Physical Mesomechanics

, Volume 21, Issue 3, pp 203–207 | Cite as

Self-Oscillating Mode of a Nanoresonator

  • D. A. IndeitsevEmail author
  • O. S. Loboda
  • N. F. Morozov
  • D. Yu. Skubov
  • L. V. Shtukin


The paper proposes a new graphene resonator circuit which operates on the principle of a self-oscillator and has no drawbacks typical of nanoresonators as mass detectors and associated with their law quality factor, eigenfrequency errors (measurements from resonance curves), and dependence of quench frequency on oscillation frequency (curves with quenching for nonlinear systems). The proposed circuit represents a self-oscillator comprising an amplifier, a graphene resonator, and a positive feedback loop with a graphene oscillation transducer, and its major advantage is in self-tuning to resonance frequency at slowly varying resonator parameters, compared to oscillation periods. The graphene layer with a conducting substrate beneath it forms a capacitor which is recharged by a dc voltage source as its capacitance varies due to graphene deformation, and the recharge current is an oscillation- dependent signal transmitted from the transducer to the amplifier input. The graphene layer is placed in a magnetic field and is deformed when a current from the amplifier output is passed through. By properly choosing the magnetic field direction and the amplifier gain, it is possible to provide swinging oscillation whose amplitude is limited by the amplifier nonlinearity. For the proposed system we present an electromechanical model, dimensionless equations of motion, and numerical data demonstrating the generation of steady-state oscillations with eigenfrequency. Also presented is an analysis showing that the system can have only one limit cycle and that this cycle is always stable. The proposed resonator circuit can be used as a mass detector which determines the added mass from a change in self-oscillation frequency.


mass detectors graphene resonator nonlinear amplifier graphene oscillation transducer magnetic field capacitor recharge positive feedback self-oscillation limit cycle stability 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Grinberg, Ya.S., Pashkin, Yu.A., and Il’ichev, E.V., Nanomechanical Resonators, Phys. Usp., 2012, vol. 55, no. 4, pp. 382–407.ADSCrossRefGoogle Scholar
  2. 2.
    Eom, K., Park, H.S., Yoon, D.S., and Kwon, T., Nanomechanical Resonators and Their Applications in Biological/ Chemical Detection: Nanomechanics Principles, Phys. Rep., 2011, vol. 503, pp. 115–163.ADSCrossRefGoogle Scholar
  3. 3.
    Scott Bunch, J., van der Zande, A.M., Verbridge, S., and McEuen, P., Electromechanical Resonators from Graphe-ne Sheets, Science, 2007, vol. 315, pp. 490–493.ADSCrossRefGoogle Scholar
  4. 4.
    Chen, C., Rosenblatt, S., Bolotin, K.I., Kalb, W., Kim, P., Kymissis, I., Stormer, H.L., Heinz, T.F., and Hone, J., Performance of Monolayer Grapheme Nanomechanical Resonators with Electrical Readout, Nat. Nanotechnol., 2009, vol. 4, pp. 861–867.ADSCrossRefGoogle Scholar
  5. 5.
    He, X.Q., Kitipornchai, S., and Liew, K.M., Resonance Analysis of Multi-Layered Graphene Sheets Used as Nanoscale Resonators, Nanotechnology, 2005, vol. 16, pp. 2086–2091.ADSCrossRefGoogle Scholar
  6. 6.
    Liu, Y., Xu, Z., and Zheng, Q., The Interlayer Shear Effect on Graphene Multilayer Resonators, J. Mech. Phys. Solid., 2011, vol. 59, pp. 1613–1622.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Toxhiaki, N., Jin-Xing, S., and Qing-Quing, N., Vibration Analysis of Nanomechanical Mass Sensors Using Double-Layered Graphene Sheets Resonators, J. Appl. Phys., 2013, vol. 114, p. 0904307.Google Scholar
  8. 8.
    van der Zande, A.M., Barton, R.A., Alden, J.S., Ruiz-Vargas, C.S., Whitney, W.S., Pham, P.H.Q., Park, J., Parpia, J.M., Craighead, H.G., and McEuen, P.L., Large-Scale Arrays of Single-Layer Graphene Resonators, Nano Lett, 2010, vol. 10(12), pp. 4869–4873.ADSCrossRefGoogle Scholar
  9. 9.
    Chen, C. and Hone, J., Graphene Nanoelectromechanical Systems, Proc. IEEE, vol. 101, no. 7, pp. 1766–1779.Google Scholar
  10. 10.
    Morozov, N.F., Berkinskii, I.E., Indeitsev, D.A., Privalova, O.V., Skubov, D.Yu., and Shtukin, L.V., Oscillation Stop as a Way to Determine Spectral Characteristics of a Graphene Resonator, Dokl. Phys., 2014, vol. 59, no. 6, pp. 254–258.ADSCrossRefzbMATHGoogle Scholar
  11. 11.
    Shtukin, L.V., Berinskii, I.E., Indeitsev, D.A., Morozov, N.F., and Skubov, D.Yu., Electromechanical Models of Nanoresonators, Phys. Mesomech., 2016, vol. 19, no. 3, pp. 248–254.CrossRefGoogle Scholar
  12. 12.
    Bonch-Bruevich, A.M., Radioelectronics in Experimental Physics, Moscow: Nauka, 1966.Google Scholar
  13. 13.
    Bautin, N.N. and Leontovich, E.A., Methods and Techniques of Qualitative Investigation of Dynamic Systems on a Plane, Moscow: Nauka, 1990.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • D. A. Indeitsev
    • 1
    • 2
    Email author
  • O. S. Loboda
    • 1
    • 2
  • N. F. Morozov
    • 2
    • 3
  • D. Yu. Skubov
    • 1
    • 2
  • L. V. Shtukin
    • 1
    • 2
  1. 1.Peter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia
  2. 2.Institute for Problems in Mechanical Engineering, Russian Academy of SciencesSt. PetersburgRussia
  3. 3.Saint Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations