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Piano string vibration modelling using coupled mobilities and a statespace approach

Piano string vibration modelling using coupled mobilities and a statespace approach
Piano string vibration modelling using coupled mobilities and a statespace approach
The two transverse motions of the string in planes parallel and perpendicular to the soundboard are believed to contribute to some of the characteristic effects of piano tones. In this work we aim to model the coupling between a single string and soundboard, considering the two transverse motions.
A stiff string model is coupled to the bridge of the soundboard. Modelling approaches are presented in both frequency and time domain, using mobility coupling and state-space equations, respectively.
For time domain modelling, the soundboard mobilities are approximated by lumped elements, springs and dampers in this case. In the frequency domain model, the mobilities of the elongated string, detached from the bridge, corresponding to the transverse response to a transverse force, are
the same in both directions and the coupling between them is neglected, while the soundboard mobilities are represented by a 22 matrix. The state-space model has the benefit of allowing inclusion of the non-linear hammer excitation. Although the frequency domain model can represent the linear characteristics of the coupling and give an insight into the importance of the cross-terms of the coupled mobility, it is the time domain model that is able to represent typical features of the interaction.
Miranda Valiente, Pablo Martin
5e6d99eb-2e25-460d-a88c-790f0955897a
Squicciarini, Giacomo
c1bdd1f6-a2e8-435c-a924-3e052d3d191e
Thompson, David
bca37fd3-d692-4779-b663-5916b01edae5
Miranda Valiente, Pablo Martin
5e6d99eb-2e25-460d-a88c-790f0955897a
Squicciarini, Giacomo
c1bdd1f6-a2e8-435c-a924-3e052d3d191e
Thompson, David
bca37fd3-d692-4779-b663-5916b01edae5

Miranda Valiente, Pablo Martin, Squicciarini, Giacomo and Thompson, David (2022) Piano string vibration modelling using coupled mobilities and a statespace approach. In Proceedings of the 51st International Congress and Exposition on Noise Control Engineering, Inter-Noise 2022, Glasgow, United Kingdom, 21-24 August 2022.

Record type: Conference or Workshop Item (Paper)

Abstract

The two transverse motions of the string in planes parallel and perpendicular to the soundboard are believed to contribute to some of the characteristic effects of piano tones. In this work we aim to model the coupling between a single string and soundboard, considering the two transverse motions.
A stiff string model is coupled to the bridge of the soundboard. Modelling approaches are presented in both frequency and time domain, using mobility coupling and state-space equations, respectively.
For time domain modelling, the soundboard mobilities are approximated by lumped elements, springs and dampers in this case. In the frequency domain model, the mobilities of the elongated string, detached from the bridge, corresponding to the transverse response to a transverse force, are
the same in both directions and the coupling between them is neglected, while the soundboard mobilities are represented by a 22 matrix. The state-space model has the benefit of allowing inclusion of the non-linear hammer excitation. Although the frequency domain model can represent the linear characteristics of the coupling and give an insight into the importance of the cross-terms of the coupled mobility, it is the time domain model that is able to represent typical features of the interaction.

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Pablo_Miranda_Internoise2022 - Accepted Manuscript
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More information

Published date: 21 August 2022
Venue - Dates: The 51st International Congress and Exposition on Noise Control Engineering: Internoise 2022, Scottish Event Campus (SEC), Glasgow, United Kingdom, 2022-08-21 - 2022-08-24

Identifiers

Local EPrints ID: 476996
URI: http://eprints.soton.ac.uk/id/eprint/476996
PURE UUID: c130eea8-67f2-468d-a433-51b08fa3c9a8
ORCID for Giacomo Squicciarini: ORCID iD orcid.org/0000-0003-2437-6398
ORCID for David Thompson: ORCID iD orcid.org/0000-0002-7964-5906

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Date deposited: 23 May 2023 16:35
Last modified: 17 Mar 2024 03:27

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