Large-amplitude membrane flutter in inviscid flow

Abstract

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

Membrane flutter induced by radiation of surface gravity waves on a uniform flow

“…Recent works on membrane flutter are motivated by such diverse applications as stability of membrane roofs in civil engineering (Sygulski 2007), flutter of travelling paper webs (Banichuk et al 2010(Banichuk et al , 2019, aerodynamics of sails and membrane wings of natural flyers (Newman & Paidoussis 1991;Tiomkin & Raveh 2017), as well as the design of piezoaeroelastic systems for energy harvesting (Mavroyiakoumou & Alben 2020).…”

Dynamics of tethered membranes in inviscid flow

“…The membrane and flow models are the same as in Mavroyiakoumou and Alben (2020) but we repeat them briefly for completeness. The membrane dynamics are described by the unsteady extensible elastica equation with body inertia, stretching resistance, and fluid pressure loading, obtained by writing a force balance equation for a small section of membrane that lies between material coordinates α and α + ∆α:…”

“…Membranes arise in various biological and technological applications including membrane aircraft and shape-morphing airfoils (Lian and Shyy, 2005;Hu et al, 2008;Stanford et al, 2008;Jaworski and Gordnier, 2012;Piquee et al, 2018;Schomberg et al, 2018;Tzezana and Breuer, 2019), sails (Colgate, 1996;Kimball, 2009), parachutes (Pepper and Maydew, 1971;Stein et al, 2000), membrane roofs (Haruo, 1975;Knudson, 1991;Sygulski, 1996Sygulski, , 1997Sygulski, , 2007, and the wings of flying animals such as bats (Swartz et al, 1996;Song et al, 2008;Cheney et al, 2015). The majority of previous studies of membranes showed that when they are held with their ends fixed in a uniform oncoming fluid flow, they tend to adopt steady shapes with a single hump (that is, when the flat state is unstable) (Song et al, 2008;Mavroyiakoumou and Alben, 2020). In the current work, we show that periodic and chaotic oscillations can occur in a simple physical setup.…”

“…In Mavroyiakoumou and Alben (2020) we investigated how the membrane dynamics change when using different boundary conditions at the two ends of the membrane. In the first case, fixed-fixed, the membrane ends were held fixed, as in most previous studies of membrane flutter (Le Maître et al, 1999;Sygulski, 2007;Tiomkin and Raveh, 2017;Nardini et al, 2018).…”

Numerical Algorithms for Water Waves with Background Flow over Obstacles and Topography

“…Many interesting phenomena in fluid mechanics occur as a result of the interaction of a fluid with solid or flexible structures. Most numerical algorithms to study such problems require discretizing the bulk fluid [5,35,75] or are tailored to the case of slender bodies [66], flexible filaments [4,52] or unbounded domains [30]. In the present paper, we propose a robust boundary integral framework for the fast and efficient numerical solution of the incompressible, irrotational Euler equations in multiply-connected domains that have numerous fixed obstacles, variable bottom topography, a background current, and a free surface.…”