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Volumn 32, Issue 1, 2012, Pages 325-338

Variational Principles for Nonlocal Continuum Model of Orthotropic Graphene Sheets Embedded in An Elastic Medium

Author keywords

Buckling; Multilayered graphene sheets; Nonlocal theory; Rayleigh quotient; Semi inverse method; Variational formulation; Vibration

Indexed keywords


EID: 84856096681     PISSN: 02529602     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0252-9602(12)60020-4     Document Type: Article
Times cited : (26)

References (58)
  • 2
    • 31044454633 scopus 로고    scopus 로고
    • Equilibrium configuration and continuum elastic properties of finite sized graphene
    • Reddy CD, Rajendran S, Liew KM Equilibrium configuration and continuum elastic properties of finite sized graphene. Nanotechnology 2006, 17(3):864-870.
    • (2006) Nanotechnology , vol.17 , Issue.3 , pp. 864-870
    • Reddy, C.D.1    Rajendran, S.2    Liew, K.M.3
  • 3
    • 39349094359 scopus 로고    scopus 로고
    • Nanomechanical properties of few-layer graphene membranes
    • Poot M, van der Zant HSJ Nanomechanical properties of few-layer graphene membranes. Applied Physics Letters 2008, 92(6):063111.
    • (2008) Applied Physics Letters , vol.92 , Issue.6 , pp. 063111
    • Poot, M.1    van der Zant, H.S.J.2
  • 4
    • 79961020865 scopus 로고    scopus 로고
    • Mechanical properties of graphyne
    • Cranford SW, Buehler MJ Mechanical properties of graphyne. Carbon 2011, 49(13):4111-4121.
    • (2011) Carbon , vol.49 , Issue.13 , pp. 4111-4121
    • Cranford, S.W.1    Buehler, M.J.2
  • 6
    • 80054052310 scopus 로고    scopus 로고
    • Multiscale modeling of graphene- and nanotube-based reinforced polymer nanocomposites
    • Montazeri A, Rafii-Tabar H Multiscale modeling of graphene- and nanotube-based reinforced polymer nanocomposites. Physics Letters A 2011, 375(45):4034-4040.
    • (2011) Physics Letters A , vol.375 , Issue.45 , pp. 4034-4040
    • Montazeri, A.1    Rafii-Tabar, H.2
  • 9
    • 78049519186 scopus 로고    scopus 로고
    • Interface-hydrothermal synthesis of Sn3S4/graphene sheet composites and their application in electrochemical capacitors
    • Yuan C, Hou L, Yang L, Fan C, Li D, Li J, Shen L, Zhang F, Zhang X Interface-hydrothermal synthesis of Sn3S4/graphene sheet composites and their application in electrochemical capacitors. Material Letters 2011, 65(2):374-377.
    • (2011) Material Letters , vol.65 , Issue.2 , pp. 374-377
    • Yuan, C.1    Hou, L.2    Yang, L.3    Fan, C.4    Li, D.5    Li, J.6    Shen, L.7    Zhang, F.8    Zhang, X.9
  • 11
    • 77950049754 scopus 로고    scopus 로고
    • Large reversible capacity of high quality graphene sheets as an anode material for lithium-ion batteries
    • Lian P, Zhu X, Liang S, Li Z, Yang W, Wang H Large reversible capacity of high quality graphene sheets as an anode material for lithium-ion batteries. Electrochimica Acta 2010, 55(12):3909-3914.
    • (2010) Electrochimica Acta , vol.55 , Issue.12 , pp. 3909-3914
    • Lian, P.1    Zhu, X.2    Liang, S.3    Li, Z.4    Yang, W.5    Wang, H.6
  • 12
    • 82755194890 scopus 로고    scopus 로고
    • Functionalized graphene sheets for arsenic removal and desalination of sea water
    • Mishra AK, Ramaprabhu S Functionalized graphene sheets for arsenic removal and desalination of sea water. Desalination 2011, 282:39-45.
    • (2011) Desalination , vol.282 , pp. 39-45
    • Mishra, A.K.1    Ramaprabhu, S.2
  • 13
    • 78650247873 scopus 로고    scopus 로고
    • Synthesis of surface-functionalized graphene nanosheets with high Pt-loadings and their applications to methanol electrooxidation
    • Choi SM, Seo MH, Kim HJ, Kim WB Synthesis of surface-functionalized graphene nanosheets with high Pt-loadings and their applications to methanol electrooxidation. Carbon 2011, 49(3):904-909.
    • (2011) Carbon , vol.49 , Issue.3 , pp. 904-909
    • Choi, S.M.1    Seo, M.H.2    Kim, H.J.3    Kim, W.B.4
  • 14
    • 79956342101 scopus 로고    scopus 로고
    • Sensitive electrochemical immuno-sensor for the detection of cancer biomarker using quantum dot functionalized graphene sheets as labels
    • Yang M, Javadi A, Gong S Sensitive electrochemical immuno-sensor for the detection of cancer biomarker using quantum dot functionalized graphene sheets as labels. Sensors and Actuators B: Chemical 2011, 155(1):357-360.
    • (2011) Sensors and Actuators B: Chemical , vol.155 , Issue.1 , pp. 357-360
    • Yang, M.1    Javadi, A.2    Gong, S.3
  • 15
    • 79951581134 scopus 로고    scopus 로고
    • A graphene functionalized electrochemical apta-sensor for selective label-free detection of cancer cells
    • Feng L, Chen Y, Ren J, Qu X A graphene functionalized electrochemical apta-sensor for selective label-free detection of cancer cells. Biomaterials 2011, 32(11):2930-2937.
    • (2011) Biomaterials , vol.32 , Issue.11 , pp. 2930-2937
    • Feng, L.1    Chen, Y.2    Ren, J.3    Qu, X.4
  • 16
    • 77950519205 scopus 로고    scopus 로고
    • Production, properties and potential of graphene
    • Soldano C, Mahmood A, Dujardin E Production, properties and potential of graphene. Carbon 2010, 48(8):2127-2150.
    • (2010) Carbon , vol.48 , Issue.8 , pp. 2127-2150
    • Soldano, C.1    Mahmood, A.2    Dujardin, E.3
  • 18
    • 0347300631 scopus 로고    scopus 로고
    • A continuum model for size-dependent deformation of elastic films of nano-scale thickness
    • He LH, Lim CW, Wu BS A continuum model for size-dependent deformation of elastic films of nano-scale thickness. Int J Solids Struct 2004, 41:847-857.
    • (2004) Int J Solids Struct , vol.41 , pp. 847-857
    • He, L.H.1    Lim, C.W.2    Wu, B.S.3
  • 19
    • 33644955639 scopus 로고    scopus 로고
    • Continuum model for the vibration of multilayered graphene sheets
    • Kitipornchai S, He XQ, Liew KM Continuum model for the vibration of multilayered graphene sheets. Phys Reviews B 2005, 72:075443.
    • (2005) Phys Reviews B , vol.72 , pp. 075443
    • Kitipornchai, S.1    He, X.Q.2    Liew, K.M.3
  • 20
    • 33745728258 scopus 로고    scopus 로고
    • Discrete homogenization in graphene sheet modeling
    • Arash B, Wang Q Discrete homogenization in graphene sheet modeling. J Elasticity 2006, 84(1):33-68.
    • (2006) J Elasticity , vol.84 , Issue.1 , pp. 33-68
    • Arash, B.1    Wang, Q.2
  • 21
    • 49349117149 scopus 로고    scopus 로고
    • A method for developing the equivalent continuum model of a single layer graphene sheet
    • Hemmasizade A, Mahzoon M, Hadi E, Khandan R A method for developing the equivalent continuum model of a single layer graphene sheet. Thin Solid Films 2008, 516:7636-7640.
    • (2008) Thin Solid Films , vol.516 , pp. 7636-7640
    • Hemmasizade, A.1    Mahzoon, M.2    Hadi, E.3    Khandan, R.4
  • 22
    • 80052033169 scopus 로고    scopus 로고
    • A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes
    • Arash B, Wang Q, Caillerie D, Mourad A, Raoult A A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Comp Mater Sci 2012, 51(1):303-313.
    • (2012) Comp Mater Sci , vol.51 , Issue.1 , pp. 303-313
    • Arash, B.1    Wang, Q.2    Caillerie, D.3    Mourad, A.4    Raoult, A.5
  • 23
    • 0037409356 scopus 로고    scopus 로고
    • Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model
    • Chang T, Gao H Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model. J Mechanics and Physics of Solids 2003, 51:1059-1074.
    • (2003) J Mechanics and Physics of Solids , vol.51 , pp. 1059-1074
    • Chang, T.1    Gao, H.2
  • 24
    • 0037439330 scopus 로고    scopus 로고
    • Size-dependent elastic moduli of platelike nanomaterials
    • Sun CT, Zhang HT Size-dependent elastic moduli of platelike nanomaterials. J Appl Phys 2003, 93:1212-1218.
    • (2003) J Appl Phys , vol.93 , pp. 1212-1218
    • Sun, C.T.1    Zhang, H.T.2
  • 25
    • 75049084975 scopus 로고    scopus 로고
    • Anisotropic mechanical properties of graphene sheets from molecular dynamics
    • Ni Z, Bu H, Zou M, Yi H, Bi K, Chen Y Anisotropic mechanical properties of graphene sheets from molecular dynamics. Physica B: Condensed Matter 2010, 405(5):1301-1306.
    • (2010) Physica B: Condensed Matter , vol.405 , Issue.5 , pp. 1301-1306
    • Ni, Z.1    Bu, H.2    Zou, M.3    Yi, H.4    Bi, K.5    Chen, Y.6
  • 26
    • 0001846701 scopus 로고
    • On the thermodynamics of systems with nonlocality
    • Edelen DGB, Laws N On the thermodynamics of systems with nonlocality. Arch Rational Mech Anal 1971, 43:24-35.
    • (1971) Arch Rational Mech Anal , vol.43 , pp. 24-35
    • Edelen, D.G.B.1    Laws, N.2
  • 27
    • 0001452092 scopus 로고
    • Linear theory of nonlocal elasticity and dispersion of plane waves
    • Eringen AC Linear theory of nonlocal elasticity and dispersion of plane waves. Int J Engineering Science 1972, 10:425-435.
    • (1972) Int J Engineering Science , vol.10 , pp. 425-435
    • Eringen, A.C.1
  • 28
  • 30
    • 63749090424 scopus 로고    scopus 로고
    • Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory
    • Murmu T, Pradhan SC Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory. J Appl Phys 2009, 105:064319.
    • (2009) J Appl Phys , vol.105 , pp. 064319
    • Murmu, T.1    Pradhan, S.C.2
  • 31
    • 77950929047 scopus 로고    scopus 로고
    • Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments
    • Shen L, Shen H-S, Zhang C-L Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments. Comp Mater Sci 2010, 48:680.
    • (2010) Comp Mater Sci , vol.48 , pp. 680
    • Shen, L.1    Shen, H.-S.2    Zhang, C.-L.3
  • 32
    • 78649944853 scopus 로고    scopus 로고
    • Strong nonlocalization induced by small scale parameter on terahertz flexural wave dispersion characteristics of a monolayer graphene
    • Narendar S, Gopalakrishnan S Strong nonlocalization induced by small scale parameter on terahertz flexural wave dispersion characteristics of a monolayer graphene. Physica E 2010, 43:423-430.
    • (2010) Physica E , vol.43 , pp. 423-430
    • Narendar, S.1    Gopalakrishnan, S.2
  • 33
    • 25444472090 scopus 로고    scopus 로고
    • Resonance analysis of multi-layered graphene sheets used as nanoscale resonators
    • He XQ, Kitipornchai S, Liew KM Resonance analysis of multi-layered graphene sheets used as nanoscale resonators. Nanotechnology 2005, 16:2086-2091.
    • (2005) Nanotechnology , vol.16 , pp. 2086-2091
    • He, X.Q.1    Kitipornchai, S.2    Liew, K.M.3
  • 34
    • 18144388704 scopus 로고    scopus 로고
    • Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium
    • Behfar K, Naghdabadi R Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium. Composites Science and Technology 2005, 65:1159-1164.
    • (2005) Composites Science and Technology , vol.65 , pp. 1159-1164
    • Behfar, K.1    Naghdabadi, R.2
  • 35
    • 33747361653 scopus 로고    scopus 로고
    • Predicting nano vibration of multi-layered graphene sheets embedded in an elastic matrix
    • Liew KM, He XQ, Kitipornchai S Predicting nano vibration of multi-layered graphene sheets embedded in an elastic matrix. Acta Mater 2006, 54:4229-4236.
    • (2006) Acta Mater , vol.54 , pp. 4229-4236
    • Liew, K.M.1    He, X.Q.2    Kitipornchai, S.3
  • 36
    • 78650682920 scopus 로고    scopus 로고
    • A study on large amplitude vibration of multilayered graphene sheets
    • Jomehzadeh E, Saidi AR A study on large amplitude vibration of multilayered graphene sheets. Computational Materials Science 2011, 50:1043-1051.
    • (2011) Computational Materials Science , vol.50 , pp. 1043-1051
    • Jomehzadeh, E.1    Saidi, A.R.2
  • 37
    • 79960350690 scopus 로고    scopus 로고
    • Nonlocal elasticity theory for the buckling of double-layer graphene nanoribbons based on a continuum model
    • Shi J-X, Ni Q-Q, Lei X-W, Natsuki T Nonlocal elasticity theory for the buckling of double-layer graphene nanoribbons based on a continuum model. Computational Materials Science 2011, 50(11):3085-3090.
    • (2011) Computational Materials Science , vol.50 , Issue.11 , pp. 3085-3090
    • Shi, J.-X.1    Ni, Q.-Q.2    Lei, X.-W.3    Natsuki, T.4
  • 38
    • 77955671764 scopus 로고    scopus 로고
    • Scale effect and buckling analysis of multilayered graphene sheets based on nonlocal continuum mechanics
    • Pradhan SC, Phadikar JK Scale effect and buckling analysis of multilayered graphene sheets based on nonlocal continuum mechanics. J Computational Theoretical Nanoscience 2010, 7(10):1948-1954.
    • (2010) J Computational Theoretical Nanoscience , vol.7 , Issue.10 , pp. 1948-1954
    • Pradhan, S.C.1    Phadikar, J.K.2
  • 40
    • 59649088252 scopus 로고    scopus 로고
    • Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models
    • Pradhan SC, Phadikar JK Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models. Phys Lett A 2009, 373:1062-1069.
    • (2009) Phys Lett A , vol.373 , pp. 1062-1069
    • Pradhan, S.C.1    Phadikar, J.K.2
  • 41
    • 77957934503 scopus 로고    scopus 로고
    • Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method
    • Pradhan SC, Kumar A Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method. Computational Materials Science 2010, 50:239-245.
    • (2010) Computational Materials Science , vol.50 , pp. 239-245
    • Pradhan, S.C.1    Kumar, A.2
  • 42
    • 77955517249 scopus 로고    scopus 로고
    • Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets
    • Ansari R, Rajabiehfard R, Arash B Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets. Computational Materials Science 2010, 49:831-838.
    • (2010) Computational Materials Science , vol.49 , pp. 831-838
    • Ansari, R.1    Rajabiehfard, R.2    Arash, B.3
  • 43
    • 79951517665 scopus 로고    scopus 로고
    • Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method
    • Pradhan SC, Kumar A Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method. Composite Structures 2011, 93:774-779.
    • (2011) Composite Structures , vol.93 , pp. 774-779
    • Pradhan, S.C.1    Kumar, A.2
  • 44
    • 78649941340 scopus 로고    scopus 로고
    • Vibration of a multilayered graphene sheet with initial stress
    • Wang L, He X Vibration of a multilayered graphene sheet with initial stress. J Nanotechnology in Engineering and Medicine 2010, 1(4):041004.
    • (2010) J Nanotechnology in Engineering and Medicine , vol.1 , Issue.4 , pp. 041004
    • Wang, L.1    He, X.2
  • 45
    • 79960987049 scopus 로고    scopus 로고
    • Variational principles and natural boundary conditions for multilayered orthotropic graphene sheets undergoing vibrations and based on nonlocal elastic theory
    • Adali S Variational principles and natural boundary conditions for multilayered orthotropic graphene sheets undergoing vibrations and based on nonlocal elastic theory. J Theoretical Applied Mechanics 2011, 49(3):621-639.
    • (2011) J Theoretical Applied Mechanics , vol.49 , Issue.3 , pp. 621-639
    • Adali, S.1
  • 46
    • 48449106795 scopus 로고    scopus 로고
    • Variational principles for multi-walled carbon nanotubes undergoing buckling based on nonlocal elasticity theory
    • Adali S Variational principles for multi-walled carbon nanotubes undergoing buckling based on nonlocal elasticity theory. Physics Letters A 2008, 372:5701-5705.
    • (2008) Physics Letters A , vol.372 , pp. 5701-5705
    • Adali, S.1
  • 47
    • 66449114600 scopus 로고    scopus 로고
    • Variational principles for transversely vibrating multi-walled carbon nanotubes based on nonlocal Euler-Bernoulli beam model
    • Adali S Variational principles for transversely vibrating multi-walled carbon nanotubes based on nonlocal Euler-Bernoulli beam model. Nano Letters 2009, 9(5):1737-1741.
    • (2009) Nano Letters , vol.9 , Issue.5 , pp. 1737-1741
    • Adali, S.1
  • 48
    • 77952000448 scopus 로고    scopus 로고
    • Variational principles for multi-walled carbon nanotubes undergoing nonlinear vibrations by semi-inverse method
    • Adali S Variational principles for multi-walled carbon nanotubes undergoing nonlinear vibrations by semi-inverse method. Micro and Nano Letters 2009, 4:198-203.
    • (2009) Micro and Nano Letters , vol.4 , pp. 198-203
    • Adali, S.1
  • 49
    • 77952003739 scopus 로고    scopus 로고
    • Variational principles for multi-walled carbon nanotubes undergoing vibrations based on nonlocal Timoshenko beam theory
    • Kucuk I, Sadek IS, Adali S Variational principles for multi-walled carbon nanotubes undergoing vibrations based on nonlocal Timoshenko beam theory. J Nanomaterials 2010, 2010:1-7.
    • (2010) J Nanomaterials , vol.2010 , pp. 1-7
    • Kucuk, I.1    Sadek, I.S.2    Adali, S.3
  • 50
    • 84859641499 scopus 로고    scopus 로고
    • Variational formulation for buckling of multi-walled carbon nanotubes modelled as nonlocal Timoshenko beams.
    • J Theoretical Applied Mechanics, to appear
    • Adali S. Variational formulation for buckling of multi-walled carbon nanotubes modelled as nonlocal Timoshenko beams. J Theoretical Applied Mechanics, 2012, to appear.
    • (2012)
    • Adali, S.1
  • 51
    • 0031441505 scopus 로고    scopus 로고
    • Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics
    • He J-H Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics. Int J Turbo Jet-Engines 1997, 14:23-28.
    • (1997) Int J Turbo Jet-Engines , vol.14 , pp. 23-28
    • He, J.-H.1
  • 52
    • 0041621600 scopus 로고    scopus 로고
    • Variational principles for some nonlinear partial differential equations with variable coefficients
    • He J-H Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, Solitons and Fractals 2004, 19:847-851.
    • (2004) Chaos, Solitons and Fractals , vol.19 , pp. 847-851
    • He, J.-H.1
  • 53
    • 12544257525 scopus 로고    scopus 로고
    • Variational approach to (2 + 1)-dimensional dispersive long water equations
    • He J-H Variational approach to (2 + 1)-dimensional dispersive long water equations. Phys Lett A 2005, 335:182-184.
    • (2005) Phys Lett A , vol.335 , pp. 182-184
    • He, J.-H.1
  • 54
    • 33644968060 scopus 로고    scopus 로고
    • Variational theory for one-dimensional longitudinal beam dynamics
    • He J-H Variational theory for one-dimensional longitudinal beam dynamics. Phys Lett A 2006, 352:276-277.
    • (2006) Phys Lett A , vol.352 , pp. 276-277
    • He, J.-H.1
  • 55
    • 35348989168 scopus 로고    scopus 로고
    • Variational principle for two-dimensional incompressible inviscid flow
    • He J-H Variational principle for two-dimensional incompressible inviscid flow. Phys Lett A 2007, 371:39-40.
    • (2007) Phys Lett A , vol.371 , pp. 39-40
    • He, J.-H.1
  • 56
    • 4243080806 scopus 로고    scopus 로고
    • Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method
    • Liu H-M Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method. Chaos, Solitons and Fractals 2005, 23:573-576.
    • (2005) Chaos, Solitons and Fractals , vol.23 , pp. 573-576
    • Liu, H.-M.1
  • 57
    • 33846616404 scopus 로고    scopus 로고
    • Variational approach to the Broer-Kaup-Kupershmidt equation
    • Zhou WX Variational approach to the Broer-Kaup-Kupershmidt equation. Phys Lett A 2006, 363:108-109.
    • (2006) Phys Lett A , vol.363 , pp. 108-109
    • Zhou, W.X.1
  • 58
    • 0020821706 scopus 로고
    • On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves
    • Eringen AC On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 1983, 54(9):4703-4710.
    • (1983) J Appl Phys , vol.54 , Issue.9 , pp. 4703-4710
    • Eringen, A.C.1


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