An analysis of a vibratory angular-rate gyroscope using polarized piezoceramic bimorph plates. Part 2: solution procedure for the gyroscope with superposed angular velocity

The variational equations derived in Part 1 of this work are extended to include the superposed angular velocity by means of the Coriolis effect. The resulting equations enable a semi-analytic treatment for the calculation of the dynamic characteristics of a vibratory angular-rate gyroscope composed of small piezoceramic bimorphs arranged in the shape of one half of a single tuning fork; use of mirror symmetries of that basic shape allows the construction of an H-shaped tuning fork gyroscope. The calculations are performed at the resonant frequency of the fundamental flexural mode. The dimensions of a typical half of a tuning fork shape structure considered in this work are approximately 2.6 mm×0.88 mm×0.16 mm, which has fundamental natural frequencies ranging between 5 and 8 kHz, and can measure rotation-rates at least as high as 40 RPM. In order to have greater sensitivity it is necessary to have simultaneously large amplitudes of vibration in both the actuating and sensing modes. On account of this the two forced vibration problems are solved only at the matched first natural frequency of the fundamental flexural mode, which is obtained from the eigenanalysis that enables the selection of geometry for the frequencies to be matched.