In this study, we propose a new method to control both the beat clarity and beat period in a ring structure. An equivalent ring which satisfies the measured mode condition is determined by using the equivalent ring theory. Theoretical analysis and finite element analysis on the equivalent ring are performed to investigate the effect of the local structural modification on the beat clarity and beat period. Beat clarity and period are improved by attaching asymmetric mass or decreasing local thickness. Through the analysis on the equivalent ring, the proper position and the amount of the local variation are determined to satisfy the required clarity and period condition. All the analysis results are compared and verified by the experiment.