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              <p>The most common type of human snoring is characterized by vibrations of the soft-palate, induced by passing air during respiration. Despite being a widespread disorder, its occurrence is poorly understood and, consequently, clinical treatment is often ineffective. This physical system can be characterized, in its essence, by a cantilevered beam subjected to axial flow in a confined passage. These type of fluid-structure interaction systems have been a subject of research for many years, as its fundamental behavior is found in many other practical applications. Most studies are concerned solely with the conditions for linear stability and do not explore the ensuing nonlinear behavior of the system. This is particularly delicate as fluttering beams in confined flows are known to often result in dynamics with intermittent impacts between the beam and the side-walls. Here we present a nonlinear analytical resolution to a simplified 1-D model, based on a modal beam and bulk-flow equations. The model accounts for dissipation through distributed (frictional) and localized head-loss terms. The latter are imposed at the boundary conditions and aims to describe the complex effects occurring outside the domain (turbulence, vortex shedding, etc.). The present analytical resolution leads to a compact system for linear stability analysis, but also to a nonlinear formulation of the fluid-structure interaction. The inclusion of a regularized contact model allows for the computation of the full nonlinear dynamics, including intermittent impacts. Linear stability results are compared to previously published results using 2-D CFD models, and the relative merits of the model are discussed. A series of limit cycles with intermittent impacts between the beam and side-walls are presented to illustrate the nature of the postinstability oscillations. To the authors knowledge, the proposed formulation presents, for the first time, a framework for the comprehensive understanding of the nonlinear dynamics associated with flexible beams in confined axial flow.</p>
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