Instability of an Elastic Strip Hanging in an Airstream

Datta, S. K.; Gottenberg, W. G.

doi:10.1115/1.3423515

Cited by 62 publications

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“…Datta & Gottenberg 1975;Lemaitre et al 2005) and if H L the problem can be treated as two-dimensional (as done by Kornecki et al 1976;Huang 1995;Watanabe et al 2002a;Guo & Païdoussis 2000). In this latter case, the flow is entirely described by point-vortices which are distributed within the plate and possibly in its wake.…”

Section: Introductionmentioning

confidence: 99%

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Aeroelastic instability of cantilevered flexible plates in uniform flow

et al. 2008

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We address the flutter instability of a flexible plate immersed in an axial flow. This instability is similar to flag flutter and results from the competition between destabilising pressure forces and stabilising bending stiffness. In previous experimental studies, the plates have always appeared much more stable than the predictions of two-dimensional models. This discrepancy is discussed and clarified in this paper by examining experimentally and theoretically the effect of the plate aspect ratio on the instability threshold. We show that the two-dimensional limit cannot be achieved experimentally because hysteretical behaviour and three-dimensional effects appear for plates of large aspect ratio. The nature of the instability bifurcation (sub-or supercritical) is also discussed in the light of recent numerical results. IntroductionThe flutter of a flexible plate immersed in an axial flow is a canonical example of flowinduced vibrations. This instability can be experienced in everyday life when one observes a flag flapping in the wind. Because this phenomenon appears in many applications (paper industry, airfoil flutter, snoring), it has motivated a large literature which has been recently reviewed by Païdoussis (2004). This instability can be regarded as a competition between fluid forces and elasticity. Indeed, when the plate experiences a small lateral deflection, a destabilising pressure jump can appear across the plate, while the bending stiffness tends to bring the plate back to the stable planar state.This system can be studied by restricting the analysis to one-dimensional flutter modes as observed in most experiments. In this case, the plate motion obeys the Euler-Bernoulli beam equation with additional pressure forces which are calculated by assuming a potential flow. To simplify the problem further, Shelley et al. (2005) considered a plate infinite in both directions in a similar way to the stability analysis of a jet by Lord Rayleigh (1879) who already noted in his seminal paper the analogy with the problem of flag flutter.In other theoretical studies, the plate length L (or chord) takes a finite value while two asymptotic limits are considered for its span H. If H L, the fluid forces can be calculated using the slender body theory of Lighthill (1960) (e.g. Datta & Gottenberg 1975Lemaitre et al. 2005) and if H L the problem can be treated as two-dimensional (as done by Kornecki et al. 1976;Huang 1995;Watanabe et al. 2002a;Guo & Païdoussis 2000). In this latter case, the flow is entirely described by point-vortices which are distributed within the plate and possibly in its wake. It is known from airfoil theory that this problem does not admit a unique solution (intrinsically because the Laplace equation has to be solved on an open domain). Kornecki et al. (1976) used two approaches to arXiv:0804.0774v2 [physics.flu-dyn]

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Section: Introductionmentioning

confidence: 99%

“…A few years later, Datta & Gottenberg (1975) carried out experiments with long ribbons hanging in airflow. This slender body limit (H L) has been reexamined recently by Lemaitre et al (2005) and results show good agreement with linear stability analysis.…”

Section: Introductionmentioning

confidence: 99%

Aeroelastic instability of cantilevered flexible plates in uniform flow

et al. 2008

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“…For large aspect ratios, a two-dimensional analysis is relevant, and Kornecki et al (1976) were the first to show that the flow around the plate can be modelled using unsteady airfoil theory. When the plate aspect ratio is asymptotically small however, the aerodynamic forces can be modelled using slender-body theory (Datta & Gottenberg 1975;Lemaitre et al 2005). The studies in these two asymptotic limits have been recently generalised by Eloy et al (2007) and Doaré et al (2011) who considered intermediate aspect ratios and confinement effects.…”

Section: Introductionmentioning

confidence: 99%

“…Since the pioneering study of Taneda (1968), different groups have performed experiments on the flag instability either for small aspect ratios (Datta & Gottenberg 1975;Lemaitre et al 2005) or for moderate to large aspect ratios (Zhang et al 2000;Tang et al 2003;Eloy et al 2008, among others). In this latter case, a large hysteresis is always observed at threshold or, said differently, the motionless state and the flapping state coexist and are both stable over a large range of airflow velocities.…”

Section: Introductionmentioning

confidence: 99%

The origin of hysteresis in the flag instability

2011

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The flapping flag instability occurs when a flexible cantilevered plate is immersed in a uniform airflow. To this day, the nonlinear aspects of this aeroelastic instability are largely unknown. In particular, experiments in the literature all report a large hysteresis loop, while the bifurcation in numerical simulations is either supercritical or subcritical with a small hysteresis loop. In this paper, this discrepancy is addressed. First weakly nonlinear stability analyses are conducted in the slender-body and two-dimensional limits, and second new experiments are performed with flat and curved plates. The discrepancy is attributed to inevitable planeity defects of the plates in the experiments.

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“…10) That problem is similar to the present one, but the present problem differs from that of Ref. 10 because the equation of motion in that reference is the fourth order linear partial differential equation with the variable coefficient resulting from the gravity force.…”

Section: Introductionmentioning

confidence: 43%

Flutter of Fixed-Free Elastic Strip in Uniform Flow.

Yamamoto¹

2001

Trans. Japan Soc. Aero. S Sci.

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The dynamic instability of a slender front-fixed-aft-free elastic strip in a uniform airflow is studied analytically. The analysis is performed by using the unsteady slender body aerodynamic theory and the beam theory. The analysis reveals that flutter may occur as a result of coupling between the first and second bending oscillation modes as a result of aerodynamic force when the flow speed overcomes the critical speed. One approximate method is derived, and the flutter speed, mode, and frequency are examined numerically. These approximate results are compared with other approximate ones derived by the two-term Galerkin method. And when the virtual-air-mass to strip mass ratio is sufficiently small, the flutter speed by the present method coincides with that by the two-term Galerkin method.

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Instability of an Elastic Strip Hanging in an Airstream

Cited by 62 publications

References 0 publications

Aeroelastic instability of cantilevered flexible plates in uniform flow

Aeroelastic instability of cantilevered flexible plates in uniform flow

The origin of hysteresis in the flag instability

Flutter of Fixed-Free Elastic Strip in Uniform Flow.

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