Surface waves in layered structures with application to vocal-fold vibration

Abstract

The initiation of surface waves over a layered structure, including an air channel, a thin elastic layer, an inviscid waterlike fluid, and an impedance boundary, is discussed. This structure is a rudimentary picture of the vocal folds near the edges. The initiation of surface waves at the interface between the air and elastic layer is similar to the problems of initiation of wind waves over water and the flutter of panels. Early linear analyses of surface wave initiation considered Kelvin-Helmholtz instability, a static instability, and the use of Jeffreys' sheltering coefficient as a destabilizing mechanism for a dynamic instability. Both static and dynamic instabilities are possible in vocal-fold vibration. However, the dynamic type of instability is the mechanism that usually is operable in a layered structure model of vocal-fold vibration, although Jeffreys' sheltering coefficient does not provide the correct term for negative damping. This is confirmed by the lumped element two-mass model, a very successful model for simulating some aspects of vocal-fold vibration [K. Ishizaka and J. L. Flanagan, Bell Syst. Tech. J. 51, 1233 (1968)]. The two-mass model also illustrates how to incorporate dynamic pressure loss into the layered structure approach to account for the negative stiffness. The layered structure approach has the advantage of allowing for testing of the effects of changing the mechanical properties of various histological layers on the initiation of the surface wave. [Work supported by NIH grants HD-1994, NS-13870, and NS-13617 to Haskins Laboratories.]