Universal resonant frequency equation for the thickness vibrations of piezoelectric plate

In present paper the resonant frequency equation for the thickness vibrations of the piezry-electric plate excited by perpendicular field has been more developed.The relations of the piezoelectrically-tunable frequency of the coupling modes were analysed in detail.And then the universal resonant frequency equation applied to the piezoelectric plate excited by a perpendicular or a parallel field is proposed.Finally,the consistance of vibrations for piezoelectric bar (or strip) and piezoelectric plate,and the internal relation excited by the perpendicular or the parallel fieldsare discussed physically.