Electrically Forced Vibrations of Partially Electroded Rectangular Quartz Plate Piezoelectric Resonators

Abstract

We performed a theoretical analysis on electrically forced, coupled thickness-shear, and flexural vibrations of a rectangular AT-cut quartz resonator, which is electroded in its central part only. Mindlin's first-order theory for piezoelectric plates is used and simplified by the flexure-twist approximation due to Mindlin and Spencer. An analytical solution is then obtained. The admittance of the resonator under a time-harmonic driving voltage, which is an important property in resonator design, is calculated and examined. The mode shapes at resonances are also presented and discussed. It is found that for a perfectly symmetric resonator only cylindrical modes depending on one of the two in-plane spatial coordinates can be excited by the applied voltage. This supports the conventional approximate analyses based on the assumption of cylindrical deformations.

Resonance Analysis of Piezoelectric Bulk Acoustic Wave Devices Based on YCOB Crystals with Monoclinic Symmetry Excited by Lateral Electric Fields

“…3 can be written as the sum of the general solution of the corresponding homogeneous equation and a particular solution. Equation (7) (2) is homogeneous; thus, the solution of u (0) 2 can be written as the general solution of the corresponding homogeneous equation [26].…”