Int J Mech Sci. 2015;90:133–144. doi: 10.1016/j.ijmecsci.2014.11.002
  • Chikh A, Tounsi A, Hebali H, et al. Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT. Smart Struct Syst. 2017;19:289–297. doi: 10.12989/sss.2017.19.3.289
  • Menasria A, Bouhadra A, Tounsi A, et al. A new and simple HSDT for thermal stability analysis of FG sandwich plates. Steel Compos Struct. 2017;25:157–175.
  • Bouderba B, Houari MSA, Tounsi A, et al. Thermal stability of functionally graded sandwich plates using a simple shear deformation theory. Struct Eng Mech. 2016;58:397–422. doi: 10.12989/sem.2016.58.3.397
  • Shimpi R, Patel H. Free vibrations of plate using two variable refined plate theory. J Sound Vib. 2006;296:979–999. doi: 10.1016/j.jsv.2006.03.030
  • Fourn H, Atmane HA, Bourada M, et al. A novel four variable refined plate theory for wave propagation in functionally graded material plates. Steel Compos Struct. 2018;27:109–122.
  • Yahia SA, Atmane HA, Houari MSA, et al. Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories. Struct Eng Mech. 2015;53:1143–1165. doi: 10.12989/sem.2015.53.6.1143
  • Beldjelili Y, Tounsi A, Mahmoud S. Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory. Smart Struct Syst. 2016;18:755–786. doi: 10.12989/sss.2016.18.4.755
  • El-Haina F, Bakora A, Bousahla AA, et al. A simple analytical approach for thermal buckling of thick functionally graded sandwich plates. Struct Eng Mech. 2017;63:585–595.
  • Attia A, Bousahla AA, Tounsi A, et al. A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations. Struct Eng Mech. 2018;65:453–464.
  • Bousahla AA, Benyoucef S, Tounsi A, et al. On thermal stability of plates with functionally graded coefficient of thermal expansion. Struct Eng Mech. 2016;60:313–335. doi: 10.12989/sem.2016.60.2.313
  • Ebrahimi F, Barati MR, Dabbagh A. A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates. Int J Eng Sci. 2016;107:169–182. doi: 10.1016/j.ijengsci.2016.07.008
  • Carrera E, Brischetto S, Cinefra M, et al. Effects of thickness stretching in functionally graded plates and shells. Compos B Eng. 2011;42:123–133. doi: 10.1016/j.compositesb.2010.10.005
  • Thai H-T, Kim S-E. A review of theories for the modeling and analysis of functionally graded plates and shells. Compos Struct. 2015;128:70–86. doi: 10.1016/j.compstruct.2015.03.010
  • Shahsavari D, Karami B, Fahham HR, et al. On the shear buckling of porous nanoplates using a new size-dependent quasi-3D shear deformation theory. Acta Mech. 2018;229:4549–4573. doi: 10.1007/s00707-018-2247-7
  • Karami B, Janghorban M, Shahsavari D, et al. A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates. Steel Compos Struct. 2018;28:99–110.
  • Younsi A, Tounsi A, Zaoui FZ, et al. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates. Geomech Eng. 2018;14:519–532.
  • Bennoun M, Houari MSA, Tounsi A. A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates. Mech Adv Mater Struct. 2016;23:423–431. doi: 10.1080/15376494.2014.984088
  • Abualnour M, Houari MSA, Tounsi A, et al. A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates. Compos Struct. 2018;184:688–697. doi: 10.1016/j.compstruct.2017.10.047
  • Karami B, Shahsavari D, Janghorban M, et al. Wave propagation of porous nanoshells. Nanomaterials. 2019;9:22. doi: 10.3390/nano9010022
  • Bourada M, Kaci A, Houari MSA, et al. A new simple shear and normal deformations theory for functionally graded beams. Steel Compos Struct. 2015;18:409–423. doi: 10.12989/scs.2015.18.2.409
  • Bouhadra A, Tounsi A, Bousahla AA, et al. Improved HSDT accounting for effect of thickness stretching in advanced composite plates. Struct Eng Mech. 2018;66:61–73.
  • Draiche K, Tounsi A, Mahmoud S. A refined theory with stretching effect for the flexure analysis of laminated composite plates. Geomech Eng. 2016;11:671–690. doi: 10.12989/gae.2016.11.5.671
  • Thai H-T, Kim S-E. A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates. Compos Struct. 2013;99:172–180. doi: 10.1016/j.compstruct.2012.11.030
  • Vo TP, Thai H-T, Nguyen T-K, et al. A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Compos Struct. 2015;119:1–12. doi: 10.1016/j.compstruct.2014.08.006
  • Shahsavari D, Shahsavari M, Li L, 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. 2018;72:134–149. doi: 10.1016/j.ast.2017.11.004
  • Bouafia K, Kaci A, Houari MSA, et al. A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams. Smart Struct Syst. 2017;19:115–126. doi: 10.12989/sss.2017.19.2.115
  • Chaht FL, Kaci A, Houari MSA, et al. Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect. Steel Compos Struct. 2015;18:425–442. doi: 10.12989/scs.2015.18.2.425
  • Ebrahimi F, Barati MR. Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory. Appl Phys A. 2016;122:843. doi: 10.1007/s00339-016-0368-1
  • Atmane HA, Tounsi A, Bernard F. Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations. Int J Mech Mater Des. 2017;13:71–84. doi: 10.1007/s10999-015-9318-x
  • Allen MJ, Tung VC, Kaner RB. Honeycomb carbon: a review of graphene. Chem Rev. 2009;110:132–145. doi: 10.1021/cr900070d
  • Shen L, Shen H-S, Zhang C-L. Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments. Comput Mater Sci. 2010;48:680–685. doi: 10.1016/j.commatsci.2010.03.006
  • Androulidakis C, Koukaras EN, Frank O, et al. Failure processes in embedded monolayer graphene under axial compression. Sci Rep. 2014;4:5271. doi: 10.1038/srep05271
  • Xiang Y, Shen H-S. Compressive buckling of rippled graphene via molecular dynamics simulations. Int J Struct Stab Dyn. 2016;16:1550071. doi: 10.1142/S0219455415500716
  • Wang Y-Z, Li F-M, Kishimoto K. Scale effects on flexural wave propagation in nanoplate embedded in elastic matrix with initial stress. Appl Phys A Mater Sci Process. 2010;99:907–911. doi: 10.1007/s00339-010-5666-4

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