Analysis of Rectangular AT-Cut Quartz Resonators with Soft Adhesive Layers Using Simplified Surface Tractions

Abstract

We studied the effect of silicone-type adhesive layers on vibrations of an AT-cut quartz plate used in a surface-mount-device resonator. Simplified surface tractions were employed for stresses at the interface between a plate and an adhesive layer. It was presumed that three displacements excited at a point of the plate surface could independently propagate and decay into only the thickness direction of the adhesive layer. Exact two-dimensional (2D) analysis confirmed the approximation. When the adhesive layer behaves like complex mass loading, the resonant characteristics of the plate are independent of the layer thickness. In such cases, we analyzed 3D vibrations of a rectangular AT-cut plate partially perturbed by the lossy surface tractions. Calculated results showed that the surface tractions produced a negligible change in frequency and a remarkable increase in resistance, and they verified that we successfully introduced the effect of soft adhesive layers into 3D analysis through the approximation.