Analysis of frequency cracking of resonator under the density error

In order to study the frequency cracking caused by the nonuniform of density distribution, the dynamics equations of resonator under the nonuniform of density distribution were established by way of Bubonov-Galerkin method which is common used for solution of differential equations, the state equation was established by the dynamics equations, and then the system characteristic equations were derived. According to the system characteristic equations, two second order natural frequency caused by the density nonuniformity around the hemispherical of vibration system and the expression of frequency cracking were solved.