[Study on the modeling of the glottic vibration: towards a nonlinear model of type stick and slip]

Mass springs models of phonation are used to describe the main behaviours observed in human voicing but their principle of functioning, based on harmonic oscillations, can appear complex.

This study has been conceived to demonstrate that a simple one mass model governed by the principle of relaxation oscillations, as already mentioned by Cornut and Lafon, can also describe, and at a reduced cost, the main behaviours of the vocal folds dynamics.

The theory of relaxation oscillations rests on the existence of phases of accumulation and release of energy. The oscillation between the two phases is self-sustained as soon as the energy source is sufficient to pass over the priming threshold. A numeric simulation allowed the testing of the model behaviour in several situations by using realistic values of the mechanic parameters of the vocal folds, the aerodynamic regimens of the subglottis pressure and of the subglottis flow.

As expected, the increasing of the mass leads to a fall of the fundamental frequency and to a rising of the vibratory amplitude of the vocal folds. The phonation threshold pressure is close to the one routinely proposed, 0.1 to 1 kPa, and increases with the fundamental frequency.

The relaxation oscillations suggest a simple and realistic model of the physical principle of the vocal cord vibration.