  Incomplete glottal closure is a laryngeal configuration wherein the glottis
is not fully obstructed prior to phonation. In this work, we introduce an
Euler-Bernoulli composite beam vocal fold (VF) model that produces
qualitatively similar incomplete glottal closure patterns as those observed in
experimental and high-fidelity numerical studies, thus offering insights in to
the potential underlying physical mechanisms. Refined physiological insights
are pursued by incorporating the beam model into a VF posturing model that
embeds the five intrinsic laryngeal muscles. Analysis of the combined model
shows that co-activating the lateral cricoarytenoid (LCA) and interarytenoid
(IA) muscles without activating the thyroarytenoid (TA) muscle results in a
bowed (convex) VF geometry with closure at the posterior margin only; this is
primarily attributed to the reactive moments at the anterior VF margin. This
bowed pattern can also arise during VF compression (due to extrinsic laryngeal
muscle activation for example), wherein the internal moment induced passively
by the TA muscle tissue is the predominant mechanism. On the other hand,
activating the TA muscle without incorporating other adductory muscles results
in anterior and mid-membranous glottal closure, a concave VF geometry, and a
posterior glottal opening driven by internal moments induced by TA muscle
activation. In the case of initial full glottal closure, the posterior
cricoarytenoid (PCA) muscle activation cancels the adductory effects of the LCA
and IA muscles, resulting in a concave VF geometry and posterior glottal
opening. Furthermore, certain maneuvers involving co-activation of all
adductory muscles result in an hourglass glottal shape due to a reactive moment
at the anterior VF margin and moderate internal moment induced by TA muscle
activation.
