TABLE OF CONTENTS In this section we analyzed the ceramic plate gyroscope in the previous section using zero-dimensional equations of a piezoelectric parallelepiped [85]. Consider the rectangular ceramic plate shown in Fig. 7.8.1.
A driving voltage V 1 is applied across the lateral electrodes at x 1= a to excite the plate into thickness-shear motion u 1 in the x 1 direction. When the plate is rotating about the x 3-axis, the Coriolis force F 2 causes a thickness-shear motion u 2 in the x 2 direction. This shear in the x 2 direction generates a voltage V 2 between x 2= b, which can be used to detect the angular rate ?.
In terms of the lowest order zero-dimensional equations [20], the equations for shear motions 
and 
are
The relevant constitutive relations take the following form:
In Eqs. (7.8.2) and (7.8.3) we have introduced a thickness-shear correction factor ?. For a ceramic plate, we have ? 2= ? 2/12 when the plate is poled in the thickness direction. For convenience we denote
Then
With successive substitutions, we obtain
The total electric charge on the electrodes at x 1= a or x 2= b and the electric currents flowing out of them are given by
Let the driving voltage be V 1=
