1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Physical mechanisms of phonation onset: A linear stability analysis of an aeroelastic continuum model of phonation
Rent:
Rent this article for
USD
10.1121/1.2773949
/content/asa/journal/jasa/122/4/10.1121/1.2773949
http://aip.metastore.ingenta.com/content/asa/journal/jasa/122/4/10.1121/1.2773949
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The two-dimensional vocal fold model and the glottal channel. The flow direction is along the positive z axis. The coupled vocal folds-flow system was assumed to be symmetric about the glottal channel centerline so that only the left half of the system was considered in this study. is the vocal fold depth in the medial-lateral direction; and are the thicknesses of the vocal fold in the superior and inferior sections in the flow direction, respectively; is the prephonatory glottal channel width; is the prephonatory glottal half width in the superior part of the glottal channel; and are the vertical coordinates of the outlet and inlet of the glottal channel, respectively.

Image of FIG. 2.
FIG. 2.

(Color online) The frequencies and growth rates of the first six eigenvalues (: first; : second; : third; : fourth; : fifth; : sixth) of Eq. (23) as a function of the matrix orders of Eq. (23). The values of model parameters specified in Eq. (28) were used, with a loss factor of 0.1. The order of the matrices in Eq. (23) equals . , 4, 5, and 6 for the four sets of data shown.

Image of FIG. 3.
FIG. 3.

(Color online) The first three in vacuo eigenmodes of the vocal fold, for model parameters specified in Eq. (28). The first and second rows show the component (medial-lateral direction) and component (inferior-superior direction) of the eigenmodes, respectively.

Image of FIG. 4.
FIG. 4.

(Color online) The frequencies and growth rates of the first three eigenvalues (– –: first; —-: second; -.-.-: third) of the coupled fluid-structure system as a function of the jet velocity. The vertical line indicates the point of onset. Model parameters specified in Eq. (28) were used. Only the flow stiffness term of the three flow-induced terms was included in Eq. (22). Figures 4(a) and 4(b): , the corresponding eigenvalue movement in the complex half plane is shown in Fig. 5(a); Figs. 4(c) and 4(d): , the corresponding eigenvalue movement in the complex half plane is shown in Fig. 5(b).

Image of FIG. 5.
FIG. 5.

(Color online) Movement of the second and third eigenvalues in half complex plane. Model parameters specified in Eq. (28) were used. (a) with only the flow stiffness term of the three flow-induced terms included, ; (b) with only the flow stiffness term of the three flow-induced terms included, ; (c) with all three flow-induced terms included, ; (d) with all three flow-induced terms included, ; : in vacuo eigenvalues; : eigenvalues before onset; : eigenvalues after onset. The arrows indicate the direction of the movement of the eigenvalues as the jet velocity increases. The vertical lines indicate the imaginary axis.

Image of FIG. 6.
FIG. 6.

(Color online) Vibration patterns of the FSI-1 (left) and FSI-2 (right) modes at onset for case shown in Fig. 5(a) (, model parameters given by Eq. (28), ). The first and second rows show the component (medial-lateral direction) and component (inferior-superior direction) of the eigenmodes, respectively.

Image of FIG. 7.
FIG. 7.

(Color online) The vocal fold velocity in medial-lateral and inferior-superior directions and the flow pressure along the vocal fold surface corresponding to the FSI-1 and FSI-2 modes as shown in Fig. (6). —-: real part; : imaginary part.

Image of FIG. 8.
FIG. 8.

(Color online) Distribution of total energy flow into the vocal fold along the vocal fold surface and its decomposition into contributions of two self-mode and two cross-mode interaction terms for the case shown in Fig. 5(a) (model parameters given in Eq. (28), , and , slightly above onset). See Eqs. (32) and (33) for the definition of different energy terms.

Image of FIG. 9.
FIG. 9.

(Color online) Correlation between the FSI-1 mode (a) and FSI-2 mode (b) and the first four in vacuo eigenmodes (: first; : second; : third; : fourth in vacuo eigenmodes), relative energy weights of the two FSI modes (c) and normalized contributions to the total energy flow by individual interaction terms (d) as a function of the structural loss factor. Model parameters were given in Eq. (28), .

Image of FIG. 10.
FIG. 10.

(Color online) Onset jet velocity (top) and frequency (bottom) as a function of the structural loss factor, for model parameters given in Eq. (28). : ; : . The two horizontal lines indicate the second and third in vacuo eigenfrequencies.

Image of FIG. 11.
FIG. 11.

(Color online) The frequencies and growth rates of the first three eigenmodes ( : first; —–: second; -.-.-: third) as a function of the jet velocity for three cases in which all three flow terms were included . (a-b): model parameters given by Eq. (28), ; (c-d): model parameters given by Eq. (28) except that , ; (e-f): model parameters given by Eq. (28), . The vertical lines indicate point of onset.

Image of FIG. 12.
FIG. 12.

(Color online) Onset jet velocity (top) and frequency (bottom) as a function of the length of the entrance section , for model parameters given in Eq. (28), for . The two solid lines indicate the second and third in vacuo eigenfrequencies.

Image of FIG. 13.
FIG. 13.

(Color online) Correlation between the FSI-1 mode (a) and FSI-2 mode (b) and the first four in vacuo eigenmodes (: first; : second; : third; : fourth in vacuo eigenmodes), relative energy weights of the two FSI modes (c), and normalized contributions to the total energy flow by individual interaction terms (d) as a function of the structural loss factor. Model parameters were given in Eq. (28), .

Image of FIG. 14.
FIG. 14.

(Color online) Comparison between the two FSI modes and the first two EEFs of the vibration dynamics along the vocal fold surface. In each subfigure, the left half is the EEF while the right half is the FSI mode. —-: equilibrium positions; : maximum or minimum displacement of the eigenfunctions superimposed on the equilibrium projections. Model parameters given in Eq. (28), , .

Loading

Article metrics loading...

/content/asa/journal/jasa/122/4/10.1121/1.2773949
2007-10-01
2014-04-25
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Physical mechanisms of phonation onset: A linear stability analysis of an aeroelastic continuum model of phonation
http://aip.metastore.ingenta.com/content/asa/journal/jasa/122/4/10.1121/1.2773949
10.1121/1.2773949
SEARCH_EXPAND_ITEM