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 stifieners embedded inside the ring are derived based on the modified couple stress theory, hamilton s principle, and in-extensionality approximation. frequency analysis indicates that the obtained mode shape of the ring gyroscope is slightly difierent from the one previously reported in the literature. size-dependent behavior of the gyroscope is studied, and related findings confirm 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 difierent orientations for the actuation electrodes of the micro-ring gyroscope are implemented, and the efiect 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.