LUMPED PARAMETER MODELLING AND SIMULATION OF A SIMPLIFIED VOCAL APPARATUS IN THE PORT-HAMILTONIAN FRAMEWORK
Résumé
In this work, we propose a power-balanced model of the full vocal apparatus, described by passive elementary components, the connection of which accounts for fluidsolid and fluid-fluid interactions. In the larynx, we consider a potential incompressible flow of an inviscid fluid between parallel moving walls whose dynamics is reduced to a mass-spring-damper oscillator equipped with an elastic cover. The vocal tract is represented by a macroscopic lumped parameter model derived for the irrotational flow of a compressible inviscid fluid with the simplest kinematics satisfying the boundary conditions. The assembly of elements admits a representation as a constrained global port-Hamiltonian system for which we propose simulations based on a projection method that preserves the power balance. Several numerical experiments show the ability of the model to reproduce a variety of regimes according to different configurations: non oscillating regimes (no phonation), periodic regimes (typical of healthy voice) and non-periodic oscillating regimes (typical of dysphonia). These simulations are used to sketch first cartographies of regimes with respect to control parameters.
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