Reproducing laryngeal mechanisms with a two-mass model Denisse Sciamarella, Christophe d’Alessandro LIMSI-CNRS, BP 133, F91403, Orsay France denisse@limsi.fr, cda@limsi.fr Abstract Evidence is produced for the correspondence between the oscil- lation regimes of an up-to-date two-mass model and laryngeal mechanisms. Features presented by experimental electroglot- tographic signals during transition between laryngeal mecha- nisms are shown to be reproduced by the model. 1. Introduction One of the main challenges in voice-production research has for long been the construction of a deterministic physical model which could describe the different mechanisms characterising vocal-fold motion as well as their acoustic correlate. The essential features in the behavior of the glottal source have been reasonably described by a series of simplified vocal- fold models which are apt for real time speech synthesis and which have followed and improved the pioneering 1972 Ishizaka and Flanagan’s model [1]. In this kind of lumped models, self-sustained vocal-fold oscillations are attributed to a varying glottal geometry that creates different intraglottal pres- sure distributions during the opening and closing phases of the vocal-fold oscillation cycle. The non-uniform deformation of vocal-fold tissue is assured by a mechanical model having at least two degrees of freedom. For this reason, the most simple lumped vocal-fold models are known as two-mass models. A systematic acoustic study of the traditional Ishizaka and Flanagan’s two-mass model has shown that vocal-fold dynam- ics could present distinct oscillation regimes which could be associated to what is known as laryngeal mechanisms of voice production [2]. A laryngeal mechanism is defined as a phona- tion mode associated to a particular glottal configuration, which is characterized by the effective mass, largeness and length of the vocal cords taking part in vibration, as well as by muscu- lar tension. The question of laryngeal mechanism reproduction with simple vocal-fold models is of great importance in vocal- fold modeling research, since it constitutes a well-known acous- tic phenomenon in direct connection with vocal-fold motion. This article revisits the problem of laryngeal mechanism re- production, in the context of a recently proposed symmetrical two-mass model which includes an up-to-date aerodynamic de- scription of the flow through the glottis. A brief description of the production model will be given in section . The method used to compute vocal-fold contact area from this production model will also be precised, since this will allow confrontation of the model predictions with certain features observed in exper- imental electroglottograms during transition between laryngeal mechanisms. The procedure used to identify different oscilla- tion regimes is outlined in section . Results concerning oscil- lations regimes will be presented in section . Section will concentrate on transitions between regimes. Conclusions will be presented in section . 2. The vocal-fold two-mass model For vocal-fold motion simulation, we will be using the model implemented by Niels Lous et al in 1998 [3]. This two-mass model assumes that the vocal-fold geometry is described by a couple of three mass-less plates as shown in figure 1. The model considers a two-dimensional structure with the third dimension taken into account by assuming vocal folds have a largeness . As usual, symmetry is assumed with respect to the flow channel axis. The flow channel height is a piecewise linear function (see figure 1) determined by : k 1 k 2 k c r 1 r 2 h 0/2 y 1=h 1/2 y 2=h 2 /2 h 3/2 symmetry axis vocal tract h c trachea x 0 x 1 x s x 2 x 3 separation: jet p0 U g p s p 3 d Lg Figure 1: Geometrical structure of the symmetrical two-mass model. (1) where and and are constant. The main flow through the glottis is approximated by a quasi-stationary, inviscid, locally incompressible, and quasi- parallel flow from the trachea up to a point where the flow separates from the wall to form a free jet. The turbulence in the free jet introduces the necessary dissipation to obtain the glot- tal flow modulation caused by the movement of the vocal folds. Further details concerning the computation of from a sim- ple geometrical flow-separation model can be found in [3]. In figure 1, is the critical height at which mechanical contact is assumed to take place. Actual contact between vocal cords takes place when . Thus, the instantaneous con- tact area during vocal-fold motion simulation can be computed as follows: (2) EUROSPEECH 2003 - GENEVA 1