High‐frequency vibrations of rectangular crystal plates coated with multiple strip electrodes

Abstract

The two‐dimensional equations of motion for the vibrations of crystal plates developed by Lee and Nikodem are extended to incorporate the mass effect of electrode platings on a crystal plate. These, together with the unplated equations of motion, are combined to govern the motion of an elastically coupled piezoelectric resonator system with multiple strip electrodes. A rectangular AT‐cut quarts plate with the strip electrodes which are parallel to the X1 axis and cover the full length of the plate in X1 direction are considered, X1 being the digonal axis of the crystal. Closed form solution is obtained for the coupled thickness‐twist and face‐shear vibrations, which satisfies the traction‐free conditions at edges of the plate and the continuity conditions for traction and displacement at the junctures of the plated and unplated regions of the plate. The calculated results are compared with experimental values with close agreement. Then the dependence of the inter‐resonator coupling, resonance frequencies, and vibrational modes on the electrode mass, on the dimensions of the electrodes' configuration, and on the plate geometry are studied and analyzed.