Page 160 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

142 SLENDER STRUCTURES AND AXIAL FLOW

8 1 I I I 20 1 I I I
p=O.l30(B) p = 0.130

0 5 IO 15 20 25

p = 0.155

I I I I I 14
IO 20 30 40 50 60 10 20 30 40 50 60
b ?
p = 0.208

-I**
1 I I 1 1 14 *
5 10 15 20 25 30 5 10 15 20 25 30

12 I I I I 40 * I I I I
p =0.241 (A)

-

10 1 I 1 1
10 20 30 40 50 60 10 20 30 40 50 60
Y Y

Figure 3.49 Comparison between theoretical and experimental values of ucf and wCf for a number
of vertical (hanging) cantilevered pipes conveying water with different B and lengths thereof
(different y): for 0.130 5 5 0.241: 0, experiment; -, theory with no damping; ---, theory
with damping (p = 0.02 for Silastic type A rubber; p = 0.10 for Silastic type B); (Pai’doussis
1970).

Long cantilevers were buckled under their own weight at zero flow velocity. The
dynamical behaviour of the system was assessed by supporting the cantilever by hand in
its unflexed shape, while the flow was incremented, and then releasing it. Long cantilevers
(y < -23) were unstable at all flow velocities. At low flows a long cantilever continued
to be unstable by buckling; at higher flow velocities, oscillations were superposed on
buckling, resulting in an erratic, thrashing motion.
Short cantilevers (y > -8 approximately) did not buckle under their own weight at zero
flow. Their behaviour with increasing flow was essentially as for hanging cantilevers; the
system remained stable with increasing flow until, at a sufficiently high flow velocity,
flutter developed spontaneously.