Electrically forced vibrations of partially electroded AT-cut quartz plates in coupled thickness-shear, flexure, and face-shear motions

We study electrically forced vibrations of an AT-cut quartz plate with partial electrodes at the central portion of the plate. The plate is driven into coupled thickness-shear, flexure, and face-shear motions. Mindlin's first-order theory of piezoelectric plates is used. An analytical solution is obtained. Numerical results are presented for the motional capacitance of the structure as a resonator and the trapped modes for resonator operation. The relationship between the dimension of the electrodes and the number of trapped modes is also examined.