Scaling Analysis for the Axial Displacement and Pressure of Flextensional Transducers

We have examined the axial displacement, Δ h , and maximum axial pressure, P _max, of flextensional transducers such as the moonies and the rainbows with both scaling and mechanical analyses. For a constant electric field E across the transducer, Δ h / t ∝ E / t ² where t is the thickness of the rainbow or the thickness of the metal end cap of the moonie and Δ h / t , the relative axial displacement. Thus, for a constant voltage V across the transducer, Δ h / t ∝ V / t ³. As for the maximum pressure, P _max t ² for the rainbows and P _max∝ wt for the moonies where t is the thickness of the rainbow or the thickness of the metal end cap of the moonie and w the thickness of the piezoelectric disk of the moonie. These predictions agree well with the experimental results found in the rainbows and the moonies. Our analysis showed that although the rainbows and the moonies differ in design and processing, the underlying physics for the enhancement in the axial displacement are essentially the same: The nonuniform distribution of d ₃₁ through the thickness of the transducer causes the transducer to arch or flatten with an applied electrical field, which leads to the enhancement in the axial displacement. The only difference is that, for the transducer to arch, the applied field is in the opposite direction to the polarization in the rainbows but in the same direction as the polarization in the moonies.