Research Papers

Bifurcation Forecasting for Large Dimensional Oscillatory Systems: Forecasting Flutter Using Gust Responses

[+] Author and Article Information
Amin Ghadami

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: aghadami@umich.edu

Bogdan I. Epureanu

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: epureanu@umich.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 26, 2016; final manuscript received June 6, 2016; published online July 22, 2016. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 11(6), 061009 (Jul 22, 2016) (8 pages) Paper No: CND-16-1035; doi: 10.1115/1.4033920 History: Received January 26, 2016; Revised June 06, 2016

Forecasting bifurcations is a significant challenge and an important need in several applications. Most of the existing forecasting approaches focus on bifurcations in nonoscillating systems. However, subcritical and supercritical flutter (Hopf) bifurcations are very common in a variety of systems, especially fluid–structural systems. This paper presents a unique approach to forecast (nonlinear) flutter based on observations of the system only in the prebifurcation regime. The proposed method is based on exploiting the phenomenon of critical slowing down (CSD) in oscillating systems near certain bifurcations. Techniques are introduced to enhance the prediction accuracy for cases of low-frequency oscillations and large-dimensional dynamical systems. The method is applied to an aeroelastic system responding to gust loads. Numerical results are provided to demonstrate the performance of the method in predicting the postbifurcation regime accurately in both supercritical and subcritical cases.

Copyright © 2016 by ASME
Topics: Bifurcation
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Fig. 1

Schematic of the response of the system during the recovery from a perturbation

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Fig. 2

Recovery rate versus bifurcation parameter and the value obtained for the forecasted μ̃

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Fig. 3

Forecasted bifurcation diagram

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Fig. 4

Schematic of a system recovery with oscillations

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Fig. 5

Eigenvalues of the fixed point at the origin as a function of the bifurcation parameter

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Fig. 6

Two-degrees-of-freedom aeroelastic model showing an airfoil of chord 2b, its aeroelastic axis (EA), its center of mass (CG) (at a distance xab from the EA), and the pitch and plunge coordinates α and h

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Fig. 7

Gust wind speed for the (1 − cos) type gust model used

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Fig. 8

λ versus LCO amplitude for different flow speed values

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Fig. 9

λ versus flow speed U* for prediction of postbifurcation regime for several pitch amplitudes

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Fig. 10

Forecasted bifurcation diagrams (*) for (a) pitch and (b) plunge displacements in a supercritical case

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Fig. 11

Forecasted (*) and exact (-) pitch bifurcation diagram without applying modal decomposition

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Fig. 12

Comparison between system gust response for (a) pitch and (b) plunge displacements before (solid line) and after (dashed line) modal decomposition

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Fig. 13

Forecasted (*) and exact (-) bifurcation diagram for (a) pitch and (b) plunge displacements in subcritical case

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Fig. 14

Forecasted (*) and exact (-) bifurcation diagram for (a) pitch and (b) plunge displacements in subcritical case for larger perturbations




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