Port-Hamiltonian Representation of Dynamical Systems. Application to Self-Sustained Oscillations in the Vocal Apparatus

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

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 Sons
3 STMS - Sciences et Technologies de la Musique et du Son

Phonation is a natural example of nonlinear dynamical system with self-sustained oscillations, here resulting from the controlled nonlinear coupling between the deformable vocal folds and the airflow expired from the lungs through the glottis and the vocal tract. As a proof of concept, we propose a minimal model of the full vocal apparatus using the port-Hamiltonian representation that emphasises on the structure of a system (on the separation between the behaviour of the subsystems and their interconnection) and on the power exchanges. Numerical results on bifurcations are qualitatively discussed in relation to voice pathologies.

Domaines: Vibrations [physics.class-ph]; Acoustique [physics.class-ph]; Biomécanique [physics.med-ph]

Fabrice Silva, Thomas Hélie, Victor Wetzel. Port-Hamiltonian Representation of Dynamical Systems. Application to Self-Sustained Oscillations in the Vocal Apparatus. 7th Int. Conf. on Nonlinear Vibrations, Localization and Energy Transfer, Jun 2019, Marseille, France. pp.ISBN 978-2-909669-26-7. ⟨hal-03020400⟩