Fundamental natural frequencies of double-walled carbon nanotubes

Elishakoff, Isaac; Pentaras, Demetris

doi:10.1016/j.jsv.2009.02.037

Cited by 70 publications

(36 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Comparison of the results with recent studies shows that the above methods constitute effective alternative techniques to exact solution for studying the vibration properties of carbon nanotubes. Hereinafter we follow closely our recent paper [15] and provide some corrections.…”

Section: Introductionmentioning

confidence: 91%

Some Modern Problems in Structural Engineering Dynamics

Elishakoff

Pentaras

2010

Shock and Vibration

View full text Add to dashboard Cite

Abstract. This review paper deals with two problems in structural engineering dynamics; one is deterministic, the other is of stochastic nature. One problem is linear, the other is nonlinear. Authors have a biased preferential view on these problems because of their active involvement in the discussed research topics. Still, these two problems reflect, at least in a small manner, some developments in this vast and fascinating field. The first part deals with deterministic linear vibrations of double-walled carbon nanotubes either in classical or refined setting; the second part is devoted to the nonlinear random vibrations of structures.

show abstract

Section: Introductionmentioning

confidence: 91%

Some Modern Problems in Structural Engineering Dynamics

Elishakoff

Pentaras

2010

Shock and Vibration

View full text Add to dashboard Cite

show abstract

“…Also some new investigation was made with some non-local parameters for nanotube aspect ratio against the fundamental resonant frequency curves different boundary conditions. Increasingly, computer simulations have been used to examine vibration characteristics of CNTs (and or SWCNTs) through different models bases (Li and Chou, 2003;SakhaeePour et al, 2009;Yakobson et al, 1996;Hsu et al, 2008;Azrar et al, 2011;Elishakoff and Pentaras, 2009). Selection of a dynamical model to analyze systems related nano level is Flügge's cylindrical shell model (CSM).…”

Section: Introductionmentioning

confidence: 99%

“…Numerical procedure to frame the CNT frequency equation employed is wave propagation approach (WPA), which admits to extract fundamental frequencies of SWCNTs over various combinations of parameters. Many numerical techniques been adopted for vibration problems like Galerkin's method (Azrar et al, 2011;Elishakoff and Pentaras, 2009), finite elements method (FEM) (Sakhaee-Pour et al, 2009), wave propagation approach (Xuebin, 2008;Zhang et al, 2001). On the other hand, CSM based WPA was found to be a very popular tool to compute the vibration characteristics of SWCNTs.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the novel Flügge's cylindrical shell model (CSM) based on WPA for estimating the natural frequencies of SWCNTs has been demonstrated to converge faster than the other models and other approaches. The Flügge CSM based on WPA is, therefore, another choice of powerful technique of CNTs whose results are applicable in the limit of acceptable statistical errors than the earlier used approaches (Natsuki and Morinobu, 2006;Hsu et al, 2008;Yakobson et al, 1996;Elishakoff and Pentaras, 2009;Sakhaee-Pour et al, 2009). In this work, the Flügge's CSM based on WPA for determining fundamental frequencies is extended to study vibrations of SWCNTs, which is our particular motivation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Vibration analysis of single-walled carbon nanotubes using wave propagation approach

Hussain

2017

Mech. Sci.

View full text Add to dashboard Cite

Abstract. In this paper, influence of boundary conditions on free vibrations of single-walled carbon nanotubes (SWCNTs) is examined. The Flügge's shell dynamical equations are utilized for governing vibrations for carbon nanotubes. The wave propagation approach (WPA) is engaged to determine vibration frequency equation in standard eigenvalue form. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers. These numbers are associated with boundary conditions specified at edges of a carbon nanotube. Computer programming is performed to obtain solutions of vibration frequency equation. In our new investigation, the vibration frequency spectra are obtained and analyzed for various physical parameters e.g., length and thickness-to-radius ratio. A number of results are presented to influence of different boundary conditions on SWCNTs. They are shown graphically and have been compared with those available in the literature.

show abstract

“…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

View full text Add to dashboard Cite

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...

show abstract

Fundamental natural frequencies of double-walled carbon nanotubes

Cited by 70 publications

References 10 publications

Some Modern Problems in Structural Engineering Dynamics

Some Modern Problems in Structural Engineering Dynamics

Vibration analysis of single-walled carbon nanotubes using wave propagation approach

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

Contact Info

Product

Resources

About