Encyclopedia of Nanotechnology

Living Edition
| Editors: Bharat Bhushan

Nonlinear Parametric MEMS

Living reference work entry
DOI: https://doi.org/10.1007/978-94-007-6178-0_100994-1

Synonyms

Definition

Nonlinear MEMS resonators excited by parametric excitation so its effective impedance is periodically modified by time-varying drive parameters

Background, Benefits, and Applications

In the rich context of physical and engineering disciplines, the first decade of systematic study on the nonlinear problems and parametrically excited systems dates back to the mid-nineteenth century, with the work of Mathieu [1], Rayleigh [2], Stoker [3], and Nayfeh [4] as important landmarks. Owing to the use of a considerable amount of exemplary nonlinear problems, the forerunners provided intuitive concepts, such as self-excited systems, forced oscillations, parametric pump, and nonlinear restoring force, and backed them up with rigorous theorems. Recent work on the parametric resonance, especially in the context of resonant microelectromechanical systems (MEMSs), investigates the utility and advantage of exploiting parametric...

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References

  1. 1.
    Mathieu, E.: Memoire sur le mouvement vibratoire d’une membrane de forme elliptique. J. Math. Pures et Appl. 13, 137–203 (1868)Google Scholar
  2. 2.
    Rayleigh, L.: On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure. Lond. Edinb. Dublin Philos. Mag. J. Sci. (Fifth Series) 24(147), 145–159 (1887)CrossRefGoogle Scholar
  3. 3.
    Stoker, J.J.: Nonlinear Vibrations in Mechanical and Electrical Systems. Wiley, New York (1950)Google Scholar
  4. 4.
    Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. John Wiley & sons, New York (1979)Google Scholar
  5. 5.
    Zhang, W., Turner, K.: Application of parametric resonance amplification in a single-crystal silicon micro-oscillator based mass sensor. Sensors Actuators A Phys. 122(1), 23–30 (2005)CrossRefGoogle Scholar
  6. 6.
    Li, L., Holthoff, E., Shaw, L., Burgner, C., Turner, K.: Noise squeezing controlled parametric bifurcation tracking of MIP-coated microbeam MEMS sensor for TNT explosive gas sensing. J. Microelectromech. Syst. (2014). doi:10.1109/JMEMS.2014.2310206Google Scholar
  7. 7.
    Kacem, N., Hentz, S., Baguet, S., Dufour, R.: Forced large amplitude periodic vibrations of non-linear Mathieu resonators for microgyroscope applications. Int. J. Non Linear Mech. 46(10), 1347–1355 (2011)CrossRefGoogle Scholar
  8. 8.
    Turner, K., Miller, S., Hartwell, P., MacDonald, N., Strogatz, S., Adams, S.: Five parametric resonances in a microelectromechanical system. Nature 396(6707), 149–152 (1998)CrossRefGoogle Scholar
  9. 9.
    Guo, C., Fedder, G.: Bi-state control of parametric resonance. Appl. Phys. Lett. 103(18), 183512 (2013)CrossRefGoogle Scholar
  10. 10.
    Ataman, C., Urey, H.: Modeling and characterization of comb-actuated resonant microscanners. J. Micromech. Microeng. 16(1), 9–16 (2006)CrossRefGoogle Scholar
  11. 11.
    Yie, Z., Zielke, M., Burgner, C., Turner, K.: Comparison of parametric and linear mass detection in the presence of detection noise. J. Micromech. Microeng. 21, 025027 (2011)CrossRefGoogle Scholar
  12. 12.
    Requa, M.: Parametric resonance in microcantilevers for applications in mass sensing. PhD dissertation, University of California, Santa Barbara (2006)Google Scholar
  13. 13.
    Prakash, G., Raman, A., Rhoads, J., Reifenberger, R.: Parametric noise squeezing and parametric resonance of microcantilevers in air and liquid environments. Rev. Sci. Instrum. 83(6), 065109 (2012)CrossRefGoogle Scholar
  14. 14.
    Thompson, M., Horsley, D.: Lorentz force MEMS magnetometer. Hilton Head Workshop 2010: A Solid-State Sensors, Actuators and Microsystems Workshop, pp. 45–48 (2010)Google Scholar
  15. 15.
    Koskenvuori, M., Tittonen, I.: GHz-range FSK-reception with microelectromechanical resonators. Sensors Actuators A Phys. 142(1), 346–351 (2008)CrossRefGoogle Scholar
  16. 16.
    DeMartini, B., Butterfield, H., Moehlis, J., Turner, K.: Chaos for a microelectromechanical oscillator governed by the nonlinear Mathieu equation. J. Microelectromech. Syst. 16(6), 1314–1323 (2007)CrossRefGoogle Scholar
  17. 17.
    Nayfeh, A.: Introduction to Perturbation Technique, pp. 234–256. Wiley, New York (1981)Google Scholar
  18. 18.
    Rhoads, J., Shaw, S., Turner, K., Moehlis, J., DeMartini, B., Zhang, W.: Generalized parametric resonance in electrostatically actuated microelectromechanical oscillators. J. Sound Vib. 296(4–5), 797–829 (2006)CrossRefGoogle Scholar
  19. 19.
    Guo, C., Fedder, G.: Behavioral modeling of a CMOS-MEMS nonlinear parametric resonator. J. Microelectromech. Syst. 22(6), 1447–1457 (2013)CrossRefGoogle Scholar
  20. 20.
    Adams, S., Bertsch, F., MacDonald, N.: Independent tuning of linear and nonlinear stiffness coefficients. J. Microelectromech. Syst. 7(2), 172–180 (1998)CrossRefGoogle Scholar
  21. 21.
    Guo, C., Fedder, G.: A quadratic-shaped-finger comb parametric resonator. J. Micromech. Microeng. 23(9), 095007 (2013)CrossRefGoogle Scholar
  22. 22.
    Hirano, T., Furuhata, T., Gabriel, K., Fujita, H.: Design, fabrication, and operation of submicron gap comb-drive microactuators. J. Microelectromech. Syst. 1(1), 52–59 (1992)CrossRefGoogle Scholar
  23. 23.
    Jensen, B., Mutlu, S., Miller, S., Kurabayashi, K., Allen, J.: Shaped comb fingers for tailored electromechanical restoring force. J. Microelectromech. Syst. 12(3), 373–383 (2003)CrossRefGoogle Scholar
  24. 24.
    Kaajakari, V., Lal, A.: Parametric excitation of circular micromachined polycrystalline silicon disks. Appl. Phys. Lett. 85(17), 3923–3925 (2004)CrossRefGoogle Scholar
  25. 25.
    Requa, M., Turner, K.: Electromechanically driven and sensed parametric resonance in silicon microcantilevers. Appl. Phys. Lett. 88(26), 263508 (2006)CrossRefGoogle Scholar
  26. 26.
    Rhoads, J., Kumar, V., Shaw, S., Turner, K.: The non-linear dynamics of electromagnetically actuated microbeam resonators with purely parametric excitations. Int. J. Non Linear Mech. 55, 79–89 (2013)CrossRefGoogle Scholar
  27. 27.
    Zalalutdinov, M., Olkhovets, A., Zehnder, A., Ilic, B., Czaplewski, D., Craighead, H., Parpia, J.: Optically pumped parametric amplification for micromechanical oscillators. Appl. Phys. Lett. 78(20), 3142 (2001)CrossRefGoogle Scholar
  28. 28.
    Rhoads, J., Shaw, S., Turner, K.: Nonlinear dynamics and its applications in micro- and nanoresonators. J. Dyn. Syst. Meas. Control. 132(3), 034001 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.ECE DepartmentCarnegie Mellon UniversityPittsburghUSA