| Abstract | Some aspects of the continuum mechanics of phonation are described here. Why should we be interested in mechanics, either fluid or solid? Further, why should we be interested in continuum mechanics? Consider the two-mass model as an example of a mechanical model in regards to the first question. This is a mechanical model because the input and output parameters are mechanical parameters and physical laws are used to relate them. The two-mass model illustrates the mechanically parameters and physical laws are used to relate them. The two-mass model illustrates the mechanically important energy flow and stability properties. Other kinds of models, perhaps of the vocal tract or of the larynx itself, are important in other contexts to tell us that a model is possible in complicated situations. For instance, it may be too complicated to explain the control of the vocal tract, or even the larynx, using a physically based model. Here, more abstract control models provide “existence proofs” for lawful behaviour.
The continuum approach to mechanics should be pursued because it can bring us closer to physically measurable quantities than can lumped-element models. Continuum mechanics treats materials, like air, as though their parameters, such as density and velocity, vary continuously in space. The smallest spatial scale studied is much larger than the molecular scale. For instance, the Young’s modulus of the epithelium can be measured (Titze and Durham, 1987) and predictions made based on a continuum model, as in certain numerical simulations. It is more difficult to relate the physically measurable quantities to a lumped-element model, like the two-mass model.
Following energy flow and being aware of stability properties in the larynx tells us the nature of the sound and the conditions under which sound is produced. We want to know under what conditions the folds will oscillate, or the instability of the open folds under the influence of air flow. When the folds are vibrating, we want to know how much energy is being absorbed by the folds, and how much of the energy that is left in the air will actually contributed to acoustic output. (Some of the energy travelling through the solid or travelling in the air in a nonacoustic mode can later be reiated as sound. ) A knowledge of the instability of the air motion itself well tell us how much energy of ar motion becomes predominatly nonacoustic turbulent energy. In the first part of this paper, the issues of energy balance and stability in air will be discussed, supposing that the folds are given sufficient energy to oscillate. The mechanics of the mucousal wave will be considered in the second part of the paper. Again, stability and energy balance are the central issues. |
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