Analysis on frequency split caused by density distribution non-uniform of hemispherical resonator

In order to analyze the influence of nonuniform density distribution on frequency split of hemispherical resonator precisely, the dynamics equations of resonator with the nonuniformity of density's circular distribution were established using Bubonov-Galerkin method, on the basis of these equations, the state equation was established, from which the system characteristic equations were derived. According to the system characteristic equations, the exact equations of natural frequency and frequency split of hemispherical resonator are solved, and the relationship between frequency split and density's nonuniformity is analyzed finally.