Frontiers of Mechanical Engineering >
Analytical and numerical investigation into the longitudinal vibration of uniform nanotubes
Received date: 09 Dec 2013
Accepted date: 17 Feb 2014
Published date: 22 May 2014
Copyright
In recent years, prediction of the behaviors of micro and nanostructures is going to be a matter of increasing concern considering their developments and uses in various engineering fields. Since carbon nanotubes show the specific properties such as strength and special electrical behaviors, they have become the main subject in nanotechnology researches. On the grounds that the classical continuum theory cannot accurately predict the mechanical behavior of nanostructures, nonlocal elasticity theory is used to model the nanoscaled systems. In this paper, a nonlocal model for nanorods is developed, and it is used to model the carbon nanotubes with the aim of the investigating into their longitudinal vibration. Following the derivation of governing equation of nanorods and estimation of nondimensional frequencies, the effect of nonlocal parameter and the length of the nanotube on the obtained frequencies are studied. Furthermore, differential quadrature method, as a numerical solution technique, is used to study the effect of these parameters on estimated frequencies for both classical and nonlocal theories.
Masoud MASOUMI , Mehdi MASOUMI . Analytical and numerical investigation into the longitudinal vibration of uniform nanotubes[J]. Frontiers of Mechanical Engineering, 2014 , 9(2) : 142 -149 . DOI: 10.1007/s11465-014-0292-z
| 1 |
IijimaS. Helical microtubules of graphitic carbon. Nature, 1991, 354(6348): 56-58
|
| 2 |
FalvoM R, ClaryG J, TaylorR M 2nd, ChiV, BrooksF P Jr, WashburnS, SuperfineR. Bending and buckling of carbon nanotubes under large strain. Nature, 1997, 389(6651): 582-584
|
| 3 |
DarkrimF L, MalbrunotP, TartagliaG P. Review of hydrogen storage by adsorption in carbon nanotubes. International Journal of Hydrogen Energy, 2002, 27(2): 193-202
|
| 4 |
BelinT, EpronF. Characterization methods of carbon nanotubes: a review. Materials Science and Engineering B, 2005, 119(2): 105-118
|
| 5 |
LiC, ThostensonE T, ChouT W. Sensors and actuators based on carbon nanotubes and their composites: a review. Composites Science and Technology, 2008, 68(6): 1227-1249
|
| 6 |
HanZ, FinaA. Thermal Conductivity of Carbon Nanotubes and their Polymer Nanocomposites: A Review. Progress in Polymer Science, 2011, 36(7): 914-944
|
| 7 |
Herrera-HerreraA V, González-CurbeloM Á, Hernández-BorgesJ, Rodríguez-DelgadoM A. Carbon nanotubes applications in separation science: a review. Analytica Chimica Acta, 2012, 734: 1-30
|
| 8 |
SunC T, ZhangH. Size-dependent elastic moduli of platelike nanomaterials. Journal of Applied Physics, 2003, 93(2): 1212-1218
|
| 9 |
EringenA C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 1983, 54(9): 4703-4710
|
| 10 |
PeddiesonJ, BuchananG R, McNittR P. Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science, 2003, 41(3-5): 305-312
|
| 11 |
WangQ, LiewK M. Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures. Physics Letters A, 2007, 363(3): 236-242
|
| 12 |
MurmuT, PradhanS C. Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory. Computational Materials Science, 2009, 46(4): 854-859
|
| 13 |
PradhanS C, PhadikarJ K. Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory. Structural Engineering & mechanics. International Journal (Toronto, Ont.), 2009, 33(2): 193-213
|
| 14 |
EringenA C. Nonlocal Continuum Field Theories. New York: Springer-Verlag, 2002
|
| 15 |
ReddyJ N, PangS D. Nonlocal continuum theories of beams for the analysis of carbon nanotubes. Journal of Applied Physics, 2008, 103(2): 023511
|
| 16 |
BellmanR, KashefB G, CastiJ. Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of Computational Physics, 1972, 10(1): 40-52
|
| 17 |
WangX, BertC W. A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates. Journal of Sound and Vibration, 1993, 162(3): 566-572
|
| 18 |
ShuC, DuH. Implementaion of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates. International Journal of Solids and Structures, 1997, 34(7): 819-835
|
| 19 |
KumarB M, SujithR I. Exact solutions for the longitudinal vibration of non-uniform rods. Journal of Sound and Vibration, 1997, 207(5): 721-729
|
| 20 |
SundararaghavanV, WaasA. Non-local continuum modeling of carbon nanotubes: physical interpretation of non-local kernels using atomistic simulations. Journal of the Mechanics and Physics of Solids, 2011, 59(6): 1191-1203
|
| 21 |
GuptaS S, BatraR C. Continuum structures equivalent in normal mode vibrations to single-walled carbon nanotubes. Computational Materials Science, 2008, 43(4): 715-723
|
| 22 |
WangQ, WangC M. The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes. Nanotechnology, 2007, 18(7): 1-4.
|
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