Investigation on precise frequency trimming of a micro shell resonator with T-shape masses using low-power femtosecond laser ablation

This paper presents a novel method to achieve precise frequency balance between degenerate modes of micro shell resonator (MSR) with T shape masses based on mass and stiffness perturbation. The reason causing the large frequency split and frequency tuning principle are simply analyzed. For the complexity of the resonator structure, variation of the mode frequency using different position and shape trimming are analyzed by finite element method (FEM). A systematic frequency trimming process including initial stiffness balance and precise mass balance is proposed based on the simulation results. Considering the small sizes and special material characteristics of the resonator, low-power femtosecond laser is used to achieve a small amount removal of material. Finally, frequency trimming experiments are conducted and results demonstrate the effectiveness of this method.