TABLE OF CONTENTS An electric field in a piezoelectric material causes strain but not curvature. Therefore, in the previous two sections, different electric fields on opposite sides of a beam are needed to produce flexure. Another way of producing flexure in a beam is to use a bimorph. Consider the gyroscope shown in Fig. 7.3.1 [80].
The part in 0< x 1< a 1 is the driving portion and a 1< x 1< l is the receiving or sensing portion. The polarizations in the two layers are opposite. When a driving voltage V 1 is applied across the electrodes at x 3= c, one layer extends while the other contracts due to switched polarizations. This allows the beam to be driven into the lowest flexural mode in the x 3 direction with a proper driving frequency. If the beam is rotating about the x 1-axis with a constant angular rate ?, the Coriolis force causes a flexural motion in the x 2 direction. This Coriolis force generated flexure produces a voltage V 2 in the receiving portion which can be picked up by the sensing electrodes. Flexure in the x 3 direction alone does not cause any output voltage.
To obtain one-dimensional equations for the elementary (classical) flexural motion of the gyroscope, we begin with the following approximations of the three-dimensional mechanical displacement and electric potential:
