TY - JOUR
T1 - Linearly-implicit schemes for collisions in musical acoustics based on energy quadratisation
AU - Ducceschi, Michele
AU - Bilbao, Stefan
AU - Willemsen, Silvin
AU - Serafin, Stefania
N1 - Funding Information:
The first author wishes to acknowledge the Royal Society of London and the Leverhulme Trust, who have supported this research with a Newton International Fellowship and an Early Career Fellowship. Dr. Vasileios Chatziioannou is kindly acknowledged for a fruitful debate around the properties of the numerical schemes presented here. The anonymous reviewers are also thanked for their suggestions.
Publisher Copyright:
© 2021 Acoustical Society of America.
PY - 2021/5/1
Y1 - 2021/5/1
N2 - 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 exists a suitable discretisation of such a model that may be resolved in a single iteration, while 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.
AB - 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 exists a suitable discretisation of such a model that may be resolved in a single iteration, while 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.
UR - http://www.scopus.com/inward/record.url?scp=85106763838&partnerID=8YFLogxK
U2 - 10.1121/10.0005008
DO - 10.1121/10.0005008
M3 - Journal article
C2 - 34241147
AN - SCOPUS:85106763838
SN - 0001-4966
VL - 149
SP - 3502
EP - 3516
JO - Journal of the Acoustical Society of America
JF - Journal of the Acoustical Society of America
IS - 5
ER -