MAC HYMAN
Los Alamos National Laboratory
http://math.lanl.gov/~mac
mac@t7.lanl.gov
Abstract:
We propose and simulate a new model the self-oscillating
acoustic behavior of the human vocal folds that are the sound
source for human speech. By increasing our understanding of
the aerodynamics of the air flow in the larynx and the vocal
tract we can improve our understanding of the complex
dynamical process of human voice production and provide new
insights into treating speech disorders. In the model, a tube
with variable elastic cross-sectional area represents the
vocal tact and the air flow is approximated by a compressible
inviscid equations of gas dynamics in a variable area flexible
tube. The approximating system of partial differential
equations couples one dimensional isentropic gas dynamic
equations with an elastic damped-driven wave equation to model
the vocal fold motion. We will illustrate numerical
simulations of the model that reproduce the rapid opening and
closing of the vocal folds modulating the rapidly pulsating
air pulses that create the vibrational sound in the glottis.
For a nearly flat fold, we analyze the linearized equations and
found a condition for the existence of small amplitude oscillations.
For a fixed Mach number less than one (subsonic), this condition
requires the flow pressure and velocity to be above a minimum value set by
an elastic modulus; and also the presence of a small fluid viscosity
for a given fold damping constant, reminiscent of the
known subsonic flutter anomaly.
We compare the numerical simulations, the mathematical
analysis and experimental data to demonstrate that this approach
yields an accurate simulation model of vocal fold dynamics.