Nonlinear oscillations of a double-walled carbon nanotube

Hawwa, Muhammad A.; Al‐Qahtani, Hussain

doi:10.1016/j.commatsci.2009.12.020

Cited by 39 publications

(19 citation statements)

References 13 publications

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“…Therefore, and since their discovery [3], CNTs have been under extensive research [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Beside their interesting mechanical and electrical properties, electrically actuated CNTs were shown to have rich nonlinear behavior characterized by inherent nonlinear response even for small electric loads [4] as well as a wide range of tunability of their natural frequencies with the DC load [5].…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of slacked single-walled carbon nanotube resonators

Ouakad

Younis

2011

Nonlinear Dyn

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This paper presents an investigation of the dynamics of electrically actuated single-walled carbon nanotube (CNT) resonators including the effect of their initial curvature due to fabrication (slack). A nonlinear shallow arch model is utilized. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response due to DC and small AC loads for various slacked CNTs of higher and lower aspect ratio. Results of the perturbation method are verified with those obtained by numerically integrating the equations of a multi-mode reduced-order model based on the Galerkin procedure. The effective nonlinearity of the CNT is calculated as a function of the slack level and the DC load. To handle computational problems associated with CNTs of small radiuses, results based on a nonlinear cable model are also demonstrated. The results have indicated that the quadratic nonlinearity due to slack has dominant effect on the dynamic behavior of the CNT.

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Section: Introductionmentioning

confidence: 99%

Dynamic response of slacked single-walled carbon nanotube resonators

Ouakad

Younis

2011

Nonlinear Dyn

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“…Similarly, physical systems involving NEMS resonators are excellent tools for theoretical and experimental studies of nonlinear dynamical systems [14,15]. Indeed, examples of complex dynamical phenomena in NEMS are numerous and include chaotic behavior [16][17][18][19], bifurcationtopology amplification [20], nonlinear switching dynamics [21] and nonlinear frequency pulling [22] to name but a few.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a suspended nanowire driven by an ac Josephson current in an inhomogeneous magnetic field

Peña-Aza

2012

Phys. Rev. E

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We consider a voltage-biased nanoelectromechanical Josephson junction, where a suspended nanowire forms a superconducting weak-link, in an inhomogeneous magnetic field. We show that a nonlinear coupling between the Josephson current and the magnetic field generates a Laplace force that induces a whirling motion of the nanowire. By performing an analytical and a numerical analysis, we demonstrate that at resonance, the amplitude-phase dynamics of the whirling movement present different regimes depending on the degree of inhomogeneity of the magnetic field: time independent, periodic and chaotic. Transitions between these regimes are also discussed.

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“…In the reported studies, researchers used the continuum mechanics and molecular dynamics theories to accurately study and predict the behavior of CNTs, and since the computational time from using the molecular dynamics is cumbersome, Some research and investigations were directed towards the continuum mechanics models due to their significant accuracy in modeling and predicting the dynamic and vibrational behavior of CNTs (Harik, 2002;Sazonova, Yaish, Ustunel, Rounday, Arias & McEuen, 2004;Mayoof & Hawwa, 2009;Hawwa & Al-Qahtani, 2010). …”

Section: Introductionmentioning

confidence: 99%

“…Even for a CNT with initial rise/imperfection, to discretize the mathematical model researchers used a straight beam eigen function or used approximate eigen function, despite the fact that CNTs or beams usually exhibit a certain degree of waviness (Farshidianfar & Soltani, 2012), which can have a significant role on the dynamic and vibrational behavior (Mehdipour, Barari, Kimiaefar & Domairry, 2102;Farshidianfar & Soltani, 2012;(Sazonova, Yaish, Ustunel, Rounday, Arias & McEuen, 2004;(Hawwa & Al-Qahtani, 2010;Mehdipour & Barari, 2012;Mettler, 1962;Al-Qaisia & Hamdan, 2009;. Due to the lack of accurate mathematical models for a CNT with an arbitrary rise/imperfection using nonlocal elastic theory and continuum mechanics, this work is motivated.…”

Section: Introductionmentioning

confidence: 99%

“…They studied the effect of the mid-plane stretching and the curved geometry on the dynamic response of a CNT and the bifurcation turns to chaos. Hawwa & Al-Qahtani (2010), used the continuum mechanics approach to study the nonlinear oscillations and chaotic motion characteristics of a double-walled CNT. Also, they used the Galerkin's approach to discretize the coupled non-linear integro-partial differential equations of the inner and outer nano-beams.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Vibrations of a SWCNT with Geometrical Imperfection Using Nonlocal Elasticity Theory

Abdel-Jaber¹,

Al-Qaisia

Shatarat³

2017

MAS

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The nonlinear free vibration and frequency veering of a single wall carbon nanotube (SWCNT) based on nonlocal elasticity theory is studied and investigated in this paper. The carbon nanotubes (CNT) is assumed to have an imperfection modeled as half sine and clamped at both ends. The Euler-Bernoulli Beam and Hamilton's principle were used to derive the nonlinear equation of motion of the SWCNT. The effect of; nonlocal elasticity, geometric initial rise/imperfection, and the effect of the axial force induced by mid-plane stretching are accounted for in the derivation of the nonlinear mathematical model of the CNT. The governing partial differential equation includes quadratic and cubic nonlinearities due to the initial imperfection and the mid-plane stretching. The derived equation of motion is discretized using the assumed mode method by inserting the exact linear eigen mode shape. The resulting nonlinear temporal equation was solved using the method of multiple scales (MMS) to obtain results for the nonlinear natural frequencies of the first three modes of vibrations, for different values of rise/imperfection amplitude, and for different values of the nonlocal parameter. The results are presented in non-dimensional characteristic curves to show the effect of variation of rise/imperfection amplitude and nonlocal parameter on the vibrational behavior of the CNT.

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Nonlinear oscillations of a double-walled carbon nanotube

Cited by 39 publications

References 13 publications

Dynamic response of slacked single-walled carbon nanotube resonators

Dynamic response of slacked single-walled carbon nanotube resonators

Dynamics of a suspended nanowire driven by an ac Josephson current in an inhomogeneous magnetic field

Nonlinear Vibrations of a SWCNT with Geometrical Imperfection Using Nonlocal Elasticity Theory

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