Page 166 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

148 SLENDER STRUCTURES AND AXIAL FLOW

1.0
1 I I I I
0.8 - S H S.E.F. -
-

0.6 - B -
4" 00
a
0.4 - 0 O0 -
0
0.2 - 0 -

0
I '
O A I I 0-J I I

Figure 3.55 Limit-cycle amplitudes of a cantilevered pipe versus U: (a) for flutter excited by
an external disturbance, (b) for spontaneously excited flutter. Region S corresponds to the stable
region: region D.E.F. to disturbance-excited flutter; Region S.E.F. to spontaneously excited flutter;
region H corresponds to the hysteresis region as U is decreased; 0, increasing flow; 0, decreasing
flow (Chen & Jendrzejczyk 1985).

no difference between amplitudes for increasing and decreasing U). For spontaneously
excited flutter, however, Ucf 'v 23.8 and AID, 2 0.6 at the onset; furthermore, there is a
great deal of hysteresis. These results, taken together, suggest that the Hopf bifurcation
in this case is subcritical [Figure 2.11(d)]; this gives quantitative substance to the earlier
observations made by Pdidoussis and discussed in conjunction with Figures 3.46 and 3.47.
The overall assessment is that the main features of the linear, free dynamics of this
system have adequately been confirmed by experiment; this successful testing of theory
is reinforced by some of the experiments described in Section 3.6.