Dynamical modelling of constrained flexible systems using a modal Udwadia-Kalaba formulation

application to musical Instruments

Research output: Contribution to journalArticle

8 Citations (Scopus)
65 Downloads (Pure)

Abstract

Most musical instruments consist of dynamical subsystems connected at a number of constraining points through which energy flows. For physical sound synthesis, one important difficulty deals with enforcing these coupling constraints. While standard techniques include the use of Lagrange multipliers or penalty methods, in this paper, a different approach is explored, the Udwadia-Kalaba (U-K) formulation, which is rooted on analytical dynamics but avoids the use of Lagrange multipliers. This general and elegant formulation has been nearly exclusively used for conceptual systems of discrete masses or articulated rigid bodies, namely, in robotics. However its natural extension to deal with continuous flexible systems is surprisingly absent from the literature. Here, such a modeling strategy is developed and the potential of combining the U-K equation for constrained systems with the modal description is shown, in particular, to simulate musical instru- ments. Objectives are twofold: (1) Develop the U-K equation for constrained flexible systems with subsystems modelled through unconstrained modes; and (2) apply this framework to compute string/body coupled dynamics. This example complements previous work [Debut, Antunes, Marques, and Carvalho, Appl. Acoust. 108, 3–18 (2016)] on guitar modeling using penalty meth- ods. Simulations show that the proposed technique provides similar results with a significant improvement in computational efficiency. VC 2017 Acoustical Society of America.
Original languageEnglish
Pages (from-to)764-778
Number of pages14
JournalJournal of the Acoustical Society of America
Volume141
Issue number2
DOIs
Publication statusPublished - 8 Feb 2017

Fingerprint

Lagrange multipliers
penalties
formulations
rigid structures
robotics
complement
strings
acoustics
synthesis
simulation
Musical Instruments
Modeling
energy
Lagrange
Equations

Cite this

@article{6dc2a3dd3b83472290e44864230fb4fe,
title = "Dynamical modelling of constrained flexible systems using a modal Udwadia-Kalaba formulation: application to musical Instruments",
abstract = "Most musical instruments consist of dynamical subsystems connected at a number of constraining points through which energy flows. For physical sound synthesis, one important difficulty deals with enforcing these coupling constraints. While standard techniques include the use of Lagrange multipliers or penalty methods, in this paper, a different approach is explored, the Udwadia-Kalaba (U-K) formulation, which is rooted on analytical dynamics but avoids the use of Lagrange multipliers. This general and elegant formulation has been nearly exclusively used for conceptual systems of discrete masses or articulated rigid bodies, namely, in robotics. However its natural extension to deal with continuous flexible systems is surprisingly absent from the literature. Here, such a modeling strategy is developed and the potential of combining the U-K equation for constrained systems with the modal description is shown, in particular, to simulate musical instru- ments. Objectives are twofold: (1) Develop the U-K equation for constrained flexible systems with subsystems modelled through unconstrained modes; and (2) apply this framework to compute string/body coupled dynamics. This example complements previous work [Debut, Antunes, Marques, and Carvalho, Appl. Acoust. 108, 3–18 (2016)] on guitar modeling using penalty meth- ods. Simulations show that the proposed technique provides similar results with a significant improvement in computational efficiency. VC 2017 Acoustical Society of America.",
author = "Vincent Debut and Antunes, {Jos{\'e} Manuel Vieira}",
note = "info:eu-repo/grantAgreement/FCT/5876/147236/PT# info:eu-repo/grantAgreement/FCT/5876/147236/PT# UID/EAT/00472/2013 EAT/00472/2013",
year = "2017",
month = "2",
day = "8",
doi = "10.1121/1.4973534",
language = "English",
volume = "141",
pages = "764--778",
journal = "Journal of the Acoustical Society of America",
issn = "0001-4966",
publisher = "Acoustical Society of America",
number = "2",

}

TY - JOUR

T1 - Dynamical modelling of constrained flexible systems using a modal Udwadia-Kalaba formulation

T2 - application to musical Instruments

AU - Debut, Vincent

AU - Antunes, José Manuel Vieira

N1 - info:eu-repo/grantAgreement/FCT/5876/147236/PT# info:eu-repo/grantAgreement/FCT/5876/147236/PT# UID/EAT/00472/2013 EAT/00472/2013

PY - 2017/2/8

Y1 - 2017/2/8

N2 - Most musical instruments consist of dynamical subsystems connected at a number of constraining points through which energy flows. For physical sound synthesis, one important difficulty deals with enforcing these coupling constraints. While standard techniques include the use of Lagrange multipliers or penalty methods, in this paper, a different approach is explored, the Udwadia-Kalaba (U-K) formulation, which is rooted on analytical dynamics but avoids the use of Lagrange multipliers. This general and elegant formulation has been nearly exclusively used for conceptual systems of discrete masses or articulated rigid bodies, namely, in robotics. However its natural extension to deal with continuous flexible systems is surprisingly absent from the literature. Here, such a modeling strategy is developed and the potential of combining the U-K equation for constrained systems with the modal description is shown, in particular, to simulate musical instru- ments. Objectives are twofold: (1) Develop the U-K equation for constrained flexible systems with subsystems modelled through unconstrained modes; and (2) apply this framework to compute string/body coupled dynamics. This example complements previous work [Debut, Antunes, Marques, and Carvalho, Appl. Acoust. 108, 3–18 (2016)] on guitar modeling using penalty meth- ods. Simulations show that the proposed technique provides similar results with a significant improvement in computational efficiency. VC 2017 Acoustical Society of America.

AB - Most musical instruments consist of dynamical subsystems connected at a number of constraining points through which energy flows. For physical sound synthesis, one important difficulty deals with enforcing these coupling constraints. While standard techniques include the use of Lagrange multipliers or penalty methods, in this paper, a different approach is explored, the Udwadia-Kalaba (U-K) formulation, which is rooted on analytical dynamics but avoids the use of Lagrange multipliers. This general and elegant formulation has been nearly exclusively used for conceptual systems of discrete masses or articulated rigid bodies, namely, in robotics. However its natural extension to deal with continuous flexible systems is surprisingly absent from the literature. Here, such a modeling strategy is developed and the potential of combining the U-K equation for constrained systems with the modal description is shown, in particular, to simulate musical instru- ments. Objectives are twofold: (1) Develop the U-K equation for constrained flexible systems with subsystems modelled through unconstrained modes; and (2) apply this framework to compute string/body coupled dynamics. This example complements previous work [Debut, Antunes, Marques, and Carvalho, Appl. Acoust. 108, 3–18 (2016)] on guitar modeling using penalty meth- ods. Simulations show that the proposed technique provides similar results with a significant improvement in computational efficiency. VC 2017 Acoustical Society of America.

U2 - 10.1121/1.4973534

DO - 10.1121/1.4973534

M3 - Article

VL - 141

SP - 764

EP - 778

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 2

ER -