Numerical tools for musical instruments acoustics: analysing nonlinear physical models using continuation of periodic solutions

Sami Karkar (1) , Christophe Vergez (1) , Bruno Cochelin (2)

1 Sons
2 M&S - Matériaux et Structures

We propose a new approach based on numerical continuation and bifurcation analysis for the study of physical models of instruments that produce self-sustained oscillations. Several physical models (clarinet and saxophone) are formulated as nonlinear dynamical systems, whose periodic solutions are directly obtained using the harmonic balance method. This method yields a set of nonlinear algebraic equations. The solution of this system, which represent a periodic solution of the instrument, is then followed using a numerical continuation tool when a control parameter (e.g. the blowing pressure) varies. This approach enables us to compute the whole periodic regime of the instruments, without any additional simplification of the models, thus giving access to characteristics such as playing frequency, sound level, as well as sound spectrum as a functions of the blowing pressure or bow velocity. Finally, we show how the same approach can be used to study the oscillation threshold.

Domaines: Acoustique [physics.class-ph]

Sami Karkar, Christophe Vergez, Bruno Cochelin. Numerical tools for musical instruments acoustics: analysing nonlinear physical models using continuation of periodic solutions. Acoustics 2012, 2012, Nantes, France. ⟨hal-01342896⟩