Realistic Guitar Modelling using a Dynamical Multibody Approach

Vincent Debut, José Antunes

Research output: Contribution to conferenceAbstract

Abstract

Most musical instruments consist on a set of dynamical subsystems connected at a number of constraining locations, through which the vibratory energy flows or tuning can be achieved. Coupling is therefore an essential feature in instrument modelling and, when addressing physically-based synthesis, most modelling and computational difficulties are connected with the manner in which the coupling constraints are enforced. Typically, these are modelled using standard techniques such as Lagrange multipliers or penalty methods, each one with specific merits and drawbacks. In this paper we explore an approach based on the Udwadia-Kalaba (U-K) formulation, originally proposed in the early 90s for discrete constrained systems, which is anchored on analytical dynamics but avoids the use of Lagrange multipliers. Up to now, this general, very elegant and appealing formulation has been nearly exclusively used to address conceptual systems of discrete masses or articulated rigid bodies, namely in robotics. In a recent publication - Antunes & Debut, JASA (2017, in print) - we developed an extension of the U-K formulation to deal with flexible systems modelled through their unconstrained modes. We explored the potential of combining the U-K formulation for constrained systems with the modal description of flexible structures, in order to achieve reliable and efficient computations of the dynamical responses. This modelling approach was shown to be particularly effective, in particular for simulating the transient responses of musical instruments, as demonstrated by computing the dynamical responses of a guitar string coupled to the instrument body at the bridge. In the present paper we further generalize our computational model by incorporating all the guitar strings with both their motion polarisations, as well as the geometrical nonlinear string effects using the Kirchoff-Carrier (K-C) simplified approach. The illustrative results presented highlight the coupling of the various strings and body dynamics through the instrument bridge, and also emphasize the significance of string nonlinearity in the responses of plucked string instruments, which often lead to audible modal coupling terms and frequency gliding effects. The results presented complement extensive work already performed in the past by the authors on guitar string modelling using penalty methods, thus enabling an interesting comparison between the computational efficiency using different modelling techniques.
Original languageEnglish
Pages99
Number of pages1
Publication statusPublished - 2017
EventInternational Symposium on Music Acoustics - Montreal, Canada
Duration: 21 Jun 2017 → …

Conference

ConferenceInternational Symposium on Music Acoustics
CountryCanada
CityMontreal
Period21/06/17 → …

Fingerprint

Musical instruments
Lagrange multipliers
Flexible structures
Computational efficiency
Transient analysis
Robotics
Tuning
Polarization

Keywords

  • Realistic Guitar Modelling
  • Dynamical Multibody Approach

Cite this

Debut, V., & Antunes, J. (2017). Realistic Guitar Modelling using a Dynamical Multibody Approach. 99. Abstract from International Symposium on Music Acoustics, Montreal, Canada.
Debut, Vincent ; Antunes, José. / Realistic Guitar Modelling using a Dynamical Multibody Approach. Abstract from International Symposium on Music Acoustics, Montreal, Canada.1 p.
@conference{8784b04243214900894c928d3ee2e83a,
title = "Realistic Guitar Modelling using a Dynamical Multibody Approach",
abstract = "Most musical instruments consist on a set of dynamical subsystems connected at a number of constraining locations, through which the vibratory energy flows or tuning can be achieved. Coupling is therefore an essential feature in instrument modelling and, when addressing physically-based synthesis, most modelling and computational difficulties are connected with the manner in which the coupling constraints are enforced. Typically, these are modelled using standard techniques such as Lagrange multipliers or penalty methods, each one with specific merits and drawbacks. In this paper we explore an approach based on the Udwadia-Kalaba (U-K) formulation, originally proposed in the early 90s for discrete constrained systems, which is anchored on analytical dynamics but avoids the use of Lagrange multipliers. Up to now, this general, very elegant and appealing formulation has been nearly exclusively used to address conceptual systems of discrete masses or articulated rigid bodies, namely in robotics. In a recent publication - Antunes & Debut, JASA (2017, in print) - we developed an extension of the U-K formulation to deal with flexible systems modelled through their unconstrained modes. We explored the potential of combining the U-K formulation for constrained systems with the modal description of flexible structures, in order to achieve reliable and efficient computations of the dynamical responses. This modelling approach was shown to be particularly effective, in particular for simulating the transient responses of musical instruments, as demonstrated by computing the dynamical responses of a guitar string coupled to the instrument body at the bridge. In the present paper we further generalize our computational model by incorporating all the guitar strings with both their motion polarisations, as well as the geometrical nonlinear string effects using the Kirchoff-Carrier (K-C) simplified approach. The illustrative results presented highlight the coupling of the various strings and body dynamics through the instrument bridge, and also emphasize the significance of string nonlinearity in the responses of plucked string instruments, which often lead to audible modal coupling terms and frequency gliding effects. The results presented complement extensive work already performed in the past by the authors on guitar string modelling using penalty methods, thus enabling an interesting comparison between the computational efficiency using different modelling techniques.",
keywords = "Realistic Guitar Modelling , Dynamical Multibody Approach",
author = "Vincent Debut and Jos{\'e} Antunes",
note = "info:eu-repo/grantAgreement/FCT/5876/147236/PT# UID/EAT/00472/2013; International Symposium on Music Acoustics ; Conference date: 21-06-2017",
year = "2017",
language = "English",
pages = "99",

}

Debut, V & Antunes, J 2017, 'Realistic Guitar Modelling using a Dynamical Multibody Approach' International Symposium on Music Acoustics, Montreal, Canada, 21/06/17, pp. 99.

Realistic Guitar Modelling using a Dynamical Multibody Approach. / Debut, Vincent; Antunes, José.

2017. 99 Abstract from International Symposium on Music Acoustics, Montreal, Canada.

Research output: Contribution to conferenceAbstract

TY - CONF

T1 - Realistic Guitar Modelling using a Dynamical Multibody Approach

AU - Debut, Vincent

AU - Antunes, José

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

PY - 2017

Y1 - 2017

N2 - Most musical instruments consist on a set of dynamical subsystems connected at a number of constraining locations, through which the vibratory energy flows or tuning can be achieved. Coupling is therefore an essential feature in instrument modelling and, when addressing physically-based synthesis, most modelling and computational difficulties are connected with the manner in which the coupling constraints are enforced. Typically, these are modelled using standard techniques such as Lagrange multipliers or penalty methods, each one with specific merits and drawbacks. In this paper we explore an approach based on the Udwadia-Kalaba (U-K) formulation, originally proposed in the early 90s for discrete constrained systems, which is anchored on analytical dynamics but avoids the use of Lagrange multipliers. Up to now, this general, very elegant and appealing formulation has been nearly exclusively used to address conceptual systems of discrete masses or articulated rigid bodies, namely in robotics. In a recent publication - Antunes & Debut, JASA (2017, in print) - we developed an extension of the U-K formulation to deal with flexible systems modelled through their unconstrained modes. We explored the potential of combining the U-K formulation for constrained systems with the modal description of flexible structures, in order to achieve reliable and efficient computations of the dynamical responses. This modelling approach was shown to be particularly effective, in particular for simulating the transient responses of musical instruments, as demonstrated by computing the dynamical responses of a guitar string coupled to the instrument body at the bridge. In the present paper we further generalize our computational model by incorporating all the guitar strings with both their motion polarisations, as well as the geometrical nonlinear string effects using the Kirchoff-Carrier (K-C) simplified approach. The illustrative results presented highlight the coupling of the various strings and body dynamics through the instrument bridge, and also emphasize the significance of string nonlinearity in the responses of plucked string instruments, which often lead to audible modal coupling terms and frequency gliding effects. The results presented complement extensive work already performed in the past by the authors on guitar string modelling using penalty methods, thus enabling an interesting comparison between the computational efficiency using different modelling techniques.

AB - Most musical instruments consist on a set of dynamical subsystems connected at a number of constraining locations, through which the vibratory energy flows or tuning can be achieved. Coupling is therefore an essential feature in instrument modelling and, when addressing physically-based synthesis, most modelling and computational difficulties are connected with the manner in which the coupling constraints are enforced. Typically, these are modelled using standard techniques such as Lagrange multipliers or penalty methods, each one with specific merits and drawbacks. In this paper we explore an approach based on the Udwadia-Kalaba (U-K) formulation, originally proposed in the early 90s for discrete constrained systems, which is anchored on analytical dynamics but avoids the use of Lagrange multipliers. Up to now, this general, very elegant and appealing formulation has been nearly exclusively used to address conceptual systems of discrete masses or articulated rigid bodies, namely in robotics. In a recent publication - Antunes & Debut, JASA (2017, in print) - we developed an extension of the U-K formulation to deal with flexible systems modelled through their unconstrained modes. We explored the potential of combining the U-K formulation for constrained systems with the modal description of flexible structures, in order to achieve reliable and efficient computations of the dynamical responses. This modelling approach was shown to be particularly effective, in particular for simulating the transient responses of musical instruments, as demonstrated by computing the dynamical responses of a guitar string coupled to the instrument body at the bridge. In the present paper we further generalize our computational model by incorporating all the guitar strings with both their motion polarisations, as well as the geometrical nonlinear string effects using the Kirchoff-Carrier (K-C) simplified approach. The illustrative results presented highlight the coupling of the various strings and body dynamics through the instrument bridge, and also emphasize the significance of string nonlinearity in the responses of plucked string instruments, which often lead to audible modal coupling terms and frequency gliding effects. The results presented complement extensive work already performed in the past by the authors on guitar string modelling using penalty methods, thus enabling an interesting comparison between the computational efficiency using different modelling techniques.

KW - Realistic Guitar Modelling

KW - Dynamical Multibody Approach

M3 - Abstract

SP - 99

ER -

Debut V, Antunes J. Realistic Guitar Modelling using a Dynamical Multibody Approach. 2017. Abstract from International Symposium on Music Acoustics, Montreal, Canada.