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

轴向气流中弹性结构的颤振分析与控制：在腭颤和能量收集中的应用

• 批准号: 1211156
• 负责人: Marianna Shubov
• 金额: $ 18.5万
• 依托单位: University of New Hampshire
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-15 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1211156&HistoricalAwards=false
• 关键词: Flutter; Analysis; Control; Elastic; Structure

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.

该项目的目的是对弹性固体结构（长矩形薄板）与轴向气流（平行于板的气流？的轴），并根据这种分析的结果，研究的颤振控制的结构问题。板的动力学由两个耦合的双曲型偏微分方程组成，在气动弹性学中称为Goland模型。气流是平行于主板轴线的气流的小扰动，假定为无粘、有势、等熵和亚音速。气流的动力学由欧拉流体动力学方程控制。由于上述物理假设，欧拉方程可以简化为一个三维线性双曲方程的扰动位。该方程通过一组特定的边界条件与结构方程系统耦合：（a）流切条件，（B）库塔-儒可夫斯基条件，以及（c）远场条件。该项目的目标包括以下内容：（a）模型的渐近、谱和稳定性分析，（B）可能的颤振控制机制分析，（c）将线性模型推广到涉及非线性结构方程的模型（Dowell-Hodges模型），并研究作为极限环振荡的颤振。该模型有两个主要的实际应用：（a）软腭的颤动（腭颤动）导致打鼾和睡眠呼吸暂停，（B）压电功率采集。该项目是PI在飞机机翼模型的渐近、谱和稳定性分析以及颤振控制方面12年工作的延续。与空气或流体流相互作用的固体结构的例子包括：飞机机翼和尾翼、吊桥、电力线、血管壁和支气管气道等。所有例子的统一现象是颤振，即，结构的突然混乱振动，当空气或流体流动的速度达到称为绝对速度的某个临界值时发生。该项目涉及对最近开发的轴向气流（平行于板主轴的气流）中弹性固体板的数学模型进行理论分析。科学界已经开始对该模型进行实验和计算研究。然而，理论分析的重要性是显而易见的：它可以提供新的见解，并为颤振控制机构的设计是必要的。轴向流的情况比正常流动的情况更具挑战性（流动垂直于板？的主轴），这发生在所有的飞机机翼模型。该模型的两个主要应用之一是医学，它处理腭音：软腭的不受控制的振动导致打鼾甚至睡眠呼吸暂停。目前，治疗涉及外科手术和设计防打鼾装置。第二个应用是一个新兴的领域，压电能量收集从彻底的振动。该研究方向的目标是开发一种新技术，用于提供替代电源和/或为电池或电容器等存储设备充电。这一概念在减少化学废物方面具有生态影响，并通过显着降低维护成本来获得潜在的金钱收益。