Flexural Wave Propagation in Single-Walled Carbon Nanotubes

Liew, K.M.; Hu, Yan-Gao; He, X. Q.

doi:10.1166/jctn.2008.019

Cited by 63 publications

(27 citation statements)

References 0 publications

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“…Other approaches or models are often compared with MD to verify the solutions. For this reason and to further confirm the validity of the ANT solutions, we present in Figure 6 a comparison of the various dispersion relations with MD results [Liew et al 2008] for a (5, 5) CNT. In this example, the parameters and properties of nanotube are the same as in the previous subsection, except that we take the Young's modulus to be E = 0.897 TPa, the diameter d = 0.96 nm and τ = 0.00355.…”

Section: Resultssupporting

confidence: 55%

“…We now present some numerical examples to illustrate the contrast between the analytical nonlocal shear deformable nanotube model (ANT) and the partial nonlocal shear deformable nanotube model (PNT) for wave propagation in a nonlocal nanotube with respect to the classical shear deformable tube model (CT). In these examples, the nanotubes are considered as homogeneous and isotropic with geometric and materials properties as in [Liew et al 2008]: diameter d = 5 nm, thickness t = 0.34 nm, length L = 10 nm, Young's modulus E = 0.72 TPa, Poisson's ratio υ = 0.254, density ρ = 2.3 g/cm 3 , vibration period T = 4 × 10 −13 s and shear correction factor κ = 10 9 . The dispersion relation between the dimensionless phase velocityc and the dimensionless wave numberk (wherec =ω/k) with various τ is illustrated in Figure 3 for shear deformable nanotube models based on the PNT solution in (37) and (39) and the ANT solution in (37) and (38).…”

Section: Resultsmentioning

confidence: 99%

“…Obviously the only difference between the solutions of this new analytical nonlocal stress model and the existing partial nonlocal stress model [Liew et al 2008] is contributed by c 1 and c 2 . The difference leads to different characteristics of the two dispersion relations and spectrum relations for wave propagation in CNTs as discussed in great details in the following section.…”

Section: And (24)mentioning

confidence: 94%

“…Using the partial nonlocal nanotube model, the corresponding relation is identical to (37) except that a 1 , b 1 , c 1 be replaced by a 2 , b 2 , c 2 , given by [Liew et al 2008]…”

Section: And (24)mentioning

confidence: 99%

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

Lim

Yang

2010

JoMMS

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We establish the physics and understanding of nonlocal nanoscale wave propagation in carbon nanotubes (CNTs) based on nonlocal elastic stress field theory. This is done by developing an analytical nonlocal nanotube model based on the variational principle for wave propagation in CNTs. Specifically, we successfully derive benchmark governing equations of motion for analyzing wave propagation based on an analytical nonlocal shear deformable model. The physical insights of the analytical nonlocal stress model are presented through examples. Analytical solutions with significant observation of wave propagation have been predicted and the prediction compares favorably with molecular dynamic simulations. Qualitative comparisons with other non-nonlocal approaches, including the strain gradients model, the couple stress model and experiments, justify the stiffness enhancement conclusion as predicted by the new nonlocal stress model. New dispersion and spectrum relations derived using this analytical nonlocal model bring an important focus onto the critical wavenumber: stiffness of CNTs and wave propagation are enhanced below the critical wavenumber, while beyond that a sharp decrease in wave propagation is observed. The physics of nanoscale wave propagation in nanotubes are further illustrated by relating the nanoscale and the phase velocity ratio.

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Section: Resultssupporting

confidence: 55%

Section: Resultsmentioning

confidence: 99%

Section: And (24)mentioning

confidence: 94%

“…Using the partial nonlocal nanotube model, the corresponding relation is identical to (37) except that a 1 , b 1 , c 1 be replaced by a 2 , b 2 , c 2 , given by [Liew et al 2008]…”

Section: And (24)mentioning

confidence: 99%

See 2 more Smart Citations

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

Lim

Yang

2010

JoMMS

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show abstract

“…Civalek and Akgöz (2010) presented free vibration analysis of microtubules (MTs) based on the Euler-Bernoulli beam theory. Liew et al (2008) simulated the flexural wave propagation in a single-walled carbon nanotube (SWCNT) by using molecular dynamics (MD) based on a second-generation reactive empirical bond order (REBO) potential. Civalek and Demir (2011) formulated the equations of motion and bending of Euler-Bernoulli beam using the nonlocal elasticity theory for cantilever microtubules (MTs).…”

Section: Introductionmentioning

confidence: 99%