Vibration characteristics of hemispherical shell resonators with coaxial error

Coaxial error of hemispherical shell resonators (HSRs) is commonly caused by machining, which can significantly influence the frequency splitting and the symmetry of mode shapes of the HSRs, ultimately affecting the performance of the resonators. This study aims to analyze the influences of coaxial error on the frequency splitting and mode shapes of the HSRs using both analytical and experimental techniques. The coaxial error is quantitatively characterized by establishing the relationship between the deviation distance e₁ and the center angle φ_a of the HSR. The analytical model of the HSR with coaxial error is established by applying Hamilton’s principle, and the vibration characteristics are conveniently analyzed. Taking into account the mass impact of the acceleration sensors, the natural frequencies, frequency splitting values, and mode shapes are obtained and compared by using the established analytical model, the finite element method (FEM) and the experimental tests, from which the accuracy of the established analytical model is also verified. The effects of the deviation distance on the vibration properties of the HSR are discussed in detail. The key contributions of this paper are the establishment of the theoretical model and the design of the modal experiments for HSRs with coaxial error, which provide references for future researches in related fields.