Localized bending vibrations of piezoceramic transverse polarized plate

Problem of the piezoceramic plate polarized along the normal of the middle plane of the plate is solved, based on the assumptions of the hypothesis of Kirchhoff, taking into account the components characterizing the electric field. The equations of planar and bending vibrations are obtained. Localized bending vibrations are considered, and the effect of the electric field on the frequency of localized vibrations is investigated.