Resonances and energy trapping in AT-cut quartz resonators operating with fast shear modes driven by lateral electric fields produced by surface electrodes.

We analyze coupled thickness-shear and extensional vibrations of a piezoelectric resonator of AT-cut quartz. Different from most of the AT-cut quartz resonators studied in the literature which are based on the slow shear mode excited by a thickness electric field, the resonator in this paper operates with the fast shear mode driven by a lateral electric field produced by a pair of electrodes on the top surface of the resonator. Mindlin's first-order theory of piezoelectric plates is used. Dispersion relations of the relevant waves in unelectroded and electroded plates are presented and compared. The motional capacitance, resonant frequencies and mode shapes near resonances are obtained from an electrically forced vibration analysis. Trapped modes without vibration near the resonator edges are identified. The effects of various structural parameters on energy trapping are examined and the mechanisms are discussed. The results can provide important bases for the parameters design of new resonators operating with the fast shear mode with new excitation schemes.