A fast analysis of vibrations of crystal plates for resonator design applications

Mindlin plate equations are the foundation of quartz crystal resonator analysis. In this paper, we implement the well-known Mindlin first-order equations in a Femlab environment, and find that useful solutions can be quickly obtained to examine the mode shapes that are important in the design of quartz crystal resonators. Such solutions are hard to obtain with the traditional finite element method, thus offering a rare opportunity to use the complete solutions for product design, improvement, and optimization. We showed the applications of these equations to a simple AT-cut quartz crystal strip resonator model.