Vibrations of a rotating piezoelectric body and applications in gyroscopes

Based on the linear theory of piezoelectricity, analyses of a few basic problems associated with the vibration of a rotating piezoelectric body are performed with applications in piezoelectric gyroscopes for measuring the angular rate of a rotating body. Thickness vibrations and propagating waves in an infinite piezoelectric plate rotating at a constant angular rate about its normal, and waves propagating over a rotating piezoelectric half-space are analyzed using the three-dimensional equations of piezoelectricity. The frequencies of the waves are determined, and rotation induced frequency shift is calculated. The dependence of the frequency shift on several physical and geometric parameters is examined. The rotation induced frequency shift can be used to detect the rotation rate. To model piezoelectric gyroscopes operating with the vibration modes of finite piezoelectric bodies, a few structural theories are developed from the three-dimensional equations of piezoelectricity. These include the zero-dimensional equations for a piezoelectric parallelepiped, the one-dimensional equations for a piezoelectric ring, and the one-dimensional equations for a piezoelectric beam bimorph. These equations can also be used to analyze piezoelectric devices other than gyroscopes. The equations for piezoelectric parallelepipeds, rings, bimorphs, and the two-dimensional equations of piezoelectric shells are used to analyze a ceramic plate gyroscope, a quartz plate gyroscope, a ceramic beam bimorph gyroscope, a ceramic ring gyroscope, and a ceramic shell gyroscope. These gyroscopes detect the rotation rate by electrical signals. The designs of some of these gyroscopes are original. Free and forced vibration solutions are obtained. Voltage and current sensitivities are calculated. The dependence of sensitivity on various parameters is studied. The vibration of a rotating piezoelectric body is a mechanics problem presented by new technology. The results of this research are fundamental to the understanding and design of piezoelectric gyroscopes