Numerical continuation of periodic solutions with constraints: application to a physical model of wind musical instrument

Vincent Fréour (1) , Louis Guillot (2) , Hideyuki Masuda (1) , Christophe Vergez (2) , Bruno Cochelin (2)

1 Yamaha Corporation
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

Numerical continuation using the Asymptotic Numerical Method (ANM), together with he Harmonic Balance Method (HBM), allows to follow the periodic solutions of non-linear dynamical systems such as physical models of wind instruments. This has been successfully applied to practical problems such as the categorization of musical instruments from the calculated bifurcation diagrams [2]. Nevertheless, one problem often encountered concerns the uncertainty on some parameters of the model, the values of which are set arbitrarily because too difficult to measure experimentally. In this work we propose a novel approach where constraints based on experimental measurements are added to the system, as well as the uncertain parameters of the model relaxed. This approach allows the continuation of the periodic solution with constraints to be performed, together with the calculation of the variation of the relaxed parameters along the solution branch. A successful application of this technique to a physical model of a trumpet is presented in this paper.

Domaines: Acoustique [physics.class-ph]

Vincent Fréour, Louis Guillot, Hideyuki Masuda, Christophe Vergez, Bruno Cochelin. Numerical continuation of periodic solutions with constraints: application to a physical model of wind musical instrument. 10th European Nonlinear Dynamics Conference (ENOC 2020), Jul 2022, Lyon, France. ⟨hal-03838133⟩