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-ram 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.     

Effects of mode coupling on the admittance of an AT-cut quartz thickness-shear resonator

We study the effects of couplings to flexure and face-shear modes on the admittance of an AT-cut quartz plate thickness-shear mode resonator. Mindlin’s two-dimensional equations for piezoelectric plates are employed. Electrically forced vibration solutions are obtained for three cases: pure thickness-shear mode alone; two coupled modes of thickness shear and flexure; and three coupled modes of thickness shear, flexure, and face shear. Admittance is calculated and its dependence on the driving frequency and the length/thickness ratio of the resonator is examined. Results show that near the thickness-shear resonance, admittance assumes maxima, and that for certain values of the length/thickness ratio, the coupling to flexure causes severe admittance drops, while the coupling to the face-shear mode causes additional admittance changes that were previously unknown and hence are not considered in current resonator design practice.