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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.
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