Analysis of the electrically forced vibrations of piezoelectric mesa resonators

We study the electrically forced thickness-shear and thickness-twist vibrations of stepped thickness piezoelectric plate mesa resonators made of polarized ceramics or 6-mm class crystals. A theoretical analysis based on the theory of piezoelectricity is performed, and an analytical solution is obtained using the trigonometric series. The electrical admittance, resonant frequencies, and mode shapes are calculated, and strong energy trapping of the modes is observed. Their dependence on the geometric parameters of the resonator is also examined.