Nonlinear instabilities in a vibratory gyroscope subjected to angular speed fluctuations

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.