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Nonlinear instabilities in a vibratory gyroscope subjected to angular speed fluctuations

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Abstract

Nonlinear instabilities in a single-axis vibrating MEMS gyroscope that is subjected to periodic fluctuations in input angular rates are investigated. For the purpose of characterizing the bifurcation behavior associated with the steady-state, when the angular rate input is subject to small intensity periodic fluctuations, dynamic behavior of periodically perturbed nonlinear gyroscopic systems is studied in detail. An asymptotic approach based on the method of averaging has been employed for this purpose, and closed-form conditions for the frequency response due to parametric resonances have been obtained. This behavior has been illustrated via amplitude-frequency plots.

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References

  1. Wang, T.: Dynamic stability of a class of rate gyroscope. Master thesis, University of Western Ontario (2004)

  2. Davis, W.O.: Mechanical analysis and design of vibratory micromachined gyroscopes. PhD thesis, University of California at Berkeley (2001)

  3. Ariaratnam, S.T., Sri Namachchivaya, N.: Periodically perturbed nonlinear gyroscopic systems. J. Struct. Mech. 14(2), 153–175 (1986)

    MathSciNet  Google Scholar 

  4. Bogoliubov, N., Mitropolsky, Y.A.: Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordon and Breach, New York (1961)

    Google Scholar 

  5. Van Doorn, E.C., Asokanthan, S.F.: Attitude stability of dual-spin asymmetric spacecraft. J. Astronaut. Sci. 44(2), 149–165 (1996)

    Google Scholar 

  6. Langhaar, H.L.: Energy Methods in Applied Mechanics. Wiley, New York (1962)

    Google Scholar 

  7. Sri Namachchivaya, N., Ariaratnam, S.T.: On the dynamic stability of gyroscopic systems. Solid Mech. Arch. 10(4), 313–355 (1985)

    MATH  MathSciNet  Google Scholar 

  8. Wang, T., Asokanthan, S.F.: Dynamic stability of a single-axis vibratory MEMS gyroscope. In: Proceedings of the ASME 2005 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Long Beach, CA, 24–28 September 2005

  9. http://jim.sagepub.com/cgi/rapidpdf/1045389X07080631v1

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada

    Samuel F. Asokanthan & Tianfu Wang

Authors
  1. Samuel F. Asokanthan
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  2. Tianfu Wang
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Correspondence to Samuel F. Asokanthan.

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Asokanthan, S.F., Wang, T. Nonlinear instabilities in a vibratory gyroscope subjected to angular speed fluctuations. Nonlinear Dyn 54, 69–78 (2008). https://doi.org/10.1007/s11071-008-9347-1

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  • DOI: https://doi.org/10.1007/s11071-008-9347-1

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