Page 185 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I 167

Figure 3.69 The flutter modes of a cantilevered pipe (/3 = 0.50, a = 0.02) with an added mass and
a translational spring at 6 = 0.25 (pl = 10, K = 600): (a) at first loss of stability (ucf = 8.17); (b) at
the second loss of stability (ucf = 9.97), after restabilization; obtained theoretically by Sugiyama
et al. (1988a).

static phenomenon; it is found that this effect, both in terms of ucf and the range of u
over which coupled-mode flutter persists, can be affected a great deal, even if h = 0. For
cantilevered pipes it is found that eccentricity of an additional mass at the free end may
further destabilize the system.

3.6.4 Pipes with additional dashpots
This problem has been studied theoretically and experimentally by Sugiyama et al.
(1988b).+ A dashpot is attached to a cantilevered pipe, located at some point .& = I/L 5 1,
and sometimes also a mass, at the same point. The effect of the damper at the downstream
end is generally destabilizing, with or without the mass, while at other locations it can
sometimes be stabilizing (see Section 3.8.3), depending on /3 and ~1 [equations (3.124)].
In some cases, multiple regions of flutter may exist.
The experiments were conducted in the same basic arrangement as for one or more
additional springs, discussed in the foregoing. The dashpot was provided by attaching a
thin flat plate to the pipe and immersing it in oil, with the motion parallel to the flat-plate
surface. The experiments generally support theory quite well.

+The interested reader is also referred to Sugiyama et al. (1985b).