Flutter Analysis and Control for Elastic Structure in Axial Air Flow: Applications to Palatal Flutter and Energy Harvesting

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The objective of this project is to carry out a detailed analysis of a mathematical model of an elastic solid structure (a long thin rectangular plate) interacting with an axial air flow (a flow parallel to the plate?s axis), and based on the results of this analysis, to investigate the problem of a flutter control for the structure. The dynamics of the plate is governed by a system of two coupled hyperbolic partial differential equations known in aeroelasticity as the Goland model. The airflow, which is a small perturbation of a stream parallel to the main plate's axis, is assumed to be inviscid, potential, isentropic, and subsonic. The dynamics of the airflow is governed by the Euler hydrodynamic equation. Owing to the above physical assumptions, the Euler equation can be reduced to a single three-dimensional linear hyperbolic equation for the perturbation potential. This equation is coupled with the system of structural equations by a set of specific boundary conditions: (a) the flow-tangency condition, (b) the Kutta-Joukowski condition, and (c) the far-field condition. The goals of the project include the following: (a) asymptotic, spectral, and stability analysis of the model, (b) analysis of possible flutter control mechanisms, (c) generalization of linear model to the model involving nonlinear structural equations (the Dowell-Hodges model) and investigation of flutter as limit cycle oscillations. The model has two major practical applications: (a) flutter of a soft palate (the palatal flutter) resulting in snoring and sleep apnoea, (b) piezoelectric power harvesting. The project is a continuation of the PI's 12-year work on asymptotic, spectral, and stability analysis and on flutter control for aircraft wing models.Examples of solid structures interacting with an air or fluid flow include: aircraft wings and tails, suspension bridges, electric power lines, walls of blood vessels and bronchial airways, etc. The phenomenon that unites all the examples is flutter, i.e., sudden chaotic vibrations of the structure, which occur when the speed of the air or fluid flow reaches certain critical value called the utter speed. The project deals with theoretical analysis of a recently developed mathematical model of an elastic solid plate in an axial air flow (an air flow parallel to the plate's main axis). An experimental and computational investigation of the model has already begun in the scientific community. However, an importance of theoretical analysis is obvious: it can provide new insights and is necessary for a design of flutter control mechanisms. The axial flow case is more challenging than a normal flow case (the flow is perpendicular to the plate?s main axis), which occurs in all aircraft wing models. One of the two major applications of the model is medical, which deals with palatal utter: uncontrolled vibrations of a soft palate resulting in snoring and even sleep apnoae. Currently, treatments involve surgical procedures and designing anti-snoring devices. The second application is a newly emerging area of piezoelectric energy harvesting from utter vibrations. The goal of this research direction is to develop a new technology for providing alternative sources of electric power and/or recharging storage devices such as batteries or capacitors. The concept has ecological ramifications in reducing the chemical waste and potential monetary gains by significantly reducing maintenance cost.