Claire Souilliez

Aeroelastic instability of cantilevered flexible plates in uniform flow

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 destabilizing pressure forces and stabilizing 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.

Flutter of a Rectangular Cantilevered Plate

We address theoretically the stability of a cantilevered rectangular plate in an uniform and incompressible axial flow. We assume that the fluid viscosity and the plate viscoelastic damping are negligible. In this limit, a flutter instability arises from a competition between the destabilising fluid pressure and the stabilising flexural rigidity of the plate. The flutter modes are assumed to be two-dimensional but the potential flow is calculated in three dimensions in the asymptotic limit of large plate span. Using a Galerkin method and Fourier transforms, we are able to predict the flutter modes, their frequencies and growth rates. The critical flow velocity is calculated as a function of the mass ratio and the plate aspect ratio. We demonstrate a new result: a plate of finite span is more stable than a plate of infinite span.Copyright

An Experimental Study of Flag Flutter

We present an experimental study of the flutter instability of a flag. Our experiments are performed in a low turbulence horizontal wind tunnel. The flags tested are made of paper or plastic of different flexural rigidities. One end of the flag is clamped to a profiled and vertical mast, the other end is left free. At low velocities, the flag is parallel to the flow and motionless. Above a critical wind velocity, the flag exhibits periodic flutter. The bifurcation is subcritical and the system shows a strong hysteresis cycle. We particulary focus on the variation of the instability threshold with respect to two non-dimensional parameters: the mass ratio and the aspect ratio. When the mass ratio increases, different flutter modes appear. We have studied systematically the effect of aspect ratio on the instability threshold. In agreement with a recent theoretical study [1], the critical velocity is a decreasing function of aspect ratio as long as three-dimensional effects are negligible (when the flag span is not too large).Copyright

Flutter modes of a flexible plate in an air flow

The flutter instability resulting from the interaction of a flexible plate with a fluid flow is experimentally investigated. The present visualizations are obtained with two square plates (i.e. of aspect ratio H/L = 1, see the sketch of the experiment in Fig. 1.) made in a plastic sheet (of flexural rigidity 4.8 10-4 kg m 2 s-2) and of length L = 8 and 21 cm. Experiments are performed in the horizontal test section of a low-turbulence wind tunnel. The upstream end of the plate is clamped into a vertical streamlined mast while the three other edges are free. For low velocities U, the plate is planar and parallel to the air flow. Then, as U is increased, two-dimensional flutter of the plate spontaneously appears at a critical value Uc depending on the plate dimensions. Figs. 2 and 3 show superimposed views of the side edge of the plates during one flutter period, captured just at the threshold Uc for both plates. Such figures allow to visualize the envelope of the futter motion. Images are captured with an high speed camera parallel to the Z-axis (see Fig. 1.), the air flow is from left to right. These visualizations reveal that different flutter modes can take place at the threshold as the plate dimensions are varied. For the material considered here, the two figures show a change of the mode shape from a single-neck (Fig. 2) to a double-neck (Fig. 3) envelope when the length is increased from 8 to 21 cm. It should be pointed out that these two flutter modes differ not only by the envelope shape but also by the flapping frequency: the measured flutter frequency for the mode shown in Fig. 2 is of 29 Hz, and of 5.6 Hz for the longest plate (Fig. 3).