메뉴 건너뛰기




Volumn 5, Issue 3, 2010, Pages 459-476

Wave propagation in carbon nanotubes: Nonlocal elasticity-induced stiffness and velocity enhancement effects

Author keywords

Critical wavenumber; Nanotube; Nonlocal elasticity; Wave propagation

Indexed keywords

ANALYTICAL SOLUTIONS; COUPLE STRESS; DEFORMABLE MODELS; ELASTIC STRESS FIELD; GOVERNING EQUATIONS OF MOTION; MODEL-BASED; MOLECULAR DYNAMIC SIMULATIONS; NANO SCALE; NONLOCAL; NONLOCAL ELASTICITY; NONLOCAL MODELS; NONLOCAL STRESS; STIFFNESS ENHANCEMENT; STRAIN GRADIENTS; VARIATIONAL PRINCIPLES; VELOCITY ENHANCEMENT; WAVE NUMBERS;

EID: 78049283439     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2010.5.459     Document Type: Article
Times cited : (57)

References (51)
  • 2
    • 0035829549 scopus 로고    scopus 로고
    • Roll up for the revolution
    • Ball, "Roll up for the revolution", Nature 414 (2001), 142-144
    • (2001) Nature , vol.414 , pp. 142-144
    • Ball, X.X.1
  • 3
    • 0037008487 scopus 로고    scopus 로고
    • Carbon nanotubes-the route toward applications
    • R. H. Baughman, A. A. Zakhidov, and W. A. de Heer, "Carbon nanotubes-the route toward applications", Science 297 (2002), 787-792.
    • (2002) Science , vol.297 , pp. 787-792
    • Baughman, R.H.1    Zakhidov, A.A.2    de Heer, W.A.3
  • 5
    • 0001996503 scopus 로고
    • Nonlocal polar elastic continua
    • A. C. Eringen, "Nonlocal polar elastic continua", Int. J. Eng. Sci. 10 (1972), 1-16.
    • (1972) Int. J. Eng. Sci. , vol.10 , pp. 1-16
    • Eringen, A.C.1
  • 6
    • 0001452092 scopus 로고
    • Linear theory of nonlocal elasticity and dispersion of plane waves
    • A. C. Eringen, "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci. 10 (1972), 425-435.
    • (1972) Int. J. Eng. Sci. , vol.10 , pp. 425-435
    • Eringen, A.C.1
  • 7
    • 0020821706 scopus 로고
    • On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves
    • A. C. Eringen, "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys. 54 (1983), 4703-4710.
    • (1983) J. Appl. Phys. , vol.54 , pp. 4703-4710
    • Eringen, A.C.1
  • 11
    • 18744400804 scopus 로고    scopus 로고
    • Bending instability of an embedded double-walled carbon nanotube based on Winkler and van der Waals models
    • Q. Han, G. X. Lu, and L. M. Dai, "Bending instability of an embedded double-walled carbon nanotube based on Winkler and van der Waals models", Compos. Sci. Technol. 65 (2005), 1337-1346.
    • (2005) Compos. Sci. Technol. , vol.65 , pp. 1337-1346
    • Han, Q.1    Lu, G.X.2    Dai, L.M.3
  • 12
    • 42549159543 scopus 로고    scopus 로고
    • Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading
    • H. Heireche, A. Tounsi, and A. Benzair, "Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading", Nanotechnology 19 (2008), 185703.
    • (2008) Nanotechnology , vol.19 , pp. 185703
    • Heireche, H.1    Tounsi, A.2    Benzair, A.3
  • 13
    • 55749110173 scopus 로고    scopus 로고
    • Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes
    • Y. G. Hu, K. M. Liew, Q. Wang, X. Q. He, and B. I. Yakobson, "Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes", J. Mech. Phys. Solids 56 (2008), 3475-3485.
    • (2008) J. Mech. Phys. Solids , vol.56 , pp. 3475-3485
    • Hu, Y.G.1    Liew, K.M.2    Wang, Q.3    He, X.Q.4    Yakobson, B.I.5
  • 14
    • 0342819025 scopus 로고
    • Helical microtubules of graphitic carbon
    • S. Iijima, "Helical microtubules of graphitic carbon", Nature 354 (1991), 56-58.
    • (1991) Nature , vol.354 , pp. 56-58
    • Iijima, S.1
  • 15
    • 20544442436 scopus 로고    scopus 로고
    • Buckling analysis of triple-walled carbon nanotubes embedded in an elastic matrix
    • S. Kitipornchai, X. Q. He, and K. M. Liew, "Buckling analysis of triple-walled carbon nanotubes embedded in an elastic matrix", J. Appl. Phys. 97 (2005), 114318.
    • (2005) J. Appl. Phys. , vol.97 , pp. 114318
    • Kitipornchai, S.1    He, X.Q.2    Liew, K.M.3
  • 17
    • 0942289162 scopus 로고    scopus 로고
    • Vibrational behaviors of multi-walled carbon nanotube-based nanomechancial resonators
    • C. Y. Li and T. W. Chou, "Vibrational behaviors of multi-walled carbon nanotube-based nanomechancial resonators", Appl. Phys. Lett. 84 (2004), 121-123.
    • (2004) Appl. Phys. Lett. , vol.84 , pp. 121-123
    • Li, C.Y.1    Chou, T.W.2
  • 18
    • 2342460373 scopus 로고    scopus 로고
    • On the study of elastic and plastic properties of multi-walled carbon nanotubes under axial tension using molecular dynamics simulation
    • K. M. Liew, X. Q. He, and C. H. Wong, "On the study of elastic and plastic properties of multi-walled carbon nanotubes under axial tension using molecular dynamics simulation", Acta Materialia 52:9 (2004), 2521-2527.
    • (2004) Acta Materialia , vol.52 , Issue.9 , pp. 2521-2527
    • Liew, K.M.1    He, X.Q.2    Wong, C.H.3
  • 19
    • 2142807342 scopus 로고    scopus 로고
    • Nanomechanics of single and multiwalled carbon nanotubes
    • K. M. Liew, C. H. Wong, X. Q. He, M. J. Tan, and S. A. Meguid, "Nanomechanics of single and multiwalled carbon nanotubes", Phys. Rev. B 69 (2004), 115429.
    • (2004) Phys. Rev. B , vol.69 , pp. 115429
    • Liew, K.M.1    Wong, C.H.2    He, X.Q.3    Tan, M.J.4    Meguid, S.A.5
  • 20
    • 23744451572 scopus 로고    scopus 로고
    • Buckling properties of carbon nanotube bundles
    • K. M. Liew, C. H. Wong, and M. J. Tan, "Buckling properties of carbon nanotube bundles", Appl. Phys. Lett. 87:4 (2005), 041901.
    • (2005) Appl. Phys. Lett. , vol.87 , Issue.4 , pp. 041901
    • Liew, K.M.1    Wong, C.H.2    Tan, M.J.3
  • 21
    • 44449129746 scopus 로고    scopus 로고
    • Flexural wave propagation in single-walled carbon nanotubes
    • K. M. Liew, Y. Hu, and X. Q. He, "Flexural wave propagation in single-walled carbon nanotubes", J. Comput. Theoretical Nanoscience 5 (2008), 581-586.
    • (2008) J. Comput. Theoretical Nanoscience , vol.5 , pp. 581-586
    • Liew, K.M.1    Hu, Y.2    He, X.Q.3
  • 23
    • 77952194106 scopus 로고    scopus 로고
    • Equilibrium and static deflection for bending of a nonlocal nanobeam
    • C. W. Lim, "Equilibrium and static deflection for bending of a nonlocal nanobeam", Adv. Vibr. Eng. 8:4 (2009), 277-300.
    • (2009) Adv. Vibr. Eng. , vol.8 , Issue.4 , pp. 277-300
    • Lim, C.W.1
  • 24
    • 74849084120 scopus 로고    scopus 로고
    • On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: Equilibrium, governing equation and static deflection
    • C. W. Lim, "On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: Equilibrium, governing equation and static deflection", Appl. Math. Mech. 31:1 (2010), 37-54.
    • (2010) Appl. Math. Mech. , vol.31 , Issue.1 , pp. 37-54
    • Lim, C.W.1
  • 25
    • 33947313177 scopus 로고    scopus 로고
    • Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams
    • C. W. Lim and C. M. Wang, "Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams", J. Appl. Phys. 101 (2007), 054312.
    • (2007) J. Appl. Phys. , vol.101 , pp. 054312
    • Lim, C.W.1    Wang, C.M.2
  • 26
    • 34047097760 scopus 로고    scopus 로고
    • Application of nonlocal beam models for carbon nanotubes
    • P. Lu, H. P. Lee, C. Lu, and P. Q. Zhang, "Application of nonlocal beam models for carbon nanotubes", Int. J. Solids Struct. 44 (2007), 5289-5300.
    • (2007) Int. J. Solids Struct. , vol.44 , pp. 5289-5300
    • Lu, P.1    Lee, H.P.2    Lu, C.3    Zhang, P.Q.4
  • 27
    • 55749091952 scopus 로고    scopus 로고
    • A microstructure-dependent Timoshenko beam model based on a modified couple stress theory
    • H. M. Ma, X. L. Gao, and J. N. Reddy, "A microstructure-dependent Timoshenko beam model based on a modified couple stress theory", J. Mech. Phys. Solids 56:12 (2008), 3379-3391.
    • (2008) J. Mech. Phys. Solids , vol.56 , Issue.12 , pp. 3379-3391
    • Ma, H.M.1    Gao, X.L.2    Reddy, J.N.3
  • 28
    • 24144462483 scopus 로고    scopus 로고
    • Role of material microstructure in plate stiffness with relevance to microcantilever sensors
    • A. W. McFarland and J. S. Colton, "Role of material microstructure in plate stiffness with relevance to microcantilever sensors", J. Micromech. Microeng. 15 (2005), 1060-1067.
    • (2005) J. Micromech. Microeng. , vol.15 , pp. 1060-1067
    • McFarland, A.W.1    Colton, J.S.2
  • 29
    • 13744263411 scopus 로고    scopus 로고
    • Wave propagation of carbon nanotubes embedded in an elastic medium
    • T. Natsuki, T. Hayashi, and M. Endo, "Wave propagation of carbon nanotubes embedded in an elastic medium", J. Appl. Phys. 97 (2005), 044307.
    • (2005) J. Appl. Phys. , vol.97 , pp. 044307
    • Natsuki, T.1    Hayashi, T.2    Endo, M.3
  • 30
    • 0032020971 scopus 로고    scopus 로고
    • Indentation size effects in crystalline materials: A law for strain gradient plasticity
    • W. Nix and H. Gao, "Indentation size effects in crystalline materials: A law for strain gradient plasticity", J. Mech. Phys. Solids 46:3 (1998), 411-425.
    • (1998) J. Mech. Phys. Solids , vol.46 , Issue.3 , pp. 411-425
    • Nix, W.1    Gao, H.2
  • 31
    • 33750597812 scopus 로고    scopus 로고
    • Bernoulli-Euler beam model based on a modified couple stress theory
    • S. K. Park and X. L. Hao, "Bernoulli-Euler beam model based on a modified couple stress theory", J. Micromech. Microeng. 16 (2006), 2355-2359.
    • (2006) J. Micromech. Microeng. , vol.16 , pp. 2355-2359
    • Park, S.K.1    Hao, X.L.2
  • 32
    • 51349157575 scopus 로고    scopus 로고
    • Variational formulation of a modified couple stress theory and its application to a simple shear problem
    • S. K. Park and X. L. Hao, "Variational formulation of a modified couple stress theory and its application to a simple shear problem", Z. Angew. Math. Phys. 59 (2008), 904-917.
    • (2008) Z. Angew. Math. Phys. , vol.59 , pp. 904-917
    • Park, S.K.1    Hao, X.L.2
  • 33
    • 0036533464 scopus 로고    scopus 로고
    • Buckling of nano-fibre reinforced composites: a re-examination of elastic buckling
    • R. Parnes and A. Chiskis, "Buckling of nano-fibre reinforced composites: a re-examination of elastic buckling", J. Mech. Phys. Solids 50 (2002), 855-879.
    • (2002) J. Mech. Phys. Solids , vol.50 , pp. 855-879
    • Parnes, R.1    Chiskis, A.2
  • 34
    • 0034666972 scopus 로고    scopus 로고
    • Effective bending stiffness of carbon nanotubes
    • C. Q. Ru, "Effective bending stiffness of carbon nanotubes", Phys. Rev. B. 62 (2000), 9973-9976.
    • (2000) Phys. Rev. B. , vol.62 , pp. 9973-9976
    • Ru, C.Q.1
  • 35
    • 0034667108 scopus 로고    scopus 로고
    • Elastic buckling of singlewalled carbon nanotube ropes under high pressure
    • C. Q. Ru, "Elastic buckling of singlewalled carbon nanotube ropes under high pressure", Phys. Rev. B 62 (2000), 10405-10408.
    • (2000) Phys. Rev. B , vol.62 , pp. 10405-10408
    • Ru, C.Q.1
  • 36
    • 3242834384 scopus 로고    scopus 로고
    • Exceptionally high Young's modulus observed for individual carbon nanotubes
    • M. M. J. Treacy, T. W. Ebbesen, and J. M. Gibson, "Exceptionally high Young's modulus observed for individual carbon nanotubes", Nature 381 (1996), 680-687.
    • (1996) Nature , vol.381 , pp. 680-687
    • Treacy, M.M.J.1    Ebbesen, T.W.2    Gibson, J.M.3
  • 37
    • 29744459272 scopus 로고    scopus 로고
    • Wave propagation in carbon nanotubes via nonlocal continuum mechanics
    • Q. Wang, "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys. 98 (2005), 124301.
    • (2005) J. Appl. Phys. , vol.98 , pp. 124301
    • Wang, Q.1
  • 38
    • 33646863278 scopus 로고    scopus 로고
    • Axi-symmetric wave propagation of carbon nanotubes with non-local elastic shell model
    • Q. Wang, "Axi-symmetric wave propagation of carbon nanotubes with non-local elastic shell model", Int. J. Struct. Stab. Dyn. 6 (2006), 285-296.
    • (2006) Int. J. Struct. Stab. Dyn. , vol.6 , pp. 285-296
    • Wang, Q.1
  • 39
    • 28544452524 scopus 로고    scopus 로고
    • Flexural wave propagation in single-walled carbon nanotubes
    • L. F. Wang and H. Y. Hu, "Flexural wave propagation in single-walled carbon nanotubes", Phys. Rev. B 71 (2005), 195412.
    • (2005) Phys. Rev. B , vol.71 , pp. 195412
    • Wang, L.F.1    Hu, H.Y.2
  • 40
    • 28044451778 scopus 로고    scopus 로고
    • Wave characteristics of carbon nanotubes
    • Q. Wang and V. K. Varadan, "Wave characteristics of carbon nanotubes", Int. J. Solids Struct. 43 (2006), 254-265.
    • (2006) Int. J. Solids Struct. , vol.43 , pp. 254-265
    • Wang, Q.1    Varadan, V.K.2
  • 41
    • 33947636719 scopus 로고    scopus 로고
    • Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes
    • Q. Wang and V. K. Varadan, "Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes", Smart Mater. Struct. 16 (2007), 178-190.
    • (2007) Smart Mater. Struct. , vol.16 , pp. 178-190
    • Wang, Q.1    Varadan, V.K.2
  • 42
    • 33748920360 scopus 로고    scopus 로고
    • Vibration of microtubules as orthotropic elastic shells
    • C. Y. Wang, C. Q. Ru, and A. Mioduchowski, "Vibration of microtubules as orthotropic elastic shells", Physica E 35 (2006), 48-56.
    • (2006) Physica E , vol.35 , pp. 48-56
    • Wang, C.Y.1    Ru, C.Q.2    Mioduchowski, A.3
  • 43
    • 33144456197 scopus 로고    scopus 로고
    • Validation of the non-local elastic shell model for studying longitudinal waves in single-walled carbon nanotubes
    • L. F. Wang, H. Y. Hu, and W. L. Guo, "Validation of the non-local elastic shell model for studying longitudinal waves in single-walled carbon nanotubes", Nanotechnology 17 (2006), 1408-1415.
    • (2006) Nanotechnology , vol.17 , pp. 1408-1415
    • Wang, L.F.1    Hu, H.Y.2    Guo, W.L.3
  • 44
    • 33846080534 scopus 로고    scopus 로고
    • Scale effect on wave propagation of double-walled carbon nanotubes
    • Q. Wang, G. Y. Zhou, and K. C. Lin, "Scale effect on wave propagation of double-walled carbon nanotubes", Int. J. Solids Struct. 43 (2006), 6071-6084.
    • (2006) Int. J. Solids Struct. , vol.43 , pp. 6071-6084
    • Wang, Q.1    Zhou, G.Y.2    Lin, K.C.3
  • 45
    • 42349090659 scopus 로고    scopus 로고
    • Group velocity of wave propagation in carbon nanotubes
    • L. F. Wang, W. L. Guo, and H. Y. Hu, "Group velocity of wave propagation in carbon nanotubes", Proc. R. Soc. A-Math Phys. Eng. Sci. 464 (2008), 1423-1438.
    • (2008) Proc. R. Soc. A-Math Phys. Eng. Sci. , vol.464 , pp. 1423-1438
    • Wang, L.F.1    Guo, W.L.2    Hu, H.Y.3
  • 46
    • 0030234647 scopus 로고    scopus 로고
    • Deformation and fracture in microlaminates
    • G. S. Was and T. Foecke, "Deformation and fracture in microlaminates", Thin Solid Films 286 (1996), 1-31.
    • (1996) Thin Solid Films , vol.286 , pp. 1-31
    • Was, G.S.1    Foecke, T.2
  • 47
    • 34547791302 scopus 로고    scopus 로고
    • Characteristic of waves in a multi-walled carbon nanotubes
    • G. Q. Xie, X. Han, and S. Y. Long, "Characteristic of waves in a multi-walled carbon nanotubes", Computers, Materials and Continua 6 (2007), 1-11.
    • (2007) Computers, Materials and Continua , vol.6 , pp. 1-11
    • Xie, G.Q.1    Han, X.2    Long, S.Y.3
  • 48
    • 33751006717 scopus 로고    scopus 로고
    • Effect of small size on dispersion characteristics of wave in carbon nanotubes
    • G. Q. Xie, X. Han, and S. Y. Long, "Effect of small size on dispersion characteristics of wave in carbon nanotubes", Int. J. Solids Struct. 44:3-4 (2007), 1242-1255.
    • (2007) Int. J. Solids Struct. , vol.44 , Issue.3-4 , pp. 1242-1255
    • Xie, G.Q.1    Han, X.2    Long, S.Y.3
  • 49
    • 33750050422 scopus 로고    scopus 로고
    • Nanomechanics of carbon tubes: instabilities beyond linear range
    • B. I. Yakobson, C. J. Brabec, and J. Bernholc, "Nanomechanics of carbon tubes: instabilities beyond linear range", Phys. Rev. Lett. 76 (1996), 2511-2514.
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 2511-2514
    • Yakobson, B.I.1    Brabec, C.J.2    Bernholc, J.3
  • 50
    • 14644421476 scopus 로고    scopus 로고
    • Terahertz vibration of short carbon nanotubes modeled as Timoshenko-beams
    • J. Yoon, C. Q. Ru, and A. Mioduchowski, "Terahertz vibration of short carbon nanotubes modeled as Timoshenko-beams", J. Appl. Mech.-Trans. ASME. 72 (2005), 10-17.
    • (2005) J. Appl. Mech.-Trans. ASME. , vol.72 , pp. 10-17
    • Yoon, J.1    Ru, C.Q.2    Mioduchowski, A.3
  • 51
    • 19444383075 scopus 로고    scopus 로고
    • Transverse vibrations of double-walled carbon nanotubes under compressive axial load
    • Y. Q. Zhang, G. R. Liu, and H. Xu, "Transverse vibrations of double-walled carbon nanotubes under compressive axial load", Phys. Lett. A 340 (2005), 258-266.
    • (2005) Phys. Lett. A , vol.340 , pp. 258-266
    • Zhang, Y.Q.1    Liu, G.R.2    Xu, H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.