Dynamic bimorph matrix of end-loaded bimorphs

Piezoelectric homogeneous benders consist of two strips of piezoelectric elements with opposing polarities joined along their length. The matrix elements relating the driving parameter (voltage across the piezoelectric elements) with the response parameters have been calculated for the bimorph with tip mass. These bimorphs can be used to move an object, such as a mirror in optics, a pyramid in atomic force microscopy, or for a chemical sensor at the tip. The effect of such an object at the tip is to lower resonance frequency, which is one of the immediately recognized results. The extra mass affects the capacitance at all frequencies and also changes all the resonance frequencies. The results of this work will enable us to design bimorphs whose deflection and resonance frequency can be controlled