Axial control for nonlinear resonances of electrostatically actuated nanobeam with graphene sensor

doi:10.1007/s10483-017-2184-6

Abstract

Abstract:

The nonlinear resonance response of an electrostatically actuated nanobeam is studied over the near-half natural frequency with an axial capacitor controller. A graphene sensor deformed by the vibrations of the nanobeam is used to produce the voltage signal. The voltage of the vibration graphene sensor is used as a control signal input to a closedloop circuit to mitigate the nonlinear vibration of the nanobeam. An axial control force produced by the axial capacitor controller can transform the frequency-amplitude curves from nonlinear to linear. The necessary and sufficient conditions for guaranteeing the system stability and a saddle-node bifurcation are studied. The numerical simulations are conducted for uniform nanobeams. The nonlinear terms of the vibration system can be transformed into linear ones by applying the critical control voltage to the system. The nonlinear vibration phenomena can be avoided, and the vibration amplitude is mitigated evidently with the axial capacitor controller.

Key words: Schrödinger system, solitary wave, asymptotic solution, graphene sensor, nonlinear vibration, electrostatic force, nanobeam

2010 MSC Number:

O322

Canchang LIU, Qian DING, Qingmei GONG, Chicheng MA, Shuchang YUE. Axial control for nonlinear resonances of electrostatically actuated nanobeam with graphene sensor. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 527-542.

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References

[1] Burg, T. P., Mirza, A. R., Milovic, N., and Tsau, C. H. Vacuum-packaged suspended microchannel resonant mass sensor for biomolecular detection. Journal of Microelectromechanical Systems, 15, 1466-1476(2006)
[2] Zhang, W. H. and Turner, K. L. Application of parametric resonance amplification in a singlecrystal silicon micro-oscillator based mass sensor. Sensors and Actuators A:Physical, 122, 23-30(2005)
[3] Yabuno, H. and Kaneko, H. Van der Pol type self-excited micro-cantilever probe of atomic force microscopy. Nonlinear Dynamics, 54, 137-149(2008)
[4] Nayfeh, A. H. and Younis, M. I. Dynamics of MEMS resonators under superharmonic and subharmonic excitations. Journal of Micromechanics and Microengineering, 15, 1840-1847(2005)
[5] Chaste, J., Eichler, A., Moser, J., Ceballos, G., Rurali, R., and Bachtold, A. A nanomechanical mass sensor with yoctogram resolution. Nature Nanotechnology, 7, 301-304(2012)
[6] Eom, K., Park, H. S.,Yoon, D. S., and Kwon, T. Nanomechanical resonators and their application in biological/chemical detection:nanomechanics principles. Physics Report, 503, 115-163(2011)
[7] Nayfeh, A. H., Younis, M. I., and Abdel-Rahman E. M. Dynamic pull-in phenomenon in MEMS resonantors. Nonlinear Dynamics, 48, 153-163(2007)
[8] Ehsan, M. M., Hossein, N. P., Aghil, Y. K., and Tajaddodianfar, F. Chaos prediction in MEMSNEMS resonators. International Journal of Engineering Science, 82, 74-83(2014)
[9] Haghighi, H. S. and Markazi, A. H. D. Chaos prediction and control in MEMS resonators. Communications in Nonlinear Science and Numerical Simulation, 15, 3091-3099(2010)
[10] Ghayesh, M. H., Farokhi, H., and Amabili, M. Nonlinear behaviour of electrically actuated MEMS resonators. International Journal of Engineering Science, 71, 137-155(2013)
[11] Haghighi, H. S. and Markazi, A. H. Chaos prediction and control in MEMS resonators. Communications in Nonlinear Science and Numerical Simulation, 15, 3091-3099(2010)
[12] Rhoads, J. F., Shaw, S. W., Turner, K. L., Moehlis, J., Demartini, B. E., and Zhang, W. Generalized parametric resonance in electrostatically actuated microelectromechanical oscillators. Journal of Sound and Vibration, 296, 797-829(2006)
[13] DeMartini, B. E., Butterfield, H. E., Moehlis, J., and Turner, K. L. Chaos for a microelectromechanical oscillator governed by the nonlinear mathieu equation. Journal of Microelectromechanical Systems, 16, 1314-1323(2007)
[14] Ke, C. K. Resonant pull-in of a double-sided driven nanotube-based electromechanical resonator. Journal of Applied Physics, 105, 1-8(2009)
[15] Caruntu, D. I. and Knecht, M. W. On nonlinear response near-half natural frequency of electrostatically actuated microresonators. International Journal of Structural Stability and Dynamics, 11, 641-672(2011)
[16] Younis, M. I. and Nayfeh, A. H. A study of the nonlinear response of a resonant microbeam to an electric actuation. Nonlinear Dynamics, 31, 91-117(2003)
[17] Kim, K. S., Zhao, Y., Jang, H., Lee, S. Y., Kim, J. M., Kim, K. S., Ahn, J. H., Kim, P., Choi, J. Y., and Hong, B. H. Large-scale pattern growth of grapheme films for stretchable transparent electrodes. nature, 457, 706-709(2009)
[18] Wang, Q. and Arash, B. A review on applications of carbon nanotubes and graphemes as nanoresonator sensors. Computational Materials Science, 82, 350-360(2014)
[19] Jiang, S. W., Gong, X. H., and Guo, X. Potential application of graphene nanomechanical resonator as pressure sensor. Solid State Communications, 193, 30-33(2014)
[20] Liu, C. C., Yue, S. C., and Xu, Y. Z. Nonlinear resonances of electrostatically actuated nanobeam. Journal of Vibroengineering, 16, 2484-2493(2014)
[21] Liang, B. B., Zhang, L., Wang, B. L., and Zhou, S. A variational size-dependent model for electrostatically actuated NEMS incorporating nonlinearities and Casimir force. Physica E, 71, 21-30(2015)
[22] Chen, C. P., Li, S. J., Dai, L. M., and Qian, C. Z. Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces. Communications in Nonlinear Science and Numerical Simulation, 19, 1626-1637(2014)
[23] Zhang, W. M., Yan, H., Peng, Z. K., and Meng, G. Electrostatic pull-in instability in MEMS/NEMS:a review. Sensors and Actuators A:Physical, 214, 187-218(2014)
[24] Duan, J., Li, Z., and Liu, J. Pull-in instability analyses for NEMS actuators with quartic shape approximation. Applied Mathematics and Mechanics (English Edition), 37(3), 303-314(2016) DOI 10.1007/s10483-015-2007-6
[25] Zhu, J. and Liu, R. Sensitivity analysis of pull-in voltage for RF MEMS switch based on modified couple stress theory. Applied Mathematics and Mechanics (English Edition), 36(12), 1555-1568(2015) DOI 10.1007/s10483-015-2005-6
[26] Huang, J. M., Liew, K. M., Wong, C. H., Rajendran, S., Tan, M. J., and Liu, A. Q. Mechanical design and optimization of capacitive micromachined switch. Sensors and Actuators A:Physical, 93, 273-285(2001)
[27] Nayfeh, A. H., Chin, C., and Nayfeh, S. A. Nonlinear normal modes of a cantilever beam. Journal of Vibration and Acoustics, 117, 477-481(1995)
[28] Chen, F. Q., Wu, Z. Q., and Chen, Y. S. Bifurcation and universal unfolding for a rotating shaft with unsymmetrical stiffness. ACTA Mechanica Sinica (English Series), 18, 181-187(2002)
[29] Stephen, S. Pitchfork bifurcation with a heteroclinic orbit:normal form, recognition criteria, and universal unfolding. Journal of Differential Equations, 105, 63-93(1993)