Dynamics of the Vocal Fold Oscillation

J.C. Lucero

Abstract


This paper presents an analysis of the dynamics of the vocal fold oscillation at phonation, using low dimensional mathematical models. It shows that the wavelike motion of the vocal fold mucosa is responsible for a transfer energy from the air flow to the tissues, which fuels the oscillation. A hysteresis effect is present at the onset-offset of the oscillation, commonly observed as different laryngeal configurations at the start and end of phonation. This phenomenon may be modeled as a combination of a Hopf bifurcation of subcritical type and a cyclic fold bifurcation between limit cycles. Finally, the analysis shows that smaller larynges have more restricted oscillation conditions, because they are less capable of absorbing energy from the airflow, in agreement with experimental results from woman and child voices.

References


[1] D.A. Berry, H. Herzel, I.R. Titze and B.H. Story, Bifurcations in excised larynx experiments, J. Voice, 10 (1996), 129-138.

J. Flanagan and L. Landgraf, Self-oscillating source for vocal-tract synthesizers, IEEE Trans. On Audio and Eletroacoustics, 16 (1968), 57-64.

H. Herzel and C. Knudsen, Bifurcation in a vocal fold model, Nonlinear Dyn., 7 (1995), 53-64.

H. Hirose and S. Niimi, The relationship between glottal opening and the transglottal pressure differences during consonant production, em “Laryngeal Function in Phonation and Respiration” (T. Baer, C. Sasaki, e K. Harris, eds.), pp. 381-390, College-Hill, Boston.

K. Ishizaka and J. L. Flanagan, Synthesis of voiced sounds from a two-mass model of the vocal folds, Bell System Technical Journal, 51 (1972), 1233-1268.

J.J. Jiang, Y. Zhang and J. Stern, Modeling of chaotic vibrations in symmetric vocal folds, J. Acoust. Soc. Am., 110 (2001), 2120-2128.

L.L. Koenig, Laryngeal factors in voiceless consonant production in men, women, and 5-year-olds, J. Speech Lang. Hear. Res., 43 (2000), 1211-1228.

J.C. Lucero, A theoretical study of the hysteresis phenomenon at vocal fod oscillation onset-offset, J. Acoust. Soc. Am., 105 (1999), 423-431 (1999).

J.C. Lucero, Dynamics of a two-mass model of the vocal folds for men, women, and children, Proceedings of the 4th International Conference on Voice Physiology and Biomechanics (2004), 191-195.

J.C. Lucero and L.L. Koenig, Simulations of VhV sequences in children, Proceedings of the 15th International Conference on Phonetic Science (2003), 2905-2908.

X. Pelorson, A. Hirschberg, R.R. van Hassel, A. P. J.Wijnands and Y. Auregan, Theoretical and experimental study of quasisteady- flow separation within the glottis during phonation. Application to a modified two-mass model, J. Acoust. Soc. Am., 96 (1994), 3416-3431.

L. Perko, “Differential Equations and Dynamical Systems”, Springer-Verlag, New York, 1991.

J.M.T. Thompson and H.B. Stewart, “Nonlinear Dynamics and Chaos”, Wiley, New York, 1996.

I.R. Titze, The physics of small-amplitude oscillation of the vocal folds, J. Acoust. Soc. Am., 83 (1988), 1536-1552.

I.R. Titze, “Principles of Voice Production”, Prentice-Hall, Englewood Cliffs, 1994.

M.A. Trevisan, M.C. Eguia and G.B. Mindlin, Nonlinear aspects of analysis and synthesis of speech time series data, Phys. Rev. E, 63 (2001), 026216.




DOI: https://doi.org/10.5540/tema.2005.06.01.0011

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.



Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia