Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T10:01:25.329Z Has data issue: false hasContentIssue false
  • English
  • Français

Magnetoelastic Instability of a Long Graphene Nano-Ribbon Carrying Electric Current

Published online by Cambridge University Press:  03 June 2015

R. D. Firouz-Abadi  and
H. Mohammadkhani
R. D. Firouz-Abadi*
Affiliation:
Department of Aerospace Engineering, Sharif University of Technology, P.O.Box 11155-8639, Tehran, Iran Institute for Nanosience and Nanotechnology, Sharif University of Technology, P.O.Box 14588-89694, Tehran, Iran
H. Mohammadkhani*
Affiliation:
Department of Aerospace Engineering, Sharif University of Technology, P.O.Box 11155-8639, Tehran, Iran
*
Corresponding author. Email: [email protected]
Email: [email protected]
Get access

Abstract

This paper aims at investigating the resonance frequencies and stability of a long Graphene Nano-Ribbon (GNR) carrying electric current. The governing equation of motion is obtained based on the Euler-Bernoulli beam model along with Hamilton’s principle. The transverse force distribution on the GNR due to the interaction of the electric current with its own magnetic field is determined by the Biot-Savart and Lorentz force laws. Using Galerkin’s method, the governing equation is solved and the effect of current strength and dimensions of the GNR on the stability and resonance frequencies are investigated.

Keywords

82D8037N1574H55Graphene nano-ribbonresonance frequencycurrent carryingHamilton’s principleBiot-SavartLorenz force
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 3 , June 2014 , pp. 299 - 306
Copyright
Copyright © Global-Science Press 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Peres, N. M. R., Guinea, F. and Neto, A. H. C., Electronic properties of disordered twodimensional carbon, Phys. Rev. B, 73 (2006), 125411.CrossRefGoogle Scholar
[2]Mcintosh, R., Mamo, M., Jamieson, B., Roy, S. and Bhattacharyya, S., Improved electronic and magnetic properties of reduced graphene oxide films, EPL, 97 (2012).Google Scholar
[3]Andersson, O. E., Prasad, B. L. V., Sato, H., Enoki, T., Hishiyama, Y., Kaburagi, Y., Yoshikawa, M. and Bandow, S., Structure and electronic properties of graphite nanoparticles, Phys. Rev. B, 58 (1998), pp. 16387–16395.Google Scholar
[4]Yelgel, C. and Srivastava, G. P., Ab initio studies of electronic and optical properties of graphene and graphenebn interface, Appl. Surf. Sci., 258 (2012), pp. 8338–8342.Google Scholar
[5]Atalaya, J., Kinaret, J. and Isacsson, A., Nanomechanical mass measurement using nonlinear response of a graphene membrane, EPL, 91 (2010).CrossRefGoogle Scholar
[6]Mamin, H. and Rugar, D., Sub-attonewton force detection at millikelvin temperatures, Appl. Phys. Lett., 79 (2001), pp. 3358–3360.Google Scholar
[7]Lahaye, M., Buu, O., Camarota, B. and Schwab, K., Approaching the quantum limit of a nanomechanical resonator, Science, 304 (2004), pp. 74–77.Google Scholar
[8]Yang, Y., Callegari, C., Feng, X., Ekinci, K. and Roukes, M., Zeptogram-scale nanomechanical mass sensing, Nano Lett., 6 (2006) pp. 583–586.Google Scholar
[9]Bunch, J., Zande, A. V. D., Verbridge, S., Frank, I., Tanenbaum, D., Parpia, j., Craighead, H. and Mceuen, P., Electromechanical resonators from graphene sheets, Science, 315 (2007), pp. 490–493.Google Scholar
[10]Prudnikov, V., Elastic oscillations of a current-carrying rod in a longitudinal magnetic field, J. Appl. Mech. Tech. Phys., 9 (1968), pp. 129–131.Google Scholar
[11]Dolbin, N. and Morozov, A., Elastic bending vibrations of a rod carrying electric current, J. Appl. Mech. Tech. Phys., 7 (1966), pp. 59–62.Google Scholar
[12]Chattopadhyay, S. and Moon, F., Magnetoelastic buckling and vibration of a rod carrying electric current, J. Appl. Mech., 42 (1975), pp. 809–814.Google Scholar
[13]Chattopadhyay, S., Magnetoelastic instability of structures carrying electric current, Int. J. Solid. Struct., 15 (1979), pp. 467–477.Google Scholar
[14]Chen, C., Rosenblatt, S., Bolotin, K., Kalb, W., Kim, P., Kymissis, I., Stormer, H., Heinz, T. and Hone, J., Performance of monolayer graphene nanomechanical resonators with electrical readout, Nature Nanotech., 4 (2009), pp. 861–867.Google Scholar
[15]Edward, P. and Furlani, Permanent Magnet and Electromechanical Devices, Academic Press, 2001.Google Scholar
[16]Cranford, S. and Buehler, M., Twisted and coiled ultralong multilayer graphene ribbons, Model. Simul. Mater. Sci. Eng., (2011).Google Scholar