Resonance and antiresonance of symmetric and asymmetric cantilevered piezoelectric flexors.

The resonances of dynamically excited symmetric piezoelectric bimorphs have been determined from the equations of state. Under the effect of sinusoidal stimuli: a moment exerted at the tip M, a force exerted perpendicular to the plane of the bimorph also applied at the tip F, a uniformly applied pressure p, and an electrode voltage V, they respond with a sinusoidal tip rotation alpha, tip deflection delta, volume displacement nu, and electrode charge Q. All of the former are related to all of the latter through a dynamic admittance matrix B. The antiresonance frequency of the capacitance C have been found while also antiresonance in off-diagonal elements have been determined. The latter indicate that at these frequencies the bimorph does not work as an actuator or sensor in the particular domain of the off-diagonal. The mode shape at these antiresonance frequencies has been determined. The antiresonance of b(14) determines that for this frequency the tip has deflection but no rotation, while the antiresonance of b(24 ) indicates that the tip has rotation but no deflection. No antiresonance in the volume displacement is found, indicating that the bimorph is a pressure converter (microphone) at all frequencies. Micromachined piezoelectric heterogeneous bimorphs have been fabricated using the techniques of I.C. fabrication. Their deflections have been measured as a function of frequency and applied voltage, while these have been compared with the theoretical predictions. An anomalously large quadratic deflection has been found, superimposed on the linear piezoelectric behavior. The agreement between the linear part of the experimental deflection and the theory was quite good.