Proposition of a Green-Volterra formalism to solve dynamics of a nonlinear string

David Roze (1) , Thomas Hélie

1 STMS - Sciences et Technologies de la Musique et du Son

The convolution kernels of a Volterra series give a generalization of impulse responses to the case of weakly nonlinear input-to-output systems. In acoustics, this formalism has yet been used to solve, e.g. the problem of a nonlinear string excited by a force $f(t)$ (considered as the input), spatially distributed by a time invariant function. In this paper, we propose a similar generalization for the case of Green functions in order to tackle inputs that depend on both the space and the time variables. The method to derive the "Green-Volterra" kernels is described and its application to the string is presented.

Mots clés: Volterra series; Green function; nonlinear; string

Domaines: Acoustique [physics.class-ph]

David Roze, Thomas Hélie. Proposition of a Green-Volterra formalism to solve dynamics of a nonlinear string. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00811301⟩