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

Michele Ducceschi; Stefan Bilbao; Silvin Willemsen; Stefania Serafin

doi:10.1121/10.0005008

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

Michele Ducceschi, Stefan Bilbao, Silvin Willemsen, Stefania Serafin

Research output: Contribution to journal › Article › Academic › peer-review

19 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	3502-3516
Number of pages	15
Journal	Journal of the Acoustical Society of America
Volume	149
Issue number	5
DOIs	https://doi.org/10.1121/10.0005008
Publication status	Published - 1 May 2021
Externally published	Yes

Bibliographical note

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.

Funding

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.

Funders	Funder number
Leverhulme Trust
Royal Society

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1121/10.0005008Licence: CC BY

Cite this

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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 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.",

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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.

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

Abstract

Bibliographical note

Funding

UN SDGs

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