研究目的
Investigating the effect of geometric asymmetries such as height and radius imperfections, notch, and mass imbalance in the rim of gyroscopes on the split in the natural frequencies of the n=2 wineglass modes.
研究成果
The frequency mismatch increases almost linearly with the increase of the rim mass imperfection. A notch at the rim of the resonator changes both wineglass resonant frequencies but does not change frequency split. Frequency split is very sensitive to edge imperfections but not very sensitive to height imperfections less than 40 ????. Using symmetric mold to prevent edge imperfections can reduce frequency split.
研究不足
The study is limited to the analysis of specific geometric imperfections and their effects on frequency split. The fabrication process may introduce other types of imperfections not considered in this study.
1：Experimental Design and Method Selection:
Numerical simulation using COMSOL Multiphysics to solve finite element eigenfrequency problem to obtain resonance frequencies and mode shapes numerically.
2：Sample Selection and Data Sources:
Fused silica shell resonators made by blow torch molding.
3：List of Experimental Equipment and Materials:
Fused silica with Young’s modulus EFS = 70 GPa, Poisson’s ratio υFS =
4：17, density ρFS = 2200 kg/mExperimental Procedures and Operational Workflow:
Adding a point mass to the rim of the shell and calculating resonance frequencies; adding a notch to the shell model and simulating its effect; distorting the edge and height of the shell to analyze geometric imperfections.
5：Data Analysis Methods:
Using first order Taylor’s series expansion to analyze the effect of extra mass on resonance frequency.
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