Advertisement

Nonlinear Dynamics

, Volume 95, Issue 2, pp 1203–1220 | Cite as

Nonlinear dynamics of micromechanical resonator arrays for mass sensing

  • S. BaguetEmail author
  • V.-N. Nguyen
  • C. Grenat
  • C.-H. Lamarque
  • R. Dufour
Original Paper
  • 141 Downloads

Abstract

This paper investigates the mass sensing capability of an array of a few identical electrostatically actuated microbeams, as a first step toward the implementation of arrays of thousands of such resonant sensors. A reduced-order model is considered, and Taylor series are used to simplify the nonlinear electrostatic force. Then, the harmonic balance method associated with the asymptotic numerical method, as well as time integration or averaging methods, is applied to this model, and its results are compared. In this paper, two- and three-beam arrays are studied. The predicted responses exhibit complex branches of solutions with additional loops due to the influence of adjacent beams. Moreover, depending on the applied voltages, the solutions with and without added mass exhibit large differences in amplitude which can be used for detection. For symmetric configurations, the symmetry breaking induced by an added mass is exploited to improve mass sensing.

Keywords

MEMS Mass sensing Resonator array Nonlinear dynamics Bifurcation Symmetry breaking Electrostatic actuation 

Notes

Acknowledgements

The authors are indebted to the Institute Carnot Ingénierie@Lyon for its support and funding of the NEMROD project.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Kacem, N., Baguet, S., Hentz, S., Dufour, R.: Nonlinear phenomena in nanomechanical resonators: mechanical behaviors and physical limitations. Mech. Ind. 11(6), 521–529 (2010)Google Scholar
  2. 2.
    Saghafi, M., Dankowicz, H., Lacarbonara, W.: Nonlinear tuning of microresonators for dynamic range enhancement. Proc. R. Soc. Lond. Ser. A 471(2179), 20140969 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Younis, M.I.: MEMS Linear and Nonlinear Statics and Dynamics. Springer, Berlin (2011)CrossRefGoogle Scholar
  4. 4.
    Narducci, M., Figueras, E., Lopez, M.J., Gracia, I., Santander, J., Ivanov, P., Fonseca, L., Cané, C.: Sensitivity improvement of a microcantilever based mass sensor. Microelectron. Eng. 86(4–6), 1187–1189 (2009)CrossRefGoogle Scholar
  5. 5.
    Dohn, S., Sandberg, R., Svendsen, W., Boisen, A.: Enhanced functionality of cantilever based mass sensors using higher modes and functionalized particles. In: Solid-State Sensors, Actuators and Microsystems TRANSDUCERS ’05., vol. 1, pp. 636–639 (2005)Google Scholar
  6. 6.
    Xie, H., Vitard, J., Haliyo, S., Régnier, S.: Enhanced sensitivity of mass detection using the first torsional mode of microcantilevers. Meas. Sci. Technol. 19(5), 055207 (2008)CrossRefGoogle Scholar
  7. 7.
    Eichler, A., Moser, J., Dykman, M.I., Bachtold, A.: Symmetry breaking in a mechanical resonator made from a carbon nanotube. Nat. Commun. 4, 2843 (2013)CrossRefGoogle Scholar
  8. 8.
    Rhoads, J.F., Shaw, S.W., Turner, K.L.: Nonlinear dynamics and its applications in micro- and nanoresonators. J. Dyn. Syst. Meas. Contr. 132(3), 034001 (2010)CrossRefGoogle Scholar
  9. 9.
    Younis, M.I., Alsaleem, F.: Exploration of new concepts for mass detection in electrostatically-actuated structures based on nonlinear phenomena. J. Comput. Nonlinear Dyn. 4(2), 021010 (2009)CrossRefGoogle Scholar
  10. 10.
    Ruzziconi, L., Lenci, S., Younis, M.I.: An imperfect microbeam under an axial load and electric excitation: nonlinear phenomena and dynamical integrity. Int. J. Bifurc. Chaos 23(02), 1350026 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kumar, V., Boley, J.W., Yang, Y., Ekowaluyo, H., Miller, J.K., Chiu, G.T.-C., Rhoads, J.F.: Bifurcation-based mass sensing using piezoelectrically-actuated microcantilevers. Appl. Phys. Lett. 98(15), 153510 (2011)CrossRefGoogle Scholar
  12. 12.
    Nguyen, V.-N., Baguet, S., Lamarque, C.-H., Dufour, R.: Bifurcation-based micro-/nano-electromechanical mass detection. Nonlinear Dyn. 79(1), 647–662 (2014)CrossRefGoogle Scholar
  13. 13.
    Zhang, W., Turner, K.L.: Application of parametric resonance amplification in a single-crystal silicon micro-oscillator based mass sensor. Sens. Actuators A 122(1), 23–30 (2005)CrossRefGoogle Scholar
  14. 14.
    Thomas, O., Mathieu, F., Mansfield, W., Huang, C., Trolier-McKinstry, S., Nicu, L.: Efficient parametric amplification in micro-resonators with integrated piezoelectric actuation and sensing capabilities. Appl. Phys. Lett. 102(16), 163504 (2013)CrossRefGoogle Scholar
  15. 15.
    Kacem, N., Baguet, S., Duraffourg, L., Jourdan, G., Dufour, R., Hentz, S.: Overcoming limitations of nanomechanical resonators with simultaneous resonances. Appl. Phys. Lett. 107(7), 073105 (2015)CrossRefGoogle Scholar
  16. 16.
    Peng, H.B., Chang, C.W., Aloni, S., Yuzvinsky, T.D., Zettl, A.: Ultrahigh frequency nanotube resonators. Phys. Rev. Lett. 97, 087203 (2006)CrossRefGoogle Scholar
  17. 17.
    Hanay, M.S., Kelber, S., Naik, A.K., Chi, D., Hentz, S., Bullard, E.C., Colinet, E., Duraffourg, L., Roukes, M.L.: Single-protein nanomechanical mass spectrometry in real time. Nat. Nanotechnol. 7, 602–608 (2012)CrossRefGoogle Scholar
  18. 18.
    Buks, E., Roukes, M.L.: Electrically tunable collective response in a coupled micromechanical array. J. Microelectromech. Syst. 11(6), 802–807 (2002)CrossRefGoogle Scholar
  19. 19.
    Lifshitz, R., Cross, M.C.: Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays. Phys. Rev. B 67, 134302 (2003)CrossRefGoogle Scholar
  20. 20.
    Cross, M.C., Zumdieck, A., Lifshitz, R., Rogers, J.L.: Synchronization by nonlinear frequency pulling. Phys. Rev. Lett. 93, 224101 (2004)CrossRefGoogle Scholar
  21. 21.
    Porfiri, M.: Vibrations of parallel arrays of electrostatically actuated microplates. J. Sound Vib. 315(4), 1071–1085 (2008)CrossRefGoogle Scholar
  22. 22.
    Karabalin, R.B., Cross, M.C., Roukes, M.L.: Nonlinear dynamics and chaos in two coupled nanomechanical resonators. Phys. Rev. B 79, 165309 (2009)CrossRefGoogle Scholar
  23. 23.
    Gutschmidt, S., Gottlieb, O.: Nonlinear internal resonances of a microbeam array near the pull-in point. In: Proceedings of the ENOC-2008, Saint Petersburg, June, 30–July, 4 (2008)Google Scholar
  24. 24.
    Gutschmidt, S., Gottlieb, O.: Internal resonances and bifurcations of an array below the first pull-in instability. Int. J. Bifurc. Chaos 20(3), 605–618 (2010)CrossRefzbMATHGoogle Scholar
  25. 25.
    Gutschmidt, S., Gottlieb, O.: Bifurcations and loss of orbital stability in nonlinear viscoelastic beam arrays subject to parametric actuation. J. Sound Vib. 329, 3835–3855 (2010)CrossRefGoogle Scholar
  26. 26.
    Gutschmidt, S., Gottlieb, O.: Nonlinear dynamic behavior of a microbeam array subject to parametric actuation at low, medium and large dc-voltages. Nonlinear Dyn. 67(1), 1–36 (2012)CrossRefzbMATHGoogle Scholar
  27. 27.
    Kambali, P.N., Swain, G., Pandey, A.K., Buks, E., Gottlieb, O.: Coupling and tuning of modal frequencies in direct current biased microelectromechanical systems arrays. Appl. Phys. Lett. 107(6), 063104 (2015)CrossRefGoogle Scholar
  28. 28.
    Younis, M.I., Abdel-Rahman, E.M., Nayfeh, A.: A reduced-order model for electrically actuated microbeam-based MEMS. J. Microelectromech. Syst. 12(5), 672–680 (2003)CrossRefGoogle Scholar
  29. 29.
    Kacem, N., Arcamone, J., Perez-Murano, F., Hentz, S.: Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive nems gas/mass sensor applications. J. Micromech. Microeng. 20(4), 045023 (2010)CrossRefGoogle Scholar
  30. 30.
    Kacem, N., Baguet, S., Hentz, S., Dufour, R.: Computational and quasi-analytical models for non-linear vibrations of resonant MEMS and NEMS sensors. Int. J. Non Linear Mech. 46(3), 532–542 (2011)CrossRefGoogle Scholar
  31. 31.
    Sansa, M., Nguyen, V.-N., Baguet, S., Lamarque, C.-H., Dufour, R., Hentz, S.: Real time sensing in the non linear regime of nems resonators. In: 2016 IEEE 29th International Conference on Micro Electro Mechanical Systems (MEMS), pp. 1050–1053, Jan 24–28 (2016)Google Scholar
  32. 32.
    Walter, V., Bourbon, G., Le Moal, P., Kacem, N., Lardis, J.: Electrostatic actuation to counterbalance the manufacturing defects in a mems mass detection sensor using mode localization. Procedia Eng. 168, 1488–1491 (2016)CrossRefGoogle Scholar
  33. 33.
    Ruzziconi, L., Bataineh, A.M., Younis, M.I., Cui, W., Lenci, S.: Nonlinear dynamics of an electrically actuated imperfect microbeam resonator: experimental investigation and reduced-order modeling. J. Micromech. Microeng. 23(7), 075012 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Univ Lyon, INSA-Lyon, CNRS UMR5259, LaMCoSVilleurbanneFrance
  2. 2.Univ Lyon, ENTPE, CNRS UMR5513, LTDSVaulx-en-VelinFrance

Personalised recommendations