Page 492 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

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1.2

1.0
1
- st mode
0.8

0.6
-
5 0.4
X
h
3
v
E 0.2
*
0

4.2 - 2nd mode -

4.4 -

4.6

Figure 6.26 Argand diagram for the lowest three eigenfrequencies w for in-plane motion of a
quarter-circular clamped-axially-sliding pipe conveying viscous fluid as functions of E* for /3 = 0.5,
#
d = lo4, according to extensible theory [no 0, d(rf + @$) # 01, (Misra et al. 1988b).
was prevented, while the experiments were designed to permit it (Section 3.4.4). In view of
the foregoing, it is now clear that, once axial sliding is permitted in the theory also (while
still accounting for steady forces), the theoretical variation of frequency with flow will
be much more like the experimental one:+ experimental observations no longer disagree
with extensible and modified inextensible theory.

+Note that li* in Figures 6.25 and 6.26 corresponds to u/x in Figure 3.26.