The Influence Mechanism and Identification Method of the First Four Harmonics of the Mass Defect of Hemispherical Resonators

The influence mechanism and identification of mass defects in hemispherical resonators are currently highly challenging and significant research directions. This paper first establishes a shell–rod coupling vibration model under the influence of mass error, and, based on this model, constructs a characterization system for the vibration characteristics (quality factor and frequency split) of the resonator. The influence of the first four harmonic components of the mass defect on the quality factor and frequency split of the resonator was systematically studied, and the analytical expression of its quantitative representation was derived, which reveals the internal physical relationship between the mass defect and the vibration characteristics. Subsequently, the theoretical model was verified by using finite element simulation. Finally, an efficient and high-precision method for identifying the first four harmonics of hemispherical resonator mass defects was proposed, and an experimental device was set up to successfully achieve the synchronous identification of the first four harmonic components. An innovative beam-split optical system that streamlines displacement metrology reduced test complexity by >60%.