Application to a Monolithic Structure

Abstract

Consider the rotated Y-cut quartz plate shown in Fig. 26 with five sections which are denoted 0, 1, 2, 3, and 4. The 1 and 3 sections contain electrodes and the others do not. The 1 section is driven by the application of an alternating voltage to the surface electrodes and the energy is detected in the 3 section by a passive detecting circuit of admittance Y. As usual, the dimension out of the paper will be ignored. The solution actually requires the full system of two-dimensional equations (13.110) which we derived for x ₁ dependence in rotated Y-cut quartz, and which contain coupled thickness-shear, flexure, and face-shear motions. However, we shall make an approximation which results in a tremendous simplification and which yields very accurate results if we confine the frequency to a certain very narrow range of great practical importance. Nevertheless, before we make the simplification we will discuss the solution of the more general problem in some detail, including the full piezoelectric coupling. When we make the approximation we will, of course, assume that the piezoelectric coupling is small.