Negative Coulomb damping, limit cycles, and self-oscillation of the vocal folds

American Journal of Physics

Volumn 74, Issue 5, 2006, Pages 386-393

  Fulcher, Lewis P ^a   Scherer, Ronald C ^a,b   Melnykov, Artem ^a   Gateva, Vesela ^a   Limes, Mark E ^a  

^a BOWLING GREEN STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CINCINNATI COLLEGE OF MEDICINE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646892868     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2173272     Document Type: Article

References (27)

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18. Our observations of the intraglottal pressures with a scaled plastic model of the glottis support this picture of intraglottal pressures higher than the pressure in the vocal tract for converging shapes and lower than that in the vocal tract for diverging shapes. Our observed intraglottal pressures for the diverging shapes do not lead to fluid forces as large as those predicted by the two-mass model, but they are large enough for the self-oscillation mechanism to operate. Guangnian Zhai (private communication).
19. R. C. Scherer, D. Shinwari, K. DeWitt, C. Zhang, B. Kucinschi, and A. Afjeh, "Intraglottal pressure profiles for a symmetric and oblique glottis with a divergence angle of 10 degrees," J. Acoust. Soc. Am. 109, 1616-1630 (2001).
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21. It is not really necessary that the intraglottal pressure be lower than the pressure of the vocal tract during the closing phase for the self-oscillation mechanism to operate. It is only necessary that it be substantially less than the intraglottal pressure during the opening phase, as noted in Ingo R. Titze, "Current topics in voice production mechanisms," Acta OtoLaryngol. 113, 421-427 (1993).
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23. The n dependence of the amplitudes in Eqs. (10)-(13) records the history of the motion, because this index indicates which half cycle has been completed. In Fig. 3 of Ref. l it is explained how the dependence of the amplitude on n is analogous to a stress-strain hysteresis.
24. H. Goldstein, C. Poole, and J. Safko, Classical Mechanics (AddisonWesley, San Francisco, 2002), pp. 489-491.
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26. The perceptive reader will recognize that the result for the maximum of Fig. 5(b) is nearer 175 ergs, about 2% lower than the value calculated from the analytic expressions. This small (and unimportant) discrepancy is a consequence of a 1% error in the numerical results for the maximum displacement, after the limit cycle has been reached. It may be removed by choosing a smaller step size.
27. F. Sean Hodge, Raymond H. Colton, and Richard T. Kelley, "Vocal intensity characteristics in normal and elderly speakers," J. Voice 15, 503-511 (2001).