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Research Papers

Flutter Control of a Two-Degrees-of-Freedom Airfoil Using a Nonlinear Tuned Vibration Absorber

[+] Author and Article Information
Arnaud Malher

IMSIA (Institute of Mechanical Sciences and
Industrial Applications),
ENSTA ParisTech—CNRS—EDF—CEA,
Université Paris-Saclay,
828 Bd des Maréchaux,
Palaiseau Cedex 91732, France
e-mails: arnaud.malher@ensta-paristech.fr,
arnaud.malher@gmail.com

Cyril Touzé

IMSIA (Institute of Mechanical Sciences
and Industrial Applications),
ENSTA ParisTech—CNRS—EDF—CEA,
Université Paris-Saclay,
828 Bd des Maréchaux,
Palaiseau Cedex 91732, France

Olivier Doaré

IMSIA (Institute of Mechanical Sciences and
Industrial Applications),
ENSTA ParisTech—CNRS—EDF—CEA,
Université Paris-Saclay,
828 Bd des Maréchaux,
Palaiseau Cedex 91732, France

Giuseppe Habib, Gaëtan Kerschen

Space Structures and Systems Laboratory,
Department of Aerospace and
Mechanical Engineering,
University of Liège,
Liège 4000, Belgium

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 28, 2016; final manuscript received February 14, 2017; published online May 4, 2017. Assoc. Editor: Bogdan I. Epureanu.

J. Comput. Nonlinear Dynam 12(5), 051016 (May 04, 2017) (11 pages) Paper No: CND-16-1456; doi: 10.1115/1.4036420 History: Received September 28, 2016; Revised February 14, 2017

The influence of a nonlinear tuned vibration absorber (NLTVA) on the airfoil flutter is investigated. In particular, its effect on the instability threshold and the potential subcriticality of the bifurcation is analyzed. For that purpose, the airfoil is modeled using the classical pitch and plunge aeroelastic model together with a linear approach for the aerodynamic loads. Large amplitude motions of the airfoil are taken into account with nonlinear restoring forces for the pitch and plunge degrees-of-freedom. The two cases of a hardening and a softening spring behavior are investigated. The influence of each NLTVA parameter is studied, and an optimum tuning of these parameters is found. The study reveals the ability of the NLTVA to shift the instability, avoid its possible subcriticality, and reduce the limit cycle oscillations (LCOs) amplitude.

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Figures

Grahic Jump Location
Fig. 1

Sketch of the two degrees-of-freedom airfoil (main structure) coupled with the NLTVA (absorber)

Grahic Jump Location
Fig. 2

Reduced flutter velocity given by the Routh–Hurwitz criterion as a function of the NLTVA-reduced eigenfrequency γ, and for a damping ratio ζ = 0.15. The gray area corresponds to the stability of the system.

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Fig. 3

Cartography of the reduced flutter velocity given by the criterion e5 as a function of the NLTVA-reduced frequency γ and damping ratio ζ

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Fig. 4

Evolution of the optimal flutter velocity gain GŨf caused by the NLTVA versus xα, rα2, and Ω2

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Fig. 5

Estimation of GŨf using the fitted parameters ζoptfit and γoptfit versus xα, rα2 and Ω2

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Fig. 6

Bifurcation diagram of pitch and plunge mode for the system without absorber (a) and (b) and in the presence of an NLTVA without nonlinearities (c) and (d)

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Fig. 7

Bifurcation diagram of (a) pitch and (b) plunge mode for four increasing values of ξ. The solid lines correspond to the stable solutions and the dashed line to the unstable ones. LP stands for limit point and NS for Neimark–Sacker bifurcation point.

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Fig. 8

Influence of the NLTVA with ξ = 0 and ξ = 0.217 on the bifurcation diagram of the 2dofs airfoil

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Fig. 9

Time series simulations corresponding to Fig. 8 with and without absorber at Ũ=1.1 (a)–(c) and Ũ=1.4 (d)–(f). The NLTVA is set such as ξ = 0.217. The initial conditions are equal to zero except for the initial amplitude of the pitch mode, which is set equal to α(0) = 10 deg for (a)–(c) and to α(0) = 6.10−3 deg for (d)–(f).

Grahic Jump Location
Fig. 10

Bifurcation diagram of (a) and (c) pitch and (b) and (d) plunge mode for increasing values of ξ. The solid lines correspond to the stable solutions and the dashed line to the unstable ones. The plots (c) and (d) detail the bifurcation diagram around the criticality for ξ ≥ −0.15. LP stands for limit point and NS for Neimark–Sacker bifurcation point.

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