Anchor Loss in Hemispherical Shell Resonators

Abstract

Micromachined hemispherical shell resonators (HSRs) can be used in high accuracy vibratory gyroscopes. These resonators need to have very low energy loss to achieve very high quality factor. Energy might be lost through the anchor, fluid-structure interaction, thermoelastic dissipation, phonon-phonon and phonon-electron interactions, and the resonator surface. This paper investigates energy loss through the anchor of HSRs using a numerical approach. To numerically determine wave radiation from the anchor to the infinite substrate, a perfectly matched layer is used around a finite substrate. Anchor loss investigations in HSRs are classified into four categories. First, the effects of shell properties-material, geometry, and imperfections-are investigated. Second, the relationships between anchor loss and properties of the stem, such as material, geometry, and stemshell misalignments, are studied. Third, the effects of substrate characteristics-substrate material, attachment material between the stem and substrate, and attachment configuration of the substrate and stem-are investigated. Finally, the effects of external motions, such as shock and rotation, are analyzed. It is found that anchor loss in HSRs strongly depends on the shell, stem, and substrate properties. This study also shows that any imperfection in the shell or any misalignment between the shell and stem increases anchor loss by orders of magnitude.