Investigations on relationship between vibration characteristics and shapes of effect cymbals with finite element method

Cymbals are musical instruments consisting of round brass plates in slightly concave shape that are struck against another or struck with a stick to make sounds. Their vibration characteristics depend on the shape of cymbals, therefore, some cymbals have been specially shaped for desired characteristics, as called effect cymbals. Usually, it takes the craftsman numerous retrials in prototyping the effect cymbals to realize the desired characteristics. This leads to a large cost of prototyping effect cymbals. On the other hand, the cost can be significantly reduced if the optimal shape for the desired sound can be estimated in advance. However, to estimate the shape, it is necessary to clarify the relationship between the shape of a certain cymbal and its vibration characteristics. In this paper, we focus on the effect cymbals with holes. Aiming to estimate the optimal hole shape for desired sound, we investigate the relationship between the hole shape of hole effect cymbals and their vibration characteristics based on frequency response analysis by finite element method. We analyzed multiple models with different hole sizes for each cymbal, the analysis results show that the vibration tends to be simpler as the hole size is larger.