A Passive Nonlinear Three-Port Junction Model For Fluid Mechanics and Acoustics

Victor Wetzel (1, 2) , Thomas Hélie (1, 2) , Fabrice Silva (3, 4)

1 IRCAM - Institut de Recherche et Coordination Acoustique/Musique
2 STMS - Sciences et Technologies de la Musique et du Son
3 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
4 Sons

Wind instruments can be seen as a main bore along which lateral holes are connected by the means of a three-port cavity called a junction. Here, we introduce a passive and physically interpretable model of a junction allowing for the connection of 3 resonators. It is build on a set of geometrical, fluid mechanical and thermodynamic hypotheses and uses a lumped parameter approach. The cavity is approximated by a 2D cartesian volume in which the volumetric mass density is homogeneous. From these hypotheses, we build a fluid mechanical macroscopic model, the passivity of which is guaranteed by the use of the port-Hamiltonian framework. The junction model is interpreted using a nonlinear equivalent electrical circuits and a state-space representation. From this base model, we build five different versions ranging from fluid mechanics to linear acoustics by the means of a shift method, preserving nonlinearities, and approximations (mass convection, behaviour law of the fluid).

Domaines: Acoustique [physics.class-ph]

Victor Wetzel, Thomas Hélie, Fabrice Silva. A Passive Nonlinear Three-Port Junction Model For Fluid Mechanics and Acoustics. 16ème Congrès Français d'Acoustique, CFA2022, Société Française d'Acoustique; Laboratoire de Mécanique et d'Acoustique, Apr 2022, Marseille, France. ⟨hal-03848284⟩