Vibrational characteristics of size-dependent vibrating ring gyroscope

Abstract

In this paper vibrational analysis of size dependent micro-ring gyroscope under electrostatic DC voltage is performed. Based on the modified couple stress theory, Hamilton's principle and in-extensionality approximation 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 is derived. Frequency analysis indicate that the obtained ring gyroscope mode shape is slightly different from the one previously reported in the literature. Size dependent behavior of the gyroscope is studied and findings confirmed 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 effect of these orientations on the static deflection, pull-in instability and device frequencies in the sense ( direction) and drive ( direction) directions is investigated. Results reveal that the pull-in phenomena take place under lower voltage for & orientation of electrodes in comparison with orientation and frequency split occurs in higher voltages for & orientation. A comparison between finite element numerical natural frequencies of single ring and previously obtained analytical ones shows excellent agreement.