Theoretical and Applied Mechanics Letters

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Onset of instability of a flag in uniform flow
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Image of Fig. 1.
Fig. 1.

Schematic diagram of the 3D flag in a uniform flow. Points A, B and C denote the lower corner, the midpoint and the upper corner on the trailing edge, respectively.

Image of Fig. 2.
Fig. 2.

Time histories of the transverse displacements of point B (Fig. 1) from their equilibrium positions at (solid line). The result of Huang and Sung16 is given for comparison (dashed line). Here, T is the period of the flag flapping.

Image of Fig. 3.
Fig. 3.

Time history of the transverse displacements of point B in bistability.

Image of Fig. 4.
Fig. 4.

Orbits in the phase plane z-w for the two cases shown in Fig. 3.

Image of Fig. 5.
Fig. 5.

Time history of the transverse displacements of point B in instability at , , and .

Image of Fig. 6.
Fig. 6.

(Color online) Vortical structures at the four instants as labeled in Fig. 5.

Image of Fig. 7.
Fig. 7.

Stability boundaries in the (S-U) plane for the flag at (2D), 1 and 2. The symbols represent the cases of numerical simulation and their stability: △, , stable; ▲, , unstable; ◇, , stable; ◆, , unstable. The dashed and dash-dotted lines approximate to the boundaries based on the numerical result.


Generic image for table
Table 1.

The Strouhal number and the amplitude of the flag for the case in Fig. 2.


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Scitation: Onset of instability of a flag in uniform flow