RESONANCE AND ANTIRESONANCE OF SYMMETRICAL 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 pe rpendicular to the plane of the bimorph also applied at the tip F, a u niformly applied pressure p, and an electrode voltage V, they respond with a sinusoidal tip rotation alpha, tip deflection delta, volume dis placement nu, and electrode charge Q. All of the former are related to all of the latter through a dynamic admittance matrix B. The antireso nance frequency of the capacitance C have been found while also antire sonance in off-diagonal elements have been determined. The latter indi cate that at these frequencies the bimorph does not work as an actuato r or sensor in the particular domain of the off-diagonal. The mode sha pe at these antiresonance frequencies has been determined. The anitire sonsance of b(14) determines that for this frequency the tip has defle ction but no rotation, while the antiresonance of b(24) indicates that the tip has rotation but no deflection. No antiresonance in the volum e displacement is found, indicating that the bimorph is a pressure con verter (microphone) at all frequencies. Micromachined piezoelectric he terogeneous bimorphs have been fabricated using the techniques of I.C. fabrication. Their deflections have been measured as a function of fr equency and applied voltage, while these have been compared with the t heoretical predictions. An anomalously large quadratic deflection has been found, superimposed on the linear piezloelectric behavior. The ag reement between the linear part of the experimental deflection and the theory was quite good.