Stability analysis of the human vocal cords
Charles Thompson, John W. Grant, Sharon A Starowicz · The Journal of the Acoustical Society of America · 1983
A mathematical model will be presented to describe the behavior of the vocal cords during the production of speech. The model for the folds consists of two-hinged gates which serve to modulate the flow through the glottis. The degree of flow modulation is related to the angular displacement of the gates. Equations governing the mechanical motion of the gates are derived by satisfying conservation of mass and momentum across the glottis. The introduction of acoustic impedance of the vocal tract serve to couple mechanical, acoustic, and fluid dynamic elements of the model. A linear stability analysis will be presented detailing the range of mechanical constants for which the motion of the gate will become stable. It is shown that stability of the gate motion is not dependent on the trans-glottal pressure distribution but on the acoustic-mechanical interaction.