Collisions in Drum Membranes: a preliminary study on a simplified system

Collisions play an important role in musical acoustics. Extensive study has already been performed on this subject for a number of systems, with notable examples being the hammer-string collision in the piano, and the mallet- membrane collision relevant in drums.
This paper uses experiments and modelling to investigate collisions in the snare drum. This is an interesting percussion instrument, as two collision mechanisms feature prominently. Initial excitation usually results from collision between a striker, such as a mallet, and the upper (‘batter’) membrane. Ensuing membrane and cavity vibrations then give rise to secondary collisions between the lower membrane and a number of metal wires (‘snares’) that are tensioned across it. These collisions are crucial for the sound qualities of the snare drum, and so a proper understanding of their nature is essential for accurate sound synthesis models.
In this preliminary paper, a simplified experimental setup will be studied, consisting of a drumskin with a single snare stretched across it. The system can be excited either by plucking the string, or by striking the membrane with a mallet. A setup involving a high speed camera and a laser vibrometer will allow the motion of the snare and membrane to be captured.
Experimental results will be used in comparison with a novel numerical model that describes both the mallet- membrane and string-membrane collisions. The interactions are described by a non-linear force expressed in terms of a power law, similar to one used in the past for modelling the hammer-string collision in pianos.