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Title: Nonlinear stability control and lambda-bifurcation

Abstract

Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of lambda-bifurcation and a generalization of it. lambda-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter lambda. When the system parameters are in the range where flutter occurs by lambda-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized lambda-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed.

Authors:
; ; ;
Publication Date:
Research Org.:
Dept. of Engineering Sciences and Applied Mathematics, Northwestern Univ., Evanston, IL 60201
OSTI Identifier:
5733009
Resource Type:
Journal Article
Journal Name:
SIAM J. Appl. Math.; (United States)
Additional Journal Information:
Journal Volume: 47:6
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; FLUID FLOW; NONLINEAR PROBLEMS; STABILITY; AMPLITUDES; CALCULATION METHODS; CONTROL; FLOW RATE; HYDRODYNAMICS; SUPERCRITICAL STATE; FLUID MECHANICS; MECHANICS; 420400* - Engineering- Heat Transfer & Fluid Flow

Citation Formats

Erneux, T, Reiss, E L, Magnan, J F, and Jayakumar, P K. Nonlinear stability control and lambda-bifurcation. United States: N. p., 1987. Web. doi:10.1137/0147078.
Erneux, T, Reiss, E L, Magnan, J F, & Jayakumar, P K. Nonlinear stability control and lambda-bifurcation. United States. https://doi.org/10.1137/0147078
Erneux, T, Reiss, E L, Magnan, J F, and Jayakumar, P K. 1987. "Nonlinear stability control and lambda-bifurcation". United States. https://doi.org/10.1137/0147078.
@article{osti_5733009,
title = {Nonlinear stability control and lambda-bifurcation},
author = {Erneux, T and Reiss, E L and Magnan, J F and Jayakumar, P K},
abstractNote = {Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of lambda-bifurcation and a generalization of it. lambda-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter lambda. When the system parameters are in the range where flutter occurs by lambda-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized lambda-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed.},
doi = {10.1137/0147078},
url = {https://www.osti.gov/biblio/5733009}, journal = {SIAM J. Appl. Math.; (United States)},
number = ,
volume = 47:6,
place = {United States},
year = {Tue Dec 01 00:00:00 EST 1987},
month = {Tue Dec 01 00:00:00 EST 1987}
}