An unconditionally stable scheme for simulation of stick-slip processes

Abstract

Stick-slip processes are often encountered in musical instruments, the most notable example being that of a bowed violin string. Modeling such nonlinear interactions has been often attempted in the field of Musical Acoustics, using a variety of time-stepping algorithms. The nonlinear nature of such problems requires careful analysis of the stability properties of the developed numerical schemes. This is usually carried out using energy based methods, in which case one needs to consider the continuous exchange of energy between the bow and the bowed object. In this paper an unconditionally stable scheme is proposed for the simulation of a bowed, lumped mass. The stability of the algorithm is ensured due to the presence of an invariant quantity. The numerical results are in agreement with well established algorithms, with the proposed methodology possessing no stability constraints and being extensible to a wide range of (lumped and distributed) acoustic systems.