One-dimensional equations for a piezoelectric ring, one-dimensional equations for a piezoelectric beam, and two-dimensional equations for piezoelectric shells are used in the study of a circular ring piezoelectric gyroscope in coupled extensional and fiexural vibrations, a beam bimorph gyroscope in fiexural vibrations, and a circular cylindrical shell gyroscope in radial and torsional vibrations. Analytical analyses are performed. Free and forced vibration solutions are obtained. Resonant frequencies, voltage sensing signals and their dependence on the driving frequency, rotation rate, impedance of the output circuit and material damping are examined. The results obtained are fundamental to the understanding of these gyroscopes and are useful in their design optimization.
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