On the stability of two-dimensional membrane wings
TL;DR: In this paper, the stability of two-dimensional membrane wings is studied by an analytical solution, obtained for inviscid incompressible flow, where the membrane is assumed to be extensible and of small camber, with constant tension along the membrane.
About: This article is published in Journal of Fluids and Structures.The article was published on 2017-05-01. It has received 25 citations till now. The article focuses on the topics: Membrane & Airfoil.
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TL;DR: In this article, a multi-functional wind barrier integrated by manifold triboelectric nanogenerator (TENG) units is proposed and investigated, which consists of two copper electrodes and one strip of fluorinated ethylene propylene (FEP) membrane.
56 citations
TL;DR: In this article, the authors study the large-amplitude flutter of membranes with vortex sheet wakes in two-dimensional inviscid fluid flows and apply small initial deflections and track their exponential decay or growth and subsequent large amplitude dynamics in the space of three dimensional parameters: membrane pretension, mass density and stretching modulus.
Abstract: We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex sheet wakes in two-dimensional inviscid fluid flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free to move in the transverse direction, the membranes flutter periodically at intermediate values of mass density. As mass density increases, the motions are increasingly aperiodic, and the amplitudes increase and spatial and temporal frequencies decrease. As mass density decreases from the periodic regime, the amplitudes decrease and spatial and temporal frequencies increase until the motions become difficult to resolve numerically. With both edges free to move in the transverse direction, the membranes flutter similarly to the fixed–free case, but also translate vertically with steady, periodic or aperiodic trajectories, and with non-zero slopes that lead to small angles of attack with respect to the oncoming flow.
21 citations
16 citations
TL;DR: An overview of recent developments in the understanding of membrane wing aerodynamics is presented, focusing on the dynamic aeroelasticity of membrane wings in steady flow conditions, with special focus on the physical mechanisms that drive membrane oscillations and the aerodynamic benefits of such oscillations.
15 citations
TL;DR: In this article, the dynamic stability of a two-dimensional membrane wing in laminar steady flow is studied, with a focus on the role of membrane mass. But the authors focus on small mass ratios of μ = ρ m h ∕ ρ c ≤ 1, which are most relevant in today's membrane-wing applications, and small angles of attack (AoAs), for which the massless membrane solution predicts a stable solution.
14 citations
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01 Jan 1943TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
27,354 citations
01 Jan 2008
TL;DR: In this paper, a model for membrane camber due to aerodynamic loading is presented, indicating that the appropriate non-dimensional parameter describing the problem is a Weber number that compares the aerodynamic load to the membrane elasticity.
Abstract: 5. The lift and drag coefficients were measured for wings of varying aspect ratio, compliancy, and prestrain values. In addition, the static and dynamic deformations of compliant membrane wings were measured using stereo photogrammetry. A theoretical model for membrane camber due to aerodynamic loading is presented, indicating that the appropriate nondimensional parameter describing the problem is a Weber number that compares the aerodynamic load to the membrane elasticity. Excellent agreement between the theory and experiments is found. Measurements of aerodynamic performance show that, in comparison with rigid wings, compliant wings have a higher lift slope, maximum lift coefficients, and a delayed stall to higher angles of attack. In addition, they exhibit a strong hysteresis botharoundazeroangleofattackaswellasaroundthestallangle.Unsteadymembranemotionswerealsomeasured, anditisobservedthatthe membranevibrateswithaspatialstructure thatisclosely relatedto thefreeeigenmodesof themembraneundertensionandthattheStrouhalnumberatwhichthemembranevibratesriseswiththefreestream velocity, coinciding with increasing multiples of the natural frequency of the membrane.
215 citations
TL;DR: In this article, a model for membrane camber due to aerodynamic loading is presented, indicating that the appropriate non-dimensional parameter describing the problem is a Weber number that compares the aerodynamic load to the membrane elasticity.
Abstract: Bats and other flying mammals are distinguished by thin, compliant membrane wings. In an effort to understand the dependence of aerodynamic performance on membrane compliancy, wind-tunnel tests of low-aspect-ratio, compliant wings were conducted for Reynolds numbers in the range of 0.7-2.0 x 10 5 . The lift and drag coefficients were measured for wings of varying aspect ratio, compliancy, and prestrain values. In addition, the static and dynamic deformations of compliant membrane wings were measured using stereo photogrammetry. A theoretical model for membrane camber due to aerodynamic loading is presented, indicating that the appropriate nondimensional parameter describing the problem is a Weber number that compares the aerodynamic load to the membrane elasticity. Excellent agreement between the theory and experiments is found. Measurements of aerodynamic performance show that, in comparison with rigid wings, compliant wings have a higher lift slope, maximum lift coefficients, and a delayed stall to higher angles of attack. In addition, they exhibit a strong hysteresis both around a zero angle of attack as well as around the stall angle. Unsteady membrane motions were also measured, and it is observed that the membrane vibrates with a spatial structure that is closely related to the free eigenmodes of the membrane under tension and that the Strouhal number at which the membrane vibrates rises with the freestream velocity, coinciding with increasing multiples of the natural frequency of the membrane.
214 citations
TL;DR: In this article, the aerodynamics of membrane and corresponding rigid wings under the MAV flight conditions are reviewed. And the proper orthogonal decomposition method is also discussed as an economic tool to describe the flow structure around a wing and to facilitate flow and vehicle control.
213 citations
TL;DR: In this article, an experimental study of unsteady aerodynamics of two-dimensional membrane airfoils at low Reynolds numbers was conducted, where the amplitude and mode of the vibrations of the membrane depend on the relative location and the magnitude of the unsteadiness of the separated shear layer.
Abstract: Membrane wings are used both in nature and small aircraft as lifting surfaces. Separated flows are common at low Reynolds numbers and are the main sources of unsteadiness. Yet, the unsteady aspects of the fluid-structure interactions of membrane airfoils are largely unknown. An experimental study of unsteady aerodynamics of two-dimensional membrane airfoils at low Reynolds numbers has been conducted. Measurements of membrane shape with a high-speed camera were complemented with the simultaneous measurements of unsteady velocity field with a high frame-rate particle image velocimetry system and flow visualization. Vibrations of the membrane and mode shapes were investigated as a function of angle of attack and free stream velocity. While the mean membrane shape is not very sensitive to angle of attack, the amplitude and mode of the vibrations of the membrane depend on the relative location and the magnitude of the unsteadiness of the separated shear layer. The results indicate strong coupling of unsteady flow with the membrane oscillations. There is evidence of coupling of membrane oscillations with the vortex shedding in the wake, in particular, for the post-stall incidences. Comparison of rigid (but cambered) and flexible membrane airfoils shows that the flexibility might delay the stall. Hence this is a potential passive flow control method using flexibility in nature and engineering applications.
159 citations