Resonant vibration failure modes of quartz resonators

This study uses the finite element method (FEM) to analyze the excitation and the resonant vibration failure modes of two-dimensional quartz plates. We first simplify three-dimensional quartz plates with plane strain simplification, and then compare the modes of the simplified three-dimensional plates to those of two-dimensional plates. We then analyze quartz vibrating elements of AT-cut plates. To understand the regularity of the resonance frequency of plates that are excitable by voltage loading, we compare the natural vibrations of quartz plates with the excitation frequency generated after the plates are excited by voltage loading.