Keynote:
Collisions in musical instruments: a numerical modelling perspective

    Maarten van Walstijn

The vibrational behaviour of musical instruments often involves some form of vibro-impact. The nature of the collisions can vary from compact in both space and time, as with hammer-string interaction, to more distributed and sustained forms, such as the string-membrane coupling in a snare drum. The former can usually be modelled in lumped form, suppressing the computation of the interaction forces to a single point, whereas the latter requires considering variations along spatial coordinates. In all cases, the impactive interaction represents an important nonlinear element that is closely linked to the characteristics and/or the gestural control of the instrument. Given the non-smooth nature of collision forces, incorporating such phenomena into time-stepping simulations can be challenging due to potential instability and further concerns around computability, accuracy and efficiency. Approaches to address these challenges are discussed in this lecture, starting from considering collision between two simple one-mass objects and culminating in the simulation of full distributed vibro-impact between a nonlinearly vibrating string and a barrier of arbitrary profile.