Frequency Split Improvement of Fused Silica Micro Shell Resonator Based on Suppression of Geometric Harmonic Error

Abstract

This paper demonstrates the impact of harmonic error on the natural frequency of micro shell resonator (MSR). Parameterized 3D model is established to analyze the frequency split of resonator with deviation along the circumferential and height direction. Both the n=1 tilt mode and n=2 wineglass modes are considered. The simulation results show that frequency split significantly increases as the growth of the 2nd and 4th harmonic errors. A rotary platform is used to reduce the harmonic error of the resonator by improving symmetry of the shell structure. Finally, more than 10 samples are electrostatically characterized and well matched with the simulation results.