Dynamic Response and Frequency Split Predictions for Cylindrical Fused Silica Resonators

Abstract

An investigation into the dynamic response and frequency split behavior of a cylindrical fused silica resonator is performed via simulations and experiments. For this purpose, a structure for the cylindrical resonators with appropriate dimensions has been designed and fabricated. A laser Doppler vibrometer is utilized for the experimental quantification of the physical characteristics of the resonator. Natural frequencies of n = 2 modes, frequency split and quality factor have been extracted from the measured frequency sweep. Then the influence of mass change on the frequency split is investigated by chemical trimming. Time response predictions utilizing a ring model is employed to predict the resonant amplitudes as well as the influence of driving force and input angular velocity variations. The numerical predictions of the relationship between the mass mismatch and the frequency split are found to be consistent with the exper imental results. Predictions of frequency split of resonators via the simulation model are envisaged to greatly increase the efficacy of the chemical trimming process.