Resonances of an unbounded piezoelectric plate with circular electrodes

We consider an unbounded piezoelectric plate with two circular electrodes. The polarization direction of the material of the plate is perpendicular to the faces of the plate. One electrode is at the upper surface and the other one at the lower surface, symmetrically with respect to the middle plane. The resonances of this system are investigated. Three types of resonances are introduced. The dependence of the occurring of the resonances on the material constants is discussed.