Finite Element Analysis of thickness shear crystals with surface irregularities

This work is a continuation of an earlier study on drive level dependence (DLD), wherein the resistance of a thickness-shear crystal changes at low drive levels as the drive level changes. The earlier work used a 2-D Finite Element Analysis (FEA) to show that a surface irregularity, such as an attached particle, causes rotational imbalance in the motion of a contoured thickness-shear crystal, which transfers motional energy from the trapped shear motion to flexural motion. The flexural motion transports motional energy to the mounts. Degradation in the Q due to this increased edge motion was inferred. This degradation in Q was strongly dependent on the location of the surface irregularity in the 2-D FEA model. The present work extends the analysis to 3-D FEA using an SC resonator along with a four-point clip mount with polyimide bonding agent. Damped eigenfrequency analysis is used to include loss in the mounting structure and directly calculate eigenmode Q as a function of the location of an attached particle on the resonator surface. The results are very informative. A 4.0E-11 kg mass can change the Q by up to 30%. The magnitude of the effect is strongly dependent on the lateral location of the mass on the surface. For example, the magnitude of the effect can change significantly between two points on the blank surface only 20 microns apart.