Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect

This paper investigates the radial breathing mode (RBM) vibration of single-walled carbon nanotubes (SWCNTs) based on doublet mechanics (DM) with a length scale parameter. A second order partial differential equation that governs the RBM vibration of SWCNTs is derived. Using DM, the relation between natural frequency and length scale parameter is derived in the RBM mode of vibration. It is shown that the length scale parameter plays significant role in the RBM vibration response of SWCNTs. The length scale parameter decreases the natural frequency of vibration compared to the predictions of the classical continuum models. However, with increase in tube radius, the effect of the scale parameter on the natural frequency decreases. The results obtained herein are compared with the existing theoretical and experimental results and good agreement with the latter is observed.

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“…which is in exact agreement with the classical expression for the frequency of the RBM mode of vibration in [19,27]. Eqs.…”

Section: Dm Model Of Rbm Vibrationsupporting

confidence: 77%

“…Continuum elastic shell models [26][27][28][29][30][31] used to study RBM vibration of SWCNTs do not consider scale effects. Also, atomistic methods [32][33][34] which do consider scale effects are costly and time consuming to implement particularly for large-scale systems.…”

Section: Introductionmentioning

confidence: 99%

Analysis of radial breathing mode of vibration of single‐walled carbon nanotubes via doublet mechanics

Fatahi-Vajari

Imam

2016

Z Angew Math Mech

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“…By modeling the zigzag CNTs as a nonlocal Levinson beam model, Maachou et al 43 studied the vibration behavior of CNTs under thermal effects. Fazelzadeh and Ghavanloo,44,45 using the anisotropic nonlocal cylindrical shell model, investigated the effects of various parameters on CNTs frequency. Besides, they studied the effect of chirality on CNT vibrations.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

Beni

Mehralian

Zeverdejani

2017

Journal of Low Frequency Noise, Vibration and Active Control

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In the present work, using the couple stress theory, a new model is provided for vibrating behavior of anisotropic carbon nanotubes. Carbon nanotubes have many applications, and careful analysis of their behavior is important. So far, using the isotropic models, several studies have been conducted on carbon nanotube vibration. According to the arrangement of carbon atoms on the nanotube walls, their properties will be different in various directions. Therefore, the behavior of carbon nanotubes must be considered as anisotropic materials. In this article, initially, using the Hamilton's principle, motion equations, and boundary conditions of carbon nanotubes are extracted based on couple stress theory. Afterwards, the equations are solved using the analytical solution method. In the results section, the effect of different parameters, particularly the anisotropic effect, on the carbon nanotube natural frequency is investigated.

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“…Beginning with the pioneering work of Jacobson [39], this approach is actively exploited in the description of the various mechanical properties of CNTs and its adequacy was repeatedly checked by comparison to experimental data as well as to data of molecular dynamic simulation [26,[32][33][34]. However, the theory of thin shells allows an analytical solution only in exceptional, stationary cases [40,41] even in the framework of linear approximation.…”

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confidence: 99%

“…Calculation of the phonon spectra of CNT is a subject of a number of studies, many of which are based on the continuum model of a single-walled carbon nanotubes as a thin elastic shell [25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Beginning with the pioneering work of Jacobson [39], this approach is actively exploited in the description of the various mechanical properties of CNTs and its adequacy was repeatedly checked by comparison to experimental data as well as to data of molecular dynamic simulation [26,[32][33][34].…”

mentioning

confidence: 99%

Localization of Low-Frequency Oscillations in Single-Walled Carbon Nanotubes

2014

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New phenomenon of a weak energy localization of optical low-frequency oscillations in carbon nanotubes (CNT) is analytically predicted in the framework of continuum shell theory. This phenomenon takes place for CNTs of finite length with medium aspect ratio. The origin of localization is clarified by means of the concept of Limiting Phase Trajectory, and the analytical results are confirmed by the MD simulation of simply supported CNT.PACS numbers: 61.48. De, 63.22.Gh, From a modern point of view, carbon nanotubes are twice the exciting subject of scientific researches. On the one hand, they are associated with great hopes for creation of super-small and ultra-fast electronic and electromechanical devices [1][2][3][4]. On the other hand, they are quasi-one-dimensional objects that allow to check out some of the funamentals of modern solid-state physics. In particular, variuos computational and in-situ measurements of thermoconductivity of CNT [5][6][7][8][9] are directly related with the problem of finiteness of thermoconductivity of one-dimensional anharmonic lattices. This problem has been formulated more than fifty years ago in the famous work by Fermi, Pasta and Ulam [10]. The widearea study of nonlinear lattices dynamics led to discovery of new class of elementary excitations -solitons, the main feature of those is the self-localization in the homogeneous lattices [11,12]. From the point of view of energy trasfer, solitons take place dual role. Being very effective energy carriers they also provide the effective scattering of small-amplitude phonons [13][14][15][16][17][18][19]. From the mathematical point of view, the solution like a breather exists only in the infinite systems with a continuous spectrum, while the nanoscale objects can be rather considered as finite ones. In such a case the problem of definition of nonlinear localized excitations has significant pecularities.It was recently shown [20][21][22] that the finite systems of weakly coupled oscillators exhibit strongly modulated non-stationary oscillations characterized by the maximum possible energy exchange between the groups of the oscillators or the maximum energy transfer from the external source of energy to the system [23]. The solutions describing these processes are referred to as Limiting Phase Trajectories (LPTs). The development and the use of the analytical framework based on the LPT concept is motivated by the fact that resonant non-stationary processes occurring in a broad variety of finite dimensional physical models are beyond the well-known paradigm of nonlinear normal modes (NNMs), fully justified only for quasi-stationary processes and non-stationary processes in non-resonant case. While the NNMs approach has been proved to be an effective tool for the analysis of instability and bifurcations of stationary processes (see, e.g., [24]), the use of the LPTs concept provides the adequate procedures for studying strongly modulated regimes as well as the transitions to energy localization and chaotic behavior [20]. Such an approach...

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Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect

Cited by 60 publications

References 47 publications

Analysis of radial breathing mode of vibration of single‐walled carbon nanotubes via doublet mechanics

Analysis of radial breathing mode of vibration of single‐walled carbon nanotubes via doublet mechanics

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

Localization of Low-Frequency Oscillations in Single-Walled Carbon Nanotubes

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