Large-Amplitude Oscillations of a Finite-Thickness Cantilevered Flexible Plate in Viscous Channel Flow

Abstract

The broad aim of the present work is to elucidate mechanisms of obstructive breathing disorders (snoring, sleep apnea) in which flow-induced instabilities of the soft palate feature. We use the well-established analogue system model wherein a two-dimensional flexible plate (soft palate) is mounted downstream of a rigid surface that separates upper and lower plane channel (oral and nasal tracts) flows that interact with the plate motion and then combine into a single plane channel (pharynx) flow. For this system, we take the next step towards biomechanical realism by modeling finite-amplitude motions of the flexible plate and incorporating finite thickness in its structure. The structural model makes use of a geometrically nonlinear formulation of the solid mechanics. Viscous flow is modeled at Reynolds numbers giving unsteady laminar flow. The fully-coupled fluid-structure interaction (FSI) model is developed using the open-source finite-element library oomph–lib. We first show the effects of finite amplitude and finite thickness on the in-vacuo modes of the plate through a validation study of the structural mechanics. Thereafter, we use the FSI model to illustrate both stable and unstable motions of the plate. Overall, this paper demonstrates the versatility of the new modeling approach and its suitability for characterizing the dependence of the plate's stability on the system parameters.