Flutter Phenomenon in Aeroelasticity and Its Mathematical Analysis
Publication: Journal of Aerospace Engineering
Volume 19, Issue 1
Abstract
The present paper is the last part of a three-part survey paper, in which I give a review of several research directions in the area of mathematical analysis of flutter phenomenon. Flutter is known as a structural dynamical instability, which 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 paper is a collection of models of fluid-structure interaction, for which precise mathematical formulations are available. My main interest is in the analytical results on such models: the results that can be used to explain flutter and its qualitative and even quantitative treatments. This study does not pretend to be a comprehensive review of an enormous 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. In this paper, I concentrate on the most well-known cases of flutter, i.e., flutter in aeroelasticity. Namely, I discuss aircraft flutter in historical retrospective and outline some future directions of flutter analysis. The last two sections of the paper are devoted to the precise analytical results obtained in my several recent works on a specific aircraft wing model in a subsonic, inviscid, incompressible airflow. I also mention that in the previous papers (Parts I and II of the survey), I discuss such topics as: (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.
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Acknowledgments
Partial support by the National Science Foundation Grants Nos. NSFECS 0080441, NSFDMS 0072247, and the Advanced Research Program-01 of Texas Grant No. UNSPECIFIED0036-44-045 is highly appreciated by the writer.
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Information
Published In
Journal of Aerospace Engineering
Volume 19 • Issue 1 • January 2006
Pages: 1 - 12
Copyright
© 2006 ASCE.
History
Received: Dec 13, 2002
Accepted: Dec 8, 2004
Published online: Jan 1, 2006
Published in print: Jan 2006
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