Camber and aerodynamic performance of compliant membrane wings

Waldman, Rye M.; Breuer, Kenneth S.

doi:10.1016/j.jfluidstructs.2016.11.013

Cited by 39 publications

(41 citation statements)

References 23 publications

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“…Subsequent shapes (ranging from light to dark gray and black) show the evolution to the eventual steady-state. The final membrane shape is nearly fore-aft symmetrical, similar to those in [73,51,19] but with larger deflection at this moderate choice of R 3 . Figure 6: Membrane profiles in the fixed-fixed case, at steady state with moderate deflections (colored background), or unphysically large or unsteady deflections (white background).…”

Section: Fixed-fixed Membranesmentioning

confidence: 57%

Large-amplitude membrane flutter in inviscid flow

Mavroyiakoumou

Alben

2020

J. Fluid Mech.

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We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex-sheet wakes in 2D 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, the membranes flutter with very small amplitudes and high spatial and temporal frequencies at small mass density. As mass density increases, the membranes transition to periodic and then increasingly aperiodic motions, and the amplitudes increase and spatial and temporal frequencies decrease. With both edges free, the membranes flutter similarly to the fixedfree case but also translate vertically with steady, periodic, or aperiodic trajectories, and with nonzero slopes that lead to small angles of attack with respect to the oncoming

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Section: Fixed-fixed Membranesmentioning

confidence: 57%

Large-amplitude membrane flutter in inviscid flow

Mavroyiakoumou

Alben

2020

J. Fluid Mech.

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“…For brevity, the Young–Laplace equation can be employed here to describe the deformed steady state of the membrane (Song et al. 2008; Waldman & Breuer 2017), which can be written as where is the curvature of the deformed membrane. In the current simulation, the first term in (4.1) remains a constant value over the full - parameter space because the Young's modulus and the thickness are fixed.…”

Section: Resultsmentioning

confidence: 99%

“…2009; Bleischwitz et al. 2015; Waldman & Breuer 2017). Different from the fluid–structure interaction problems for freely vibrating rigid bodies with a fixed natural frequency, the natural frequency of the flexible membrane can be changed when the aerodynamic loads are applied to a stretchable membrane surface.…”

Section: Introductionmentioning

confidence: 99%

Flow-excited membrane instability at moderate Reynolds numbers

Jaiman

Khoo

2021

J. Fluid Mech.

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In this paper, we study the fluid–structure interaction of a three-dimensional (3-D) flexible membrane immersed in an unsteady separated flow at moderate Reynolds numbers. We employ a body-conforming variational fluid–structure interaction solver based on the recently developed partitioned iterative scheme for the coupling of turbulent fluid flow with nonlinear structural dynamics. Of particular interest is to understand the flow-excited instability of a 3-D flexible membrane as a function of the non-dimensional mass ratio ( $m^{*}$ ), Reynolds number ( $Re$ ) and aeroelastic number ( $Ae$ ). For a wide range of parameters, we examine two distinct stability regimes of the fluid–membrane interaction: deformed steady state (DSS) and dynamic balance state (DBS). We propose stability phase diagrams to demarcate the DSS and DBS regimes for the parameter space of mass ratio versus Reynolds number ( $m^{*}$ - $Re$ ) and mass ratio versus aeroelastic number ( $m^{*}$ - $Ae$ ). With the aid of the global Fourier mode decomposition technique, the distinct dominant vibrational modes are identified from the intertwined membrane responses in the parameter space of $m^{*}$ - $Re$ and $m^{*}$ - $Ae$ . Compared to the deformed steady membrane, the flow-excited vibration produces relatively longer attached leading-edge vortices which improve the aerodynamic performance when the coupled system is near the flow-excited instability boundary. The optimal aerodynamic performance is achieved for lighter membranes with higher $Re$ and larger flexibility. Based on the global aeroelastic mode analysis, we observe a frequency lock-in phenomenon between the vortex-shedding frequency and the membrane vibration frequency causing self-sustained vibrations in the dynamic balance state. To characterize the origin of the frequency lock-in, we propose an approximate analytical formula for the nonlinear natural frequency by considering the added mass effect and employing a large deflection theory for a simply supported rectangular membrane. Through our systematic high-fidelity numerical investigation, we find that the onset of the membrane vibration and the mode transition has a direct dependence on the frequency lock-in between the natural frequency of the tensioned membrane and the vortex-shedding frequency or its harmonics. These findings on the fluid-elastic instability of membranes have implications for the design and development of control strategies for membrane wing-based unmanned systems and drones.

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“…The resulting tension in the bulged membrane, T b , is derived from the first Piola-Kirchhoff stress as T b = G m h(1 − 1/λ 6 ). With the tension, T b , in the bulged membrane known, the static equilibrium shape under uniform pressure loading can be obtained from the Young-Laplace equation 34 ,…”

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confidence: 99%

Nonlinear modeling and characterization of ultrasoft silicone elastomers

Das,

Breuer,

Mathai

2020

Preprint

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We introduce a strain-energy based nonlinear hyper-elastic formulation to model the material properties of ultrasoft dielectric elastomers over a wide range of elastic properties, prestretch, and thicknesses. We build on the uniaxial Gent formulation, and under the conditions of equi-biaxial strain, derive an expression for the bulge deformation versus pressure. A circular bulge test methodology is developed to experimentally measure the mechanical response of the silicone membranes. The Gent model captures both neo-Hookean and strain-stiffening behaviors, and gives predictions which are in agreement with experimental measurements. Membranes with different thinner fractions are characterized over nearly one order of magnitude variation in shear modulus. Stiffer membranes are observed to harden at lower stretch ratios due to the increased fraction of polymer chains in them. The present approach offers a simple and costeffective procedure for characterizing soft membranes under commonly encountered biaxial deformation conditions.

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Camber and aerodynamic performance of compliant membrane wings

Cited by 39 publications

References 23 publications

Large-amplitude membrane flutter in inviscid flow

Large-amplitude membrane flutter in inviscid flow

Flow-excited membrane instability at moderate Reynolds numbers

Nonlinear modeling and characterization of ultrasoft silicone elastomers

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