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Research Papers

Selective Self-Excitation of Higher Vibrational Modes of Graphene Nano-Ribbons and Carbon Nanotubes Through Magnetomotive Instability

[+] Author and Article Information
A. Nordenfelt

Department of Physics,
University of Gothenburg,
SE-412 96 Göteborg, Sweden
e-mail: anders.nordenfelt@physics.gu.se

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 14, 2011; final manuscript received April 3, 2012; published online June 14, 2012. Assoc. Editor: Carmen M. Lilley.

J. Comput. Nonlinear Dynam 8(1), 011011 (Jun 14, 2012) (6 pages) Paper No: CND-11-1245; doi: 10.1115/1.4006563 History: Received December 14, 2011; Revised April 03, 2012

We demonstrate theoretically the feasibility of selective self-excitation of higher-mode flexural vibrations of graphene nano-ribbons and carbon nanotubes by the means of magnetomotive instability. Apart from the mechanical resonator, the device consists only of a constant voltage source, an inductor, a capacitor, a gate electrode, and a constant magnetic field. Numerical simulations were performed on both graphene and carbon nanotubes displaying an overall similar behavior, but with some differences arising mainly due to the nonlinear forces caused by the mechanical deformation. The advantages and disadvantages of both materials are discussed.

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Figures

Grahic Jump Location
Fig. 1

Sketch of the proposed electronic circuit (upper figure). The resistor is comprised of either a graphene sheet or a carbon nanotube suspended over a gate electrode (lower figure).

Grahic Jump Location
Fig. 4

Saturation amplitudes for the respective modes as a result of computer simulations aimed at selective self-excitation of the fourth harmonic of a carbon nanotube of radius r = 1 nm and length L = 1 μm. The coupling parameter β was in the range −23 to −27, which, assuming a stationary current of 1 μA, corresponds to a magnetic field strength in the interval 9.0–10.6 T. The other parameters were Q = 2·104, ωL = 8.485, and ωR = 4.397. Initial conditions were 0 in all variables.

Grahic Jump Location
Fig. 5

Saturation amplitudes for the respective modes as a result of computer simulations aimed at selective self-excitation of the second harmonic of a graphene nano-ribbon of width w = 10 nm and length L = 1 μm. The coupling parameter β was in the range −9 to −13, which, assuming a stationary current of 20 μA, corresponds to a magnetic field strength in the interval 6.6–9.6 T. The other parameters were Q = 104, ωL = 1.732, and ωR = 2.000. Initial conditions were 0 in all variables.

Grahic Jump Location
Fig. 6

Saturation amplitudes for the respective modes as a result of computer simulations aimed at selective self-excitation of the fourth harmonic of a graphene nano-ribbon of width w = 10 nm and length L = 1 μm. The coupling parameter β was in the range −14 to −18, which, assuming a stationary current of 20 μA, corresponds to a magnetic field strength in the interval 10.3–13.2 T. The other parameters were Q = 4·104, ωL = 3.873, and ωR = 2.000. Initial conditions were 0 in all variables.

Grahic Jump Location
Fig. 3

Time evolution of the envelopes of the rapid oscillations in the fundamental mode u0 (upper figure) and second harmonic u2 (lower figure) as the results of a computer simulation on a carbon nanotube with radius r = 1 nm and length L = 1 μm. The dashed lines mark the displacement averaged over a period of 2π. The parameters were β =-0.007, Q = 104, ωL = 2.323, and ωR = 4.397. Initial conditions were 0 in all variables.

Grahic Jump Location
Fig. 2

Saturation amplitudes for the respective modes as a result of computer simulations aimed at selective self-excitation of the second harmonic of a carbon nanotube with radius r = 1 nm and length L = 1 μm. The coupling parameter β was in the range −6.6 to −7.1, which, assuming a stationary current of 1 μA, corresponds to a magnetic field strength in the interval 2.6–2.8 T. The other parameters were Q = 104, ωL = 2.323, and ωR = 4.397. Initial conditions were 0 in all variables.

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