SIMULATION OF THE SNARE-MEMBRANE COLLISION IN MODAL FORM USING THE SCALAR AUXILIARY VARIABLE (SAV) METHOD

Collisions play an essential role in the sound production of many musical instruments, such as in the snare drum. Here, collisions occur between the stick and the batter head and between the snares and the bottom head. The latter involve interactions between fully distributed objects and are the subject of this work. From a simulation standpoint, simple explicit or semi-implicit schemes are prone to unstable numerical behaviour and an appropriate energy-conserving framework is required for stable simulation designs. Usually, this is accomplished via fully-implicit designs that are known to conserve energy but that require iterative solvers such as Newton-Raphson. Other than representing a computational bottleneck, iterative schemes present a variable operational cost per timestep and, furthermore, are serial in nature. This work will explore the possibility of simulating the snare-membrane collision using explicit designs obtained via a quadratisation of the nonlinear potential energy. A modal function basis will be employed for the spatial discretisation, allowing for fine-tuning damping ratios and natural frequencies.