Page 158 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

140 SLENDER STRUCTURES AND AXIAL FLOW

Figure 3.48 Photograph of a fluttering vertical pipe (pipe #3) from the experiments by Greenwald
& Dugundji (1967). The arrow shows the end of the pipe; what is seen below that point is the free
water jet.

Table 3.3 Comparison between the experimental and theoretical
values of ucf from Greenwald & Dugundji’s (1967) experiments;
the values have been scaled from their figure 13a.
B Values of ucf
Theory Experiment Theory
(no damping) (with damping)
0.342 8.48 6.85 7.50
0.47 1 9.15 8.30 8.10
0.500 9.32 9.55 8.30

to make. The first is that, before the occurrence of flutter, in some cases, small movements
of the cantilever away from its vertical position of rest were observed with increasing
flow. These movements developed gradually with flow and never exceeded 6 mm (1 -2%
of the length); they could be made to vanish by suitable, slight circumferential adjustments
of the tubular cantilever at its upstream support. Clearly, these could not be construed to
be a buckling instability. They must be interpreted as ‘localized’ buckling resulting from
small nonuniformities in the cantilever, or due to release of strains imposed by imperfect
circumferential support at the clamped end. Similar occurrences of localized buckling
were observed in experiments with horizontal cantilevers, and by Benjamin (1961b) in