Vibrational characteristics of size dependent vibrating ring gyroscope

Abstract

Abstract. 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 nite-element formulation of circular micro ring along with eight half circular sti eners embedded inside the ring are derived based on the modi ed couple stress theory, Hamilton's principle, and in-extensionality approximation. Frequency analysis indicates that the obtained mode shape of the ring gyroscope is slightly di erent from the one previously reported in the literature. Size-dependent behavior of the gyroscope is studied, and related ndings con rm 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 di erent orientations for the actuation electrodes of the micro-ring gyroscope are implemented, and the e ect 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 nite-element numerical natural frequencies of single ring and previously obtained analytical ones shows excellent agreement.

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“…The mode coupling in terms of stiffness, arising from the structural imperfection, contributes to the rotations of the principal axes of vibration modes. As a result, the angle of the principal axis (θ 0 ) with respect to the 0 • pickoff electrode can be determined by assigning the coupling stiffness terms to be zero [25,26]:…”

Piezoelectric wind energy harvesting from vortex- induced vibrations of an elastic beam

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