On anti-symmetric waves in an unbounded piezoelectric plate with axisymmetric electrodes

In this paper we consider an unbounded piezoelectric plate with electrodes at its surfaces, which are axisymmetric with respect to an axis normal to the plate. The electromechanical waves in this plate are assumed to have an electric potential which is symmetric with respect to the middle plane of the plate. The electric field outside the plate will appear to be important. This external electric field is investigated, particularly in connection with the resonances of the plate.