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Sound synthesis of a nonlinear string using Volterra series

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text
 

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article
 

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Titre

Sound synthesis of a nonlinear string using Volterra series
 

Nom(s)

Helie, Thomas (auteur)
 
Roze, David (auteur)
 

Publication

2008
 

Description

Sujet(s)

string   nonlinear model   Volterra series   analytic solution   modal decomposition   sound synthesis
 

Résumé

This paper proposes to solve and simulate various Kirchhoff models of nonlinear strings using Volterra series. Two nonlinearities are studied: the string tension is supposed to depend either on the global elongation of the string (first model), or on the local strain located at $x$ (second, and more precise, model). The boundary conditions are simple Dirichlet homogeneous ones or general dynamic conditions (allowing the string to be connected to any system; typically a bridge). For each model, a Volterra series is used to represent the displacement as a functional of excitation forces. The Volterra kernels are solved using a modal decomposition: the first kernel of the series yields the standard modes of the linearized problem while the next kernels introduce the nonlinear dynamics. As a last step, systematic identification of the kernels lead to a structure composed of linear filters, sums, and products which are well-suited to the sound synthesis, using standard signal processing techniques. The nonlinear dynamic introduced through this simulation is significant and perceptible in sound results for sufficiently large excitations.
 

Note(s)

Article paru dans : Journal of Sound and Vibration vol. 314
 

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Date de la notice

2010-02-25 01:00:00
 

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