Piezoelectric ceramic disks with thickness-graded material properties

A system of two-dimensional, first-order equations for electroded piezoelec tric crystal plates with general symmetry and thickness-graded material pro perties recently was deduced from the three-dimensional equations of linear piezoelectricity. These equations are simplified for the two limiting case s of thickness-graded piezoelectric properties, i.e., the homogeneous plate and bimorph of piezoelectric ceramics. Closed-form solutions are obtained from these reduced equations for the flexural and thickness-shear vibration s and static response of bimorph disks as well as for the extensional and t hickness-stretch vibrations of homogeneous disks. Frequency spectra and mod es are computed and examined. Resonance frequencies for both homogeneous an d bimorph disks of PZT-857 are computed and measured. The comparison of the results shows that the agreement is close.