Tension in Fluttering Flags

The boundary layer development and traveling wave mechanisms during flapping of a flexible foil

“…Since the wall shear stress varies significantly after s¼0.85, these observations indicates that the normal pressure effects dominate viscous effects in terms of induced tension. This is in agreement with Moretti's (2003) work which underlines the importance of induced tension in the competition against skin-friction and foil inertia. Additional simulations at a mass ratio of 0.1 show that the tension experienced at the leading edge, or total tension, remains fairly constant in the range of Re between 600 and 1000, around 0:192ð 7 1:5%Þ.…”

Motions of a cantilevered flexible plate in viscous channel flow driven by a constant pressure drop

“…Nevertheless, we recognize that a two-dimensional nonlinear model (e.g. [12,17]), that includes additional phenomena and the full description of flexure, should be adopted when our tip deflection is as large as seen at the later time-steps in Figure 2. The corresponding sequence for the stiffer Plate 1, not presented here, shows attenuating second-mode motion of the flexible plate.…”

“…Skin-friction additionally couples the fluid and structural sides of the system through the tension term. In a nonlinear plate model, such as those developed in [12,17] it would play an additional, and perhaps more significant, role in driving the horizontal motion of material points of the plate. However, the main fluid force that drives the plate motion remains the pressure difference between its upper and lower surfaces, p, on the right-hand side of (2).…”

Flutter of an elastic plate in a channel flow: Confinement and finite-size effects

“…The effects of gravity and internal tension are neglected in this modelling [see Moretti (2003) for a discussion of tensile forces]. Considering a finite length L, boundary conditions will be those of a clamped-free beam, W ¼ W X ¼ 0 in X= 0, and W XX ¼ W XXX ¼ 0 in X= L.…”