Abstract
Cymbals are thin domed plates used as percussion instruments. When cymbals are struck, they vibrate and radiate sound. Cymbals are made through spin forming, hammering, and lathing. The spin forming creates the basic shape of the cymbal, which determines its basic vibration characteristics. The hammering and lathing produce specific sound adjustments by changing the cymbal's vibration characteristics. In this study, we study how hammering cymbals affects their vibration characteristics. The hammering produces plastic deformation (small, shallow dents) on the cymbal's surface, generating residual stresses throughout it. These residual stresses change the vibration characteristics. We perform finite element analysis of a cymbal to obtain its stress distribution and the resulting change in vibration characteristics. To reproduce the stress distribution, we use thermal stress analysis, and then with this stress distribution we perform vibration analysis. These results show that each of the cymbal's modes has a different sensitivity to the thermal load (i.e., hammering). This difference causes changes in the frequency response and the deflection shape that significantly improves the sound radiation efficiency. In addition, we explain the changes in natural frequencies by the stress and modal strain energy distributions.
Highlights
Cymbals are thin domed plates made of bronze, used as percussion instruments
The sound radiation efficiency of a cymbal depends on its deflection shape, which is expressed as a linear combination of the mode shapes
We studied how hammering cymbals affects their vibration characteristics
Summary
Cymbals are thin domed plates made of bronze, used as percussion instruments. They are played by hitting them with a drumstick or with another cymbal. The sound of a cymbal is complex and inharmonic, containing many frequencies, which is related to the cymbal’s vibration characteristics. Cymbals vibrate in many different mode shapes and radiate sound with complex overtones. Perrin et al [8, 9] identified over a hundred normal modes of cymbals by various experimental methods including electronic speckle pattern interferometry, laser vibrometry, and Chladni sand patterns They compared the experimental results with predictions from a FE model and showed that the modes couple with others that are close in frequency and that the high density of modes might cause coupling. As stated in Pinksterboer [10], a cymbal’s sound depends on its size and shape and on the applied manufacturing processes such as hammering and lathing. To further demonstrate the effect of hammering, we examine the deflection shapes and their sound radiation efficiencies at the peak of the frequency response
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