This paper presents a novel method to identify and suppress the undesired spurious mode caused by the 1st and 3rd harmonics of eccentric mass defects in shell resonators. This approach eliminates the need for pre-trimming of frequency split, simplifying the identification and trimming process, with the advantages of high efficiency and minimal structural damage. Firstly, the influence of the mass defects on the dynamics of resonators is analyzed using the mass ring model. The shear force caused by the 1st and 3rd harmonics of the eccentric mass, as well as the axial force caused by the 2nd harmonic, result in forced bending vibration and axial vibration of resonators. These two types of vibrations are superimposed as spurious modes with the operating mode. The bending vibration caused by eccentric mass is decoupled from the mixed vibration signal by analyzing the dynamic characteristics. An analytic scheme is proposed to identify the 1st and 3rd harmonics without eliminating frequency split. To validate the proposed scheme, the identification and trimming process for eccentric mass is simulated by the finite element method based on the geometric model with preset first four harmonics. Finally, experimental identification and trimming of the eccentric mass for the hemispherical resonator are performed based on the laser Doppler vibrometer and ion beam etching process. After multiple iterations, the 1st and 3rd harmonics are reduced by 87.2% and 49.8%, and the quality factors of the operating modes increase by 26.7% and 40.7%, respectively, demonstrating the effectiveness of the proposed method.

中文翻译：

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壳谐振器中偏心质量的识别和修整


本文提出了一种新方法来识别和抑制由壳谐振器中偏心质量缺陷的一阶和三阶谐波引起的不良寄生模式。该方法无需对分频进行预修整，简化了识别和修整过程，具有效率高、结构损伤最小等优点。首先，利用质量环模型分析了质量缺陷对谐振器动力学的影响。偏心质量的1次和3次谐波引起的剪切力，以及2次谐波引起的轴向力，导致谐振器的受迫弯曲振动和轴向振动。这两种类型的振动作为寄生模式与工作模式叠加。通过分析动态特性，将偏心质量引起的弯曲振动与混合振动信号解耦。提出了一种解析方案来识别第一和第三谐波而不消除频率分裂。为了验证所提出的方案，基于预设前四次谐波的几何模型，采用有限元方法对偏心质量的识别和修整过程进行了仿真。最后，基于激光多普勒测振仪和离子束刻蚀工艺，对半球谐振腔偏心质量进行了实验识别和修整。经过多次迭代，一次和三次谐波分别降低了87.2%和49.8%，工作模式的品质因数分别增加了26.7%和40.7%，证明了该方法的有效性。