Effect of Electrode Design on Frequency Tuning in Shell Resonators

The fabrication of shell resonators for vibratory gyroscopes is often accompanied by a split between drive and sense mode frequencies. To tune these frequencies and reduce the frequency split, a voltage can be applied between the shell and electrodes placed around it. This paper investigates electrostatic frequency tuning in shell resonators as a function of voltage, capacitive gap between the shell and electrode, electrode span angle and height, and electrode placement and configuration using a numerical approach. The results of this investigation show that conformal electrodes placed around the shell rim with a uniform gap provide the best tuning capability. Considering fabrication challenges and shell aspect-ratio, other electrode configurations might be more practical in some devices, although they have worse tuning capability.