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首页> 外文期刊>Journal of aerospace engineering >Mathematical Modeling and Analysis of Flutter in Bending-Torsion Coupled Beams, Rotating Blades, and Hard Disk Drives
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Mathematical Modeling and Analysis of Flutter in Bending-Torsion Coupled Beams, Rotating Blades, and Hard Disk Drives

机译：弯扭耦合梁，旋转刀片和硬盘驱动器中颤振的数学建模和分析

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In this study I present a review of several research directions in the area of mathematical analysis of flutter phenomenon. Flutter is known as a structural dynamical instability that occurs in a solid elastic structure interacting with a flow of gas or fluid, and consists of violent vibrations of the structure with rapidly increasing amplitudes. The focus of this review is a collection of models of fluid-structure interaction, for which precise mathematical formulations are available. The main objects of interest are analytical results on such models, which can be used for flutter explanation, its qualitative and even quantitative treatments. This paper does not pretend to be a comprehensive review of the enormous amount of engineering literature on analytical, computational, and experimental aspects of the flutter problem. I present a brief exposition of the results obtained in several selected papers or groups of papers on the following topics: (1) bending-torsion vibrations of coupled beams; (2) flutter in transmission lines; (3) flutter in rotating blades; (4) flutter in hard disk drives; (5) flutter in suspension bridges; and (6) flutter of blood vessel walls. Finally, I concentrate on the most well-known case of flutter, i.e., flutter in aeroelasticity. The last two sections of this review are devoted to the precise analytical results obtained in my several recent papers on a specific aircraft wing model in a subsonic, inviscid, incompressible airflow.
机译：在这项研究中，我对颤振现象的数学分析领域中的几个研究方向进行了综述。颤振被称为结构动力学不稳定性，它发生在与气体或流体流相互作用的固体弹性结构中，并由振幅急剧增加的剧烈振动组成。这篇综述的重点是流体-结构相互作用模型的集合，为此可以使用精确的数学公式。感兴趣的主要对象是此类模型的分析结果，可用于抖动解释，定性甚至定量处理。本文并不假装是对颤振问题的分析，计算和实验方面的大量工程文献的全面综述。我对以下主题的几篇论文或几组论文中的结果进行了简要说明：（1）耦合梁的弯曲扭转振动； （2）传输线抖动； （3）旋转叶片颤振； （4）硬盘驱动器抖动； （5）悬索桥颤振； （6）血管壁的扑动。最后，我将重点介绍最著名的颤振情况，即气动弹性颤振。这篇评论的最后两节专门介绍了我最近在几篇论文中获得的关于亚音速，无粘性，不可压缩气流中特定飞机机翼模型的精确分析结果。

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