Thickness shearing vibration of the tangentially polarized piezoelectric ceramic thin circular ring

The thickness shearing vibration of the tangentially polarized piezoelectric ceramic thin circular ring is studied. The electrical and mechanical characteristics of the ring are analyzed in detail. The electro-mechanical equivalent circuit, the input electrical impedance, and the frequency equations for the resonance and anti-resonance frequencies are derived. A new concept that is characterized by the cross sectional shape and dimension is presented. An important conclusion is obtained that the thickness shearing vibration of the tangentially polarized piezoelectric ceramic ring is different from the traditional thickness extensional and radial extensional vibrations in that the electro-mechanical conversion coefficient, the electro-mechanical coupling coefficient, and the resonance frequency equation depend not only on the material parameters and the longitudinal dimension, but also on the lateral dimension, such as the cross sectional radius. It is shown that the measured resonance frequencies are in agreement with the theoretically calculated results, and the theoretical relationship between the resonance frequency and the cross sectional radius is also verified.