A key way to reduce vibration and noise of motor is to effectively suppress the vibration of the motor stator excited by the radial electromagnetic force in the motor， whereas the accurate calculation of modal frequencies and modal shapes is the basis for suppressing the radial vibration of the motor stator. The elasticity analytical model of the circular ring is used as the vibration analysis model of the motor stator， based on which the modal analysis of the motor stator under the unconstrained state is carried out， and the analytical solutions of the modal frequencies and modal shapes of the stator’s radial vibration are obtained. Taking cogging and footing as typical additional structures， the perturbation method is introduced to analyze the frequency splitting phenomenon in the motor stator， and the criteria for determining whether the frequency is split or not and the order of the splitting are summarized. The validity of the theoretical methods and calculations in this paper is verified by finite element software ANSYS. The results show that the established two-dimensional ring model can be accurately and efficiently applied to the analysis of the modal characteristics of the motor stator， and the distribution form of the additional structure has an important influence on the frequency splitting characteristics of the stator.