A three-dimensional, time-dependent simulation of a Turkish cymbal using the finite element method
Malte Muenster · The Journal of the Acoustical Society of America · 2006
We built computer-aided simulations of several musical instruments to study microstructural behavior of initial transients and eigenvalues. Our finite element model (FEM) of a cymbal is an example for the possibilities of this method. Proceeding from a three-dimensional mindlin plate model, we discovered some former unknown, sometimes moving fundamentals, depending on striking positions, hammering during production process, sizes, forms, and alloys. Special movements of the bell of the cymbal have been investigated. Moreover, experimental studies and simulation are able to be compared directly concerning their variety of dynamic behavior. This leads to more and more precise formulation of requirements of musical instruments. Cymbals are among the oldest instruments. The production techniques, some were real secrets, were given from father to son to the next generations of instrument builders. But only recent developments in musical acoustic research include computational modeling and signal processing power to show that most parts of musical sounds of a cymbal are caused by the features mentioned above, in regard to styles, expression, and instrument qualities important to musicians. Our studies try to give an idea of formulating and influencing sound parameters of musical instruments using FEM simulations. The target is to describe how to build a cymbal fulfilling any condition of sound.