Page 232 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

214 SLENDER STRUCTURES AND AXIAL FLOW
ambient minus internal) caused local shell-type collapse of the pipe near the support.
Reinforcing the pipe at that point simply postponed the collapse to a higher flow rate, at
a lower point along the pipe; but there was still no sign of the elusive flutter! At the time,
this was chalked up as due to ‘experimental difficulties’ and forgotten for a while.
Some time later, the author became aware of ocean mining and some aspects of research
into the dynamics of such systems [e.g. Chung et al. (1981), Whitney et al. (1981),
Felippa & Chung (1981), Koehne (1978, 1982), Chung & Whitney (1983), Aso & Kan
(1986)], and work into the problem of sucking pipes received a new impetus. Ocean
mining is basically the ‘vacuuming’ of minerals, notably of manganese nodules, which
lie on the floor of the ocean, e.g. in the Northeast Pacific, at depths of the order of 5 km.
The system involves a very long ‘vacuum hose’, with a massive ‘vacuum head’ which
walks along the ocean floor and scours and sucks up nodule-rich sea-water, as shown in
Figure 4.12(a). It occurred to the author that, the moment the bottom head loses contact
with the sea floor, this becomes a cantilevered pipe with an end-mass, aspirating fluid
and hence subject to flutter, as per equation (3.1 1). Therefore, it was decided that a more
careful study of the problem was warranted.

4.3.2 Analysis of the ocean mining system

In most of the papers just cited, external flow and wave-related problems, as well as the
dynamics of the long pipe itself, are the main concern. Only Koehne (1982) discusses
briefly the modelling of the pipe with internal flow, but does not present any results.
A systematic analysis of the general system of Figure 4.12(b) has been undertaken by
Paidoussis & Luu (1985), which will be outlined briefly in what follows.
For simplicity, the pipe is assumed to be initially straight. Then, proceeding as in
Section 4.2, the equation of motion is found to bet
a4w a2w a2 w a2w
ax4 ax2 ax at at2
El- + MUUj ~ - 2MU ~ + (M + m + Mu)-

(4.26)

with boundary conditions
aw
w = 0, -=o (4.27a)
ax
at x = 0, and

a’w -- a3w - - h - - aw
-
EI - -Md - (Mg - Fb)- - (M +Mu)- - C - = 0,
ax3 ax at2 ax at2 at (4.27b)
a2 -aw --a2w --2 a3w
+
+
EZ - (Mg - Fb) d - + Md - (J+Md )- = 0,
ax2 ax at2 ax at2
‘The reader should consult the text in Section 4.3.3.