THE NORMAL MODES OF CYMBALS
Robert Perrin, Gerry Swallowe, Sarah A. Zietlow, Thomas R. Moore · 2023
1we described an investigation into the normal modes of an 18 inch crash cymbal. Various experimental methods were used in turn including electronic speckle pattern interferometry (ESPI), laser vibrometry and Chladni sand patterns as well as more conventional approaches involving transducers and accelerometers. Over 100 modes, plus many split “degenerate” partners, were found and identified. The results were compared with the predictions of a finite-element model and the requirements of group representation theory. Although overall agreement was good it was found that, contrary to prediction, the vast majority of patterns produced were of mixed symmetry types. This could not be explained by conventional mode coupling because all the modes involved had high Q values, of the order of 10 3 as measured by the decay method. We have further investigated some of these mixed modes by using ESPI and laser vibrometry simultaneously. Additionally the combination of ESPI and laser vibrometry has been used to study the modes of a 12” ridged cymbal. This is stiffer than the cymbal previously investigated and its profile does not include the ‘lip’ formed by a sharp change in slope close to the outside of the 18” cymbal. Profiles are illustrated in Figure 1. After reviewing some background theory and the previous results, we shall discuss some of the findings of these new experiments and their interpretation.