Nonlinear resonances of a single-wall carbon nanotube cantilever

Kim, I.K.; Lee, S.I.

doi:10.1016/j.physe.2014.11.022

Cited by 4 publications

(1 citation statement)

References 33 publications

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“…Using the direct perturbation technique, Fang [17] studied chaotic behavior and its control in the single-wall carbon nanotube. With theoretical and numerical approaches, Kim and Lee [18] discussed the dynamics of an electrostatically actuated carbon nanotube cantilever. It was presented that high electrostatic excitation could lead to complex nonlinear responses such as softening, multiple stability changes at saddle nodes, or period-doubling bifurcation points in the primary and secondary resonance branches.…”

Section: Introductionmentioning

confidence: 99%

Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

Zhou¹

2016

ACM

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Bifurcation behaviors are very important for the design of sensors. Using the sub-harmonic Melnikov method, the sub-harmonic bifurcation of single-walled carbon nanotube based mass sensor is investigated in this paper. The parametric conditions for sub-harmonic bifurcation of this system are obtained. It is presented that when the ratio of the excitation amplitude to the damping coefficient crosses a critical value, sub-harmonic bifurcations of m order (odd) can occur. The stability conditions of the bifurcation solution for the system parameters are also obtained by using the affection-angle transformation and average method. The result can provide some guidance for the design of this class of sensors.

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Section: Introductionmentioning

confidence: 99%

Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

Zhou¹

2016

ACM

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A size-dependent model for beam-like MEMS driven by electrostatic and piezoelectric forces: A variational approach

Yin

Wang

Zhou

et al. 2016

Physica E: Low-dimensional Systems and Nanostructures

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Subharmonic bifurcation and chaos of a carbon nanotube supported by a Winkler and Pasternak foundation

Zhou

Chen

Zhao

2019

Int. J. Mod. Phys. B

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In this paper, by employing both analytical and numerical methods, global dynamic responses including subharmonic bifurcations and chaos are investigated for a carbon nanotube supported by a Winkler and Pasternak foundation. The criteria of chaos arising from transverse intersections for stable and unstable manifolds of homoclinic orbits are proposed with the Melnikov method. The critical curves separating the chaotic and nonchaotic regions are plotted in the parameter plane. The parameter conditions for subharmonic bifurcations are also obtained by the subharmonic Melnikov method. It is proved rigorously that the route to chaos for this model is infinite subharmonic bifurcations. The stability of subharmonic bifurcations is also studied by the characteristic multipliers. Numerical simulations are given to confirm the analytical results.

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Nonlinear resonances of a single-wall carbon nanotube cantilever

Cited by 4 publications

References 33 publications

Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

A size-dependent model for beam-like MEMS driven by electrostatic and piezoelectric forces: A variational approach

Subharmonic bifurcation and chaos of a carbon nanotube supported by a Winkler and Pasternak foundation

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