메뉴 건너뛰기




Volumn 11, Issue 2, 2011, Pages 257-271

Analytical solutions for vibration of simply supported nonlocal nanobeams with an axial force

Author keywords

Frequency; nanobeam; nonlocal bending moment; nonlocal elasticity; vibration

Indexed keywords

FREQUENCY; NANOBEAM; NONLOCAL BENDING MOMENT; NONLOCAL ELASTICITY; VIBRATION;

EID: 79951664066     PISSN: 02194554     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219455411004087     Document Type: Article
Times cited : (89)

References (43)
  • 1
    • 79953644500 scopus 로고    scopus 로고
    • Adhesion research of digital micromirror nano-contact
    • W. C. Tian and J. Y. Jia, Adhesion research of digital micromirror nano-contact, Micronanoelectronic Technology 39 (2002) 27-30.
    • (2002) Micronanoelectronic Technology , vol.39 , pp. 27-30
    • Tian, W.C.1    Jia, J.Y.2
  • 2
    • 79953648640 scopus 로고    scopus 로고
    • The development of nanotechnology and nanoelectronics
    • L. Pellizzari, The development of nanotechnology and nanoelectronics, Elettronica Oggi 320 (2003) 40-44.
    • (2003) Elettronica Oggi , vol.320 , pp. 40-44
    • Pellizzari, L.1
  • 3
    • 0015636248 scopus 로고
    • Transverse modes and frequencies of beams translating between fixed end supports
    • A. Simpson, Transverse modes and frequencies of beams translating between fixed end supports, J. Mech. Eng. Sci. 15 (1973) 159-164.
    • (1973) J. Mech. Eng. Sci. , vol.15 , pp. 159-164
    • Simpson, A.1
  • 4
    • 33646877494 scopus 로고    scopus 로고
    • Vibration of parabolic tied-arch beams due to moving loads
    • J. D. Yau, Vibration of parabolic tied-arch beams due to moving loads, Int. J. Struct. Stab. Dyn. 2 (2006) 193-214.
    • (2006) Int. J. Struct. Stab. Dyn. , vol.2 , pp. 193-214
    • Yau, J.D.1
  • 5
    • 0030123557 scopus 로고    scopus 로고
    • An approximate analytical solution of beam vibrations during axial motion
    • DOI 10.1006/jsvi.1996.0181
    • B. O. Al-Bedoor and Y. A. Khulief, An approximate analytical solution of beam vibrations during axial motion, Journal of Sound and Vibration 192 (1996) 159-171. (Pubitemid 126368604)
    • (1996) Journal of Sound and Vibration , vol.192 , Issue.1 , pp. 159-171
    • Al-Bedoor, B.O.1    Khulief, Y.A.2
  • 6
    • 4544229121 scopus 로고    scopus 로고
    • Principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string
    • L. Q. Chen, J. W. Zu and J. Wu, Principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string, Acta Mech. Solida Sinica 20 (2004) 307-316.
    • (2004) Acta Mech. Solida Sinica , vol.20 , pp. 307-316
    • Chen, L.Q.1    Zu, J.W.2    Wu, J.3
  • 7
    • 0001381311 scopus 로고    scopus 로고
    • Transition behaviour from string to beam for an axially accelerating material
    • H. R. Oz, M. Pakdemirli and E. Ozkaya, Transition behavior from string to beam for an axially accelerating material, Jouranl of Sound Vibration 215 (1998) 571-576. (Pubitemid 128379357)
    • (1998) Journal of Sound and Vibration , vol.215 , Issue.3 , pp. 571-576
    • Oz, H.R.1    Pakdemirli, M.2    Ozkaya, E.3
  • 8
    • 34347382536 scopus 로고    scopus 로고
    • The size-dependent bending elastic properties of nanobeams with surface effects
    • J. G. Guo and Y. P. Zhao, The size-dependent bending elastic properties of nanobeams with surface effects, Nanotechnology 18 (2007) 295701.
    • (2007) Nanotechnology , vol.18 , pp. 295701
    • Guo, J.G.1    Zhao, Y.P.2
  • 9
    • 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, Jouranl of Applied Physics 101 (2007) 054312.
    • (2007) Jouranl of Applied Physics , vol.101 , pp. 054312
    • Lim, C.W.1    Wang, C.M.2
  • 10
    • 0000450433 scopus 로고
    • A unified theory of thermomechanical materials
    • A. C. Eringen, A unified theory of thermomechanical materials, Int. J. Eng. Sci. 4 (1966) 179-202.
    • (1966) Int. J. Eng. Sci. , vol.4 , pp. 179-202
    • Eringen, A.C.1
  • 11
    • 0020821706 scopus 로고
    • On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves
    • DOI 10.1063/1.332803
    • A. C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Jouranl of Applied Physics 54 (1983) 4703-4710. (Pubitemid 14450262)
    • (1983) Journal of Applied Physics , vol.54 , Issue.9 , pp. 4703-4710
    • Eringen A.Cemal1
  • 12
    • 49949143801 scopus 로고
    • Elasticity theory of materials with long-ranges cohesive forces
    • E. Kroner, Elasticity theory of materials with long-ranges cohesive forces, Int. J. Solids Struct. 3 (1967) 731-742.
    • (1967) Int. J. Solids Struct. , vol.3 , pp. 731-742
    • Kroner, E.1
  • 13
    • 0037338249 scopus 로고    scopus 로고
    • Application of nonlocal continuum models to nanotechnology
    • J. Peddieson, G. G. Buchanan and R. P. McNitt, Application of nonlocal continuum models to nanotechnology, Int. J. Eng. Sci. 41 (2003) 305-312.
    • (2003) Int. J. Eng. Sci. , vol.41 , pp. 305-312
    • Peddieson, J.1    Buchanan, G.G.2    McNitt, R.P.3
  • 14
    • 33645026349 scopus 로고    scopus 로고
    • Vibration of carbon nanotubes studied using nonlocal continuum mechanics
    • Q. Wang and V. K. Varadan, Vibration of carbon nanotubes studied using nonlocal continuum mechanics, Smart Mater. Struct. 15 (2006) 659-666.
    • (2006) Smart Mater. Struct. , vol.15 , pp. 659-666
    • Wang, Q.1    Varadan, V.K.2
  • 15
  • 16
    • 79953658358 scopus 로고
    • Progress and applications of solid mechanics considering microstructure
    • J. L. Yu, Progress and applications of solid mechanics considering microstructure, Adv. in Mech. 15 (1985) 82-89.
    • (1985) Adv. in Mech. , vol.15 , pp. 82-89
    • Yu, J.L.1
  • 17
    • 0033069135 scopus 로고    scopus 로고
    • The analysis of crack problems with non-local elasticity
    • M. H. Zhao, G. J. Cheng, G. N. Liu and Y. P. Shen, The analysis of crack problems with non-local elasticity, Appl. Math. Mech. 20 (1999) 135-143
    • (1999) Appl. Math. Mech. , vol.20 , pp. 135-143
    • Zhao, M.H.1    Cheng, G.J.2    Liu, G.N.3    Shen, Y.P.4
  • 18
    • 33645904821 scopus 로고    scopus 로고
    • Dynamic properties of flexural beams using a nonlocal elasticity model
    • P. Lu, H. P. Lee, C. Lu and P. Q. Zhang, Dynamic properties of flexural beams using a nonlocal elasticity model, Journal of Applied Physics 99 (2006) 073510.
    • (2006) Journal of Applied Physics , vol.99 , pp. 073510
    • Lu, P.1    Lee, H.P.2    Lu, C.3    Zhang, P.Q.4
  • 19
    • 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
  • 20
    • 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
  • 21
    • 0346331500 scopus 로고    scopus 로고
    • Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics
    • L. J. Sudak, Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics, Journal of Applied Physics 94 (2003) 7281-7287.
    • (2003) Journal of Applied Physics , vol.94 , pp. 7281-7287
    • Sudak, L.J.1
  • 22
    • 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, Journal of Applied Physics 98 (2005) 124301.
    • (2005) Journal of Applied Physics , vol.98 , pp. 124301
    • Wang, Q.1
  • 23
    • 33747626951 scopus 로고    scopus 로고
    • Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory
    • DOI 10.1088/0022-3727/39/17/029, PII S0022372706258108, 029
    • C. M. Wang, Y. Y. Zhang, S. S. Ramesh and S. Kitipornchai, Buckling analysis of microand nano-rods/tubes based on nonlocal Timoshenko beam theory, Journal of Physics D: Applied Physics 39 (2006) 3904-3909. (Pubitemid 44261950)
    • (2006) Journal of Physics D: Applied Physics , vol.39 , Issue.17 , pp. 3904-3909
    • Wang, C.M.1    Zhang, Y.Y.2    Ramesh, S.S.3    Kitipornchai, S.4
  • 24
    • 42749107543 scopus 로고    scopus 로고
    • Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression
    • Y. Q. Zhang, G. R. Liu and J. S. Wang, Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression, Physical Review. B, Condensed Mater 70 (2004) 205430.
    • (2004) Physical Review. B, Condensed Mater , vol.70 , pp. 205430
    • Zhang, Y.Q.1    Liu, G.R.2    Wang, J.S.3
  • 25
    • 33947547136 scopus 로고    scopus 로고
    • The constitutive relation and small scale parameter of nonlocal continuum mechanics for modeling carbon nanotubes
    • Q. Wang and C. M. Wang, The constitutive relation and small scale parameter of nonlocal continuum mechanics for modeling carbon nanotubes, Nanotechnology 18 (2007) 75702.
    • (2007) Nanotechnology , vol.18 , pp. 75702
    • Wang, Q.1    Wang, C.M.2
  • 27
    • 48249093097 scopus 로고    scopus 로고
    • The small length scale effect for a non-local cantilever beam: A paradox solved
    • Article No.: 345703
    • N. Challamel and C. M. Wang, The small length scale effect for a non-local cantilever beam: A paradox solved, Nanotechnolgy 19 (2008) Article No.: 345703.
    • (2008) Nanotechnolgy , vol.19
    • Challamel, N.1    Wang, C.M.2
  • 29
    • 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. Vib. Eng. 8 (2009) 277-300.
    • (2009) Adv. Vib. Eng. , vol.8 , pp. 277-300
    • Lim, C.W.1
  • 30
    • 74849084120 scopus 로고    scopus 로고
    • Nanoscale for nanobeams based on the theory of nonlocal elastic stress field theory: Equilibrium, governing equation and static deflection
    • C. W. Lim, Nanoscale for nanobeams based on the theory of nonlocal elastic stress field theory: equilibrium, governing equation and static deflection, Appl. Math. Mech. 31 (2010) 37-54.
    • (2010) Appl. Math. Mech. , vol.31 , pp. 37-54
    • Lim, C.W.1
  • 31
    • 79953659405 scopus 로고    scopus 로고
    • Nonlocal elasticity theory and application for nanostructures
    • Elsevier Scirus, March 2010
    • C. W. Lim, Nonlocal elasticity theory and application for nanostructures, SciTopics, Elsevier Scirus, March 2010. http://www.scitopics.com/Nonlocal- Elasticity-Theory- and-Application-for-Nanostructures.html.
    • SciTopics
    • Lim, C.W.1
  • 32
    • 77953167584 scopus 로고    scopus 로고
    • A nanorod (or nanotube) with lower Young's modulus is more stiff? Is not Young's modulus a stiffness indicator?
    • C. W. Lim, A nanorod (or nanotube) with lower Young's modulus is more stiff? Is not Young's modulus a stiffness indicator? Science in China Series G: Physics, Mechanics & Astronomy 53(4) (2010) 712-724.
    • (2010) Science in China Series G: Physics, Mechanics & Astronomy , vol.53 , Issue.4 , pp. 712-724
    • Lim, C.W.1
  • 33
    • 77953141631 scopus 로고    scopus 로고
    • The effects of stiffness strengthening nonlocal stress and axial tension on free vibration of cantilever nanobeams
    • C. W. Lim, C. Li and J. L. Yu, The effects of stiffness strengthening nonlocal stress and axial tension on free vibration of cantilever nanobeams, Interaction and Multiscale Mech. 2(3) (2009) 223-233.
    • (2009) Interaction and Multiscale Mech. , vol.2 , Issue.3 , pp. 223-233
    • Lim, C.W.1    Li, C.2    Yu, J.L.3
  • 34
    • 77953141632 scopus 로고    scopus 로고
    • New predictions of size-dependent nanoscale based on nonlocal elasticity for wave propagation in carbon nanotubes
    • C. W. Lim and Y. Yang, New predictions of size-dependent nanoscale based on nonlocal elasticity for wave propagation in carbon nanotubes, Journal Computational and Theoretical Nanoscience 7(6) (2010) 988-995.
    • (2010) Journal Computational and Theoretical Nanoscience , vol.7 , Issue.6 , pp. 988-995
    • Lim, C.W.1    Yang, Y.2
  • 35
    • 78049283439 scopus 로고    scopus 로고
    • Wave propagation in carbon nanotubes: Nonlocal elasticity induced stiffness and velocity enhancement effects
    • in press
    • C. W. Lim and Y. Yang, Wave propagation in carbon nanotubes: Nonlocal elasticity induced stiffness and velocity enhancement effects, Journal of Mechanics of Materials and Structures (in press).
    • Journal of Mechanics of Materials and Structures
    • Lim, C.W.1    Yang, Y.2
  • 36
    • 77953157633 scopus 로고    scopus 로고
    • Nonlocal stress theory for buckling instability of nanobeams: New prediction on stiffness strengthening effects of nanoscales
    • in press
    • C. W. Lim, J. C. Niu and Y. M. Yu, Nonlocal stress theory for buckling instability of nanobeams: New prediction on stiffness strengthening effects of nanoscales, Journal of Computational and Theoretical Nanoscience (in press).
    • Journal of Computational and Theoretical Nanoscience
    • Lim, C.W.1    Niu, J.C.2    Yu, Y.M.3
  • 42
    • 0008757718 scopus 로고    scopus 로고
    • Apparently first closed-form solutions for inhomogeneous vibrating beams under axial loading
    • Z. Guede and I. Elishakoff, Apparently first closed-form solutions for inhomogeneous vibrating beams under axial loading, Proceedings of Royal Society London A 457 (2001) 623-649.
    • (2001) Proceedings of Royal Society London A , vol.457 , pp. 623-649
    • Guede, Z.1    Elishakoff, I.2
  • 43
    • 25644458690 scopus 로고    scopus 로고
    • Molecular dynamics study on size-dependent elastic properties of silicon nanocantilevers
    • DOI 10.1016/j.tsf.2005.06.056, PII S0040609005007133
    • S. H. Park, J. S. Kim, J. H. Park, J. S. Lee, Y. K. Choi and O. M. Kwon, Molecular dynamics study on size-dependent elastic properties of silicon nanocantilevers, Thin Solid Films 492 (2005) 285-289. (Pubitemid 41383733)
    • (2005) Thin Solid Films , vol.492 , Issue.1-2 , pp. 285-289
    • Park, S.H.1    Kim, J.S.2    Park, J.H.3    Lee, J.S.4    Choi, Y.K.5    Kwon, O.M.6


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.