On radial breathing vibration of carbon nanotubes

Cheng, Hsien‐Chie; Liu, Yang-Lun; Wu, Changxu; Chen, Wen‐Hwa

doi:10.1016/j.cma.2010.05.003

Cited by 32 publications

(25 citation statements)

References 29 publications

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“…A strong dependence can be observed between the elastic properties and the dimension of the polycrystalline aggregates, in which an increasing dimension would lead to a significantly decreasing polycrystalline Young's modulus, bulk modulus, and shear modulus but a slightly increasing Poisson's ratio. These results conform to the published data [21,51,52]. These polycrystalline elastic properties would eventually converge to a constant value as N becomes roughly larger than 7, where it is about 132.7 GPa for the Young's modulus, 128.9 GPa for the bulk modulus, 49.9 GPa for the shear modulus and 0.328 for the Poisson's ratio.…”

Section: Polycrystalline Elastic Propertiessupporting

confidence: 90%

Crystal size and direction dependence of the elastic properties of Cu3Sn through molecular dynamics simulation and nanoindentation testing

Chen¹,

Yu²,

Cheng³

et al. 2012

Microelectronics Reliability

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Section: Polycrystalline Elastic Propertiessupporting

confidence: 90%

Crystal size and direction dependence of the elastic properties of Cu3Sn through molecular dynamics simulation and nanoindentation testing

Chen¹,

Yu²,

Cheng³

et al. 2012

Microelectronics Reliability

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“…Molecular dynamics simulations (MDS) provide accurate predictions of RBM natural frequencies for SWNTs with different chiralities, geometries and boundary conditions under external forces, by taking into account atomic structure and interaction potential energy of the carbon atoms associated with bond stretching, torsion and angle changes between adjacent bonds, electrostatic interactions, coupling among different deformations and transverse inertia forces [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Radial breathing modes

Strozzi

Смірнов

Manevitch

et al. 2018

Composite Structures

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In this paper, the nonlinear vibrations and energy exchange of single-walled carbon nanotubes (SWNTs) are analysed. The Sanders-Koiter shell theory is used to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported, clamped and free boundary conditions are applied. The resonant interaction between radial breathing (axisymmetric) modes (RBMs) is analysed. An energy method, based on the Lagrange equations, is considered in order to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is then solved applying the implicit Runge-Kutta numerical method. The present model is validated in linear field comparing the RBM natural frequencies numerically predicted with data reported in the literature from experiments and molecular dynamics simulations. The nonlinear energy exchange between the two halves along the SWNT axis in the time is studied for different amplitudes of initial excitation applied to the two lowest frequency resonant RBMs. The influence of the SWNT aspect ratio on the numerical value of the nonlinear energy beating period under different boundary conditions is analysed

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“…In the RBM, all of the carbon atoms in a CNT move in a radial direction synchronously as if the tube is "breathing" [7,8]. This mode is unique to CNTs, and is not observed in other carbon systems [9].…”

Section: Introductionmentioning

confidence: 99%

“…Lawler and Kurti et al [25,26] presented first-principle calculations for the RBM of bundled SWCNTs. A study exploring the frequencies and mode shapes of the RBM of various CNTs using a modified molecular structural mechanics model was reported by Cheng et al [9]. Based on a multiple-elastic shell model, Wang et al [27] showed that the frequencies of the RBM of MWCNTs generally increase as the external pressure increases, and the effects of pressure are associated with RBMs of different frequency for MWCNTs with innermost tubes of different diameter.…”

Section: Introductionmentioning

confidence: 99%

Radial breathing vibration of double-walled carbon nanotubes subjected to pressure

et al. 2011

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A theoretical vibrational analysis of the radial breathing mode (RBM) of double-walled carbon nanotubes (DWCNTs) subjected to pressure is presented based on an elastic continuum model. The results agree with reported experimental results obtained under different conditions. Frequencies of the RBM in DWCNTs subjected to increasing pressure depend strongly on circumferential wave numbers, but weakly on the aspect ratio and axial half-wave numbers. For the inner and outer tubes of DWCNTs, the frequency of the RBM increases obviously as the pressure increases under different conditions. The range of variation is smaller for the inner tube than the outer tube.

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On radial breathing vibration of carbon nanotubes

Cited by 32 publications

References 29 publications

Crystal size and direction dependence of the elastic properties of Cu3Sn through molecular dynamics simulation and nanoindentation testing

Crystal size and direction dependence of the elastic properties of Cu3Sn through molecular dynamics simulation and nanoindentation testing

Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Radial breathing modes

Radial breathing vibration of double-walled carbon nanotubes subjected to pressure

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