Vibrations and static responses of asymmetric bimorph disks of piezoelectric ceramics

In an earlier article, the flexural vibrations in bimorph disks and extensi onal vibrations in homogeneous disks of piezoelectric ceramics were studied . In the present paper, the coupled flexural and extensional vibrations and static responses in an asymmetric bimorph disk, which is formed by bonding together two piezoelectric ceramic disks of unequal thickness and opposite polarization? are investigated. Governing equations of coupled motions for asymmetric bimorphs are deduced from the recently derived 2-D, first-order equations for piezoelectric crys tal plates with thickness-graded material properties. Then, closed form sol utions of these equations for circular disks are obtained for free vibratio ns, piezoelectrically forced vibrations, and responses under static voltage difference. Resonance frequencies, distribution of displacements and surface charges, i mpedances, and static responses are calculated for asymmetric bimorph disks of various thickness ratios and diameter-to-thickness ratios. Experimental data on resonances and impedances are obtained for asymmetric bimorph disk s of PZT-857 for different thickness ratios. Comparisons of predicted and m easured results show that the agreements are close.