Vibrational characteristics of size-dependent vibrating ring gyroscope

In this paper, vibrational analysis of a size-dependent micro-ring gyroscope under electrostatic DC voltage is performed. Governing equations of size-dependent micro rings and corresponding finite-element formulation of circular micro ring along with eight half circular stiffeners embedded inside the ring are derived based on the modfiied couple stress theory, Hamilton's principle, and in-extensionality approximation. Frequency analysis indicates that the obtained mode shape of the ring gyroscope is slightly different from the one previously reported in the literature. Size-dependent behavior of the gyroscope is studied, and related ndings conrm the gap between classic and non-classic natural frequencies and pull-in voltage when the ring thickness is in order of material length scale parameter. Two different orientations for the actuation electrodes of the micro-ring gyroscope are implemented, and the effect of these orientations on the static de ection, pull-in instability, and device frequencies in the sense (45 direction) and drive (0 direction) directions is investigated. Results reveal that the pull-in phenomena take place under lower voltages for 0 and 45 orientation of electrodes in comparison with 0 orientation; frequency split occurs in higher voltages for 0 and 45 orientation. A comparison between finite-element numerical natural frequencies of single ring and previously obtained analytical ones shows excellent agreement.