Simulation of vocal fold oscillation with a pseudo-one-mass physical model

This paper presents a novel ``pseudo-one-mass model'' of the vocal folds, which is derived from a previously proposed two-mass model. Two-mass models account for effects of vertical phase differences in fold motion by means of a pair of coupled oscillators that describe the lower and upper fold portions. Instead, the proposed model employs a single mass-spring oscillator to describe only the oscillation of the lower fold portion, while phase difference effects are simulated through an approximate phenomenological description of the upper glottal area. This approximate description is derived in the hypothesis that $1:1$ modal entrainment occurs between the two masses in the large-amplitude oscillation regime, and is then exploited to derive the equations of the pseudo-one-mass model. Numerical simulations of the reference two-mass model are analyzed to show that the proposed approximation remains valid when values of the physical parameters are varied in a large region of the control space. The effects on the shape of the glottal flow pulse are also analyzed. Comparison of simulations with the reference two-mass model and the pseudo-one-mass model show that the dynamic behavior of the former is accurately approximated by the latter. The similarity of flow signals synthesized with the two models is assessed in terms of four acoustic parameters: fundamental frequency, maximum amplitude, open quotient, and speed quotient. The results confirm that the pseudo-one-mass model fit with good accuracy the behavior of the reference two-mass model, while requiring significantly lower computational resources and roughly half of the mechanical parameters.