Linearly-implicit schemes for collisions in musical acoustics based on energy quadratisation

Michele Ducceschi, Stefan Bilbao, Silvin Willemsen, Stefania Serafin

Research output: Contribution to journalArticlepeer-review

Abstract

Collision modelling represents an active field of research in musical acoustics. Common examples of collisions include the hammer-string interaction in the piano, the interaction of strings with fretboards and fingers, the membrane-wire interaction in the snare drum,reed-beating effects in wind instruments, and others. At the modelling level, many current approaches make use of conservative potentials in the form of power-laws, and discretisations proposed for such models rely in all cases on iterative root-finding routines. Here, a method based on energy quadratisation of the nonlinear collision potential is proposed. It is shown that there exist a suitable discretisation of such model that may be resolved in a single iteration, whilst guaranteeing stability via energy conservation. Applications to the case of lumped as well as fully distributed systems will be given, using both finite-difference and modal methods
Original languageEnglish
Pages (from-to)3502-3516
JournalThe Journal of the Acoustical Society of America
Volume149
Issue number5
Early online date24 May 2021
DOIs
Publication statusPublished - May 2021

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