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%0 Journal Article
%A Hélie, Thomas
%A Roze, David
%T Sound synthesis of a nonlinear string using Volterra series
%D 2008
%B Journal of Sound and Vibration
%V 314
%P 275-306
%F Helie08a
%K string
%K nonlinear model
%K Volterra series
%K analytic solution
%K modal decomposition
%K sound synthesis
%X 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.
%1 1
%2 3
%U http://articles.ircam.fr/textes/Helie08a/