Predictive analytical model of fundamental frequency and imperfections in glassblown fused quartz hemi-toroidal 3D micro shells

Glassblown 3D micro shells are released by a multi-step mechanical lapping process, introducing structural imperfections to the sensing element. We present an analytical model predicting the frequency mismatch in micro shells due to imperfections induced by the release process. The analytical model of such micro shells was derived based on inextensional assumption. Mode shapes and the resonant frequencies were calculated and compared to results from both Finite Element Analysis (FEA) and experiments. The predictive frequency of the n=2 wineglass mode shape was within 10% of the finite element results and 20% of the experimental results for thin shells, showing the fidelity of the model. The effect of imperfections of the shell release process on frequency mismatch was studied both analytically and experimentally.