Dual mode tuning strategy of a slightly asymmetric ring

Clear beats with proper periods in the first and the second vibration modes are very important factors for the sound of the Korean bell. In this study, the Korean bell is expressed as a circular ring with multiple point masses and a dual mode tuning strategy for clear beat with proper period. For the dual mode tuning, a dual mode equivalent ring model is composed with two point masses, which satisfies the mode pair conditions of the first mode and second mode simultaneously. By adding a suitable amount of additional masses to the dual mode equivalent ring model at appropriate positions, a clear beat with proper period in both of the two important modes is generated. The position and amount of the additional masses are determined analytically. Analytical tuning results are compared and verified with those of the finite element analysis.